so good evening everyone my name is 那么晚上好， 我的名字就是这样
Ahmed ebony I'm assistant professor of 艾哈迈德乌木是我的助​​理教授
structure engineering welcome to the 结构工程欢迎光临
2014-2015 numark distinguished lecture 2014-2015年numark杰出讲座
this serial this lecture series was 这个系列这个系列讲座是
inaugurated in the early 2000s to 在二十一世纪初开始启用
celebrate the legacy of professor Nathan 庆祝Nathan教授的遗产
numark who was the former head of civil 曾担任民间负责人的numark
engineering department as well as the 工程部门以及
former dean of engineering at University 大学前工程学院院长
of Illinois urbana-champaign professor 伊利诺伊州Urbana-champaign教授
knew mark was a great researcher teacher 知道马克是一个伟大的研究员老师
and mentor and with no doubt he is 和导师，毫无疑问他是
considered one of the founding fathers 被认为是创始人之一
of earthquake engineering he gave this 他给了这个地震工程
discipline the rigor it lacked in the 纪律严格缺乏
beginning of the 20th century and he 20世纪初和他
developed many theoretical tools that 开发了许多理论工具
were very effective in producing safe 在生产安全方面非常有效
designs under the great uncertainty in 在很大的不确定性下设计
associated with earthquake loads his 与地震相关的负荷
work stands out till this very moment as 直到现在这个时刻，工作才脱颖而出
you can see here in in this poster you 你可以在这张海报中看到你
see a tower it's called the Tory 看到一座被称为保守党的塔
latinoamericana in Mexico professor 拉丁美洲墨西哥教授
numark designed that tower and this numark设计了塔和这个
tower stood two big earthquakes in 1957 1957年，塔楼发生了两次大地震
1957 and 1985 and the one in 1985 was 1957年和1985年是1985年的一次
magnitude 8.1 so this is just a to 量级8.1，所以这只是一个
testify for his great ability as a 作为他的巨大能力作证
scientist and engineer however neumarkt 然而科学家和工程师neumarkt
legacy didn't stop at the boundaries of 遗产并没有停止在边界
structural engineering his work in 结构工程他的工作
numerical analysis is by no means less 数值分析绝不是那么简单
profound the numark beta method which he 他深刻的numark beta方法
developed in 1959 is widely used to 1959年开发的应用广泛
integrate differential equations that 积分微分方程
appear in different fields like 出现在不同的领域像
electromagnetics hydraulic solid 电磁液压固体
mechanics and biology and it has 机械和生物学，它有
remarkable 卓越
that we are still discovering till this 我们至今仍在发现
moment it has become such a standard 现在它已经成为这样一个标准
technique that its name is just 它的名字就是这样的技术
mentioned similar to Newton's law or 提到类似于牛顿法则或
owners law without citing new marks 1959 所有者法律没有引用新标志1959年
s papers so please don't be fooled by 所以请不要被骗了
the 3500 citation he only got in Google 他仅在Google中获得了3500条引用
today we are very pleased to have 今天我们很高兴有
professor Ali segment from the technical 来自阿里教授的技术部分
university of denmark as our 丹麦大学
distinguished speaker and personally it 尊敬的演讲者并亲自出席
won't be an exaggeration to say that 这并不夸张
Professor segment to the field of 教授细分领域
topology optimization is like Professor 拓扑优化就像教授一样
new mark to earthquake engineering I can 我可以给地震工程带来新的印记
go on but I think it will be best if I 继续， 但我认为这将是最好的，如果我
leave the introduction to one of 把介绍留给其中一个
Professor Ali's friends and close 阿里教授的朋友和密切关系
collaborators professor glass super you 合作者教授玻璃超级你
know so i would like to invite professor 知道所以我想请教授
Paolino say a few words about signal 保利诺对信号说几句话
Thank You are mad I am a professor 谢谢你生气我是教授
glossy paulino from the Department of a a部门光滑的paulino
civil and environmental engineering it 它是民用和环境工程
is my great pleasure to introduce to you 我非常高兴地向你介绍
professor all at Sigmund and to get 所有在西格蒙德教授， 并得到
started with the introduction I would 从我的介绍开始
like to tell my colleague professor are 想告诉我的同事都是教授
made the opponent that I agree with his 让对手赞同他的看法
comparison professor zigmund he got his 他比较教授齐格蒙德
PhD from her the technical university of 她的技术大学博士学位
denmark in 95 he has a lot of research 他在95年丹麦进行了大量的研究
interests including applications of 包括应用程序的利益
topology optimization design of his math 他的数学拓扑优化设计
materials compliant mechanisms 材料兼容机制
crashworthiness acoustics and more 耐撞性声学等等
recently sustainable energy applications 最近可持续能源应用
he has had a distinguished career he has 他拥有出色的职业生涯
won several honors and awards that are 赢得了几项荣誉和奖项
listed here and to make the 在这里列出并使之成为可能
introductions water I will not go 介绍水我不会去
through all this I just would like to 通过这一切我只是想
point out a few things is the author of 指出几件事情是笔者的
the book topology optimization theory 书籍拓扑优化理论
methods and applications that has more 方法和应用程序有更多
than 2,000 citations 超过2000次引用
he is presently the president of the 他现任总统
International Society for the structural 国际结构学会
and the multidisciplinary optimization 并进行多学科优化
and this society sponsors the world 这个社会赞助了这个世界
congress in structural and 国会在结构和
multidisciplinary optimization 多学科优化
confidence the next one will be in 下一个将会有信心
Australia next year professor Sigmund is 澳大利亚明年是西格蒙教授
also in the editorial board of all the 也在所有的编辑委员会
most important journals in applied 应用中最重要的期刊
mechanics engineering and so on 力学工程等
including structural and the 包括结构性和
multidisciplinary optimization IGN Emmy 多学科优化IGN艾美奖
cm AME and so on this morning I looked 厘米AME等等，今天早上我看了看
in the web of science his h-index is 41 在科学网络中，他的H指数是41
and that means he has more than 7,000 这意味着他有超过7000人
citations ladies and gentlemen please 引用女士们，先生们请
join me to give a very warm welcome to 请和我一起非常热烈地欢迎
Professor all easy okay thank you very 教授一切都很好， 非常感谢你
much for the kind introduction to emit 非常适合引入散发
and Klaus you and thank you so much for 和Klaus你，谢谢你这么多
the invitation to come here I've been 邀请来到这里我一直
looking forward to this very much I 我非常期待这一点
arrived Saturday nights and I had a long 星期六晚上抵达，我有一段很长的时间
and very interesting day to day it is 每天都非常有趣
causing with several of the people in 导致与几个人在一起
the faculty here and so I already feel I 这里的教师，我已经感受到了我
learned a lot and now it's getting late 了解了很多，现在已经很晚了
at night for me so it's like one in the 在夜晚对我来说它就像一个在
in the morning by now so i hope i can 在现在的早晨，所以我希望我能
get through this lecture without getting 通过这个讲座没有得到
too much sort of saying weird stuff on 说太多奇怪的东西
the way here so anyway my speciality is 无论如何，我的专业是这里的方式
topology optimization i've been working 拓扑优化我一直在努力
on that since my PhD as you see here I'm 因为我在这里看到了我的博士学位
a mechanical engineer and I'm certainly 一个机械工程师，我当然
not the only one working in this field 不是唯一在这个领域工作的人
there are many people in the world and 有许多人在世界上
certainly I also have a big group of 当然我也有一大群人
people who have contributed to this talk 为这次演讲做出贡献的人
that I'm going to talk about today so 我今天要谈的是这样的
the field of topology optimization was 拓扑优化的领域是
originally developed for mechanical 最初是为机械开发的
engineering and I have my favorite way 工程和我有我最喜欢的方式
to introduce the problem and that is 介绍这个问题，那就是
with a case from the aerospace industry 以航空航天业为例
so to save weight in airplanes so you 所以为了减轻飞机的重量
want to make lighter and lighter 想要做得更轻更轻
aeroplanes to save fuel or load more 飞机节省燃油或装载更多
passengers in them but of course at the 乘客在他们当然在那里
same time you cannot cut away too much 同时你不能削减太多
material or it would compromise flight 材料或它会危及飞行
safety so there's an ongoing 安全，所以这是一个持续的
optimization of structure in airplanes 飞机结构的优化
and one example we could take was to 我们可以采取的一个例子是
optimize or rather to minimize the 优化或宁可最小化
weight of the leading edge part of this 这个的前沿部分的重量
airplane and we could do that by taking 飞机，我们可以通过采取
out one of these ribs and asking the 拿出这些肋骨中的一根，然后问
question where should the holes be such 问题在哪里应该是这样的
that we get the lightest and at the same 我们得到最轻和相同的
time stiff its structure and what you 时间僵硬的结构和你
often see a certain in mechanical 经常看到一定的机械
engineering but maybe even more in civil 工程，但可能更公民
engineering is that people create 工程就是人们创造的
circular homes and they look light but 圆形的家园，他们看起来很轻，但
if you look at the colors here this is a 如果你看这里的颜色，这是一个
stress plot and you see regions with 压力情节，你看到的地区
high stresses indicated by right here 这里指出的高压力
but also large regions by dark blue 还有深蓝色的大片地区
regions where there are no stresses so 那里没有压力的地区
essentially this material is not playing 基本上这种材料不是在玩
any structural role there so it's 任何结构性角色都是如此
obvious that this rip could be designed 显然这个rip可以被设计
in a better way and that's where 以一种更好的方式，那就是在哪里
topology optimization comes into the 拓扑优化进入
play so the idea is essentially that you 发挥，所以这个想法本质上就是你
take your design domain and you 把你的设计领域和你
discretize it with a large number of 离散它与大量的
finite elements and then you allow the 有限元素，然后你允许
density of materials in each of these 每种材料的密度
elements to be a design variable then 元素将成为设计变量
you make a finite element analysis and 你做一个有限元分析和
you add material where the structure is 你在结构所在的位置添加材料
highly stressed and you subtract where 高度强调，你减去在哪里
it slowly stress that's the popular 它慢慢强调这是受欢迎的
version of it in reality we do some 它的现实版本我们做一些
right advanced sensitivity analysis but 正确的高级灵敏度分析
anyway this results in an iterative 无论如何，这导致了迭代
procedure where we do find an element 我们确实找到一个元素的过程
analysis sensitivity analysis and design 分析灵敏度分析和设计
updates and it would look something like 更新和它看起来像
this so each picture here denoting one 这使得这里的每张图片都表示一个
step in the design procedure and you see 在设计过程中的一步，你会看到
certainly it doesn't have the circular 当然它没有通告
holes as we saw before but it comes out 就像我们之前看到的那样，但它会出来
as a more like trust like structure and 作为更像结构和信任的信任
so this is what they're using in the 所以这就是他们在使用的东西
airplane industry by now and you see now 飞机行业，现在你看到了
you have sort of a uniform distribution 你有一个统一的分布
of stresses in the whole structure this 这在整个结构中的应力
would be the design from the 将是从设计
optimization part and they do some post 优化部分，他们做一些职位
processing and this is actually what you 处理，这实际上是你
see in the a380 airplane and so just as 在A380飞机上看到，就这样
a matter of fact here then they saved 事实上在这里他们得救了
something like 500 kilos in this 在这个500公斤的东西
leading-edge part 前沿部分
doing the intensive topology 做密集的拓扑结构
optimization of the whole structure so 所以整个结构的优化
this is a basic idea and you can imagine 这是一个基本的想法，你可以想象
this can be used everywhere where the 这可以在任何地方使用
distribution of material is important so 材料的分配非常重要
certainly the automotive industry uses 肯定是汽车行业使用的
it heavily both to do the whole Chace's 它很大程度上要做整个Chace的
of the car but also seat belt restrainer 的汽车还有安全带限制器
zand other things the wind turbine zand风力涡轮机的其他东西
industry is adopting it and essentially 工业正在采用它并且基本上
all mechanical engineering fact or 所有机械工程事实或
industry is used intensively to save 工业用于集中储存
weight and then there are some method is 重量然后有一些方法是
spreading to other areas like Paolino 传播到其他地区像保利诺
has done some very intriguing work on 做了一些非常有趣的工作
doing bio implants for people and we 为人类和我们做生物植入物
have been looking into micro 一直在研究微观
electromechanical systems that I will 机电系统， 我会
come back to later and certainly it 回到以后肯定它
doesn't stop here you can also go into 不停止在这里，你也可以进入
all kinds of other physics problems so 所有其他各种物理问题
you can do wave propagation problems in 你可以做波传播问题
acoustics and optics for energy 声学和光学能源
harvesting you can do nanophotonics you 收获你可以做纳米光子你
can do fluids and you can do antenna so 可以做流体， 你可以做天线
everywhere in may in engineering systems 在工程系统中可能在任何地方
where the distribution of material plays 材料分配的地方
a role we try to apply these concepts 我们尝试应用这些概念
here and I don't have time to get into 在这里， 我没有时间进入
all of these years Oh today I'm mainly 所有这些年哦，今天我主要是
talking about structural optimization 谈论结构优化
things and then in an other talk 事情，然后在其他谈话
tomorrow i will talk about some of the 明天，我将谈论 一些
wave propagation and fluid problems and 波传播和流体问题和
other things like you see here so now 像你现在看到的其他东西
the outcome of this is often quite 这个结果往往相当
beautiful structures and so if you 美丽的结构，所以如果你
compare the outcome of an optimization 比较优化的结果
process so here to the left we have some 处理这样左边我们有一些
topology optimizations to the right we 拓扑优化的权利我们
have some architectural structures and 有一些建筑结构和
you certainly see here that there are 你当然看到这里有
lots of similarities these structures to 这些结构有许多相似之处
the right were not optimized but you 右边没有优化，但是你
could imagine that you could apply these 可以想象你可以应用这些
techniques to maybe get even better 技术可能会变得更好
structures and so they're people working 结构，所以他们是人在工作
on that also allows you is working on 在这也可以让你正在努力
this aspect so he has some beautiful 这方面让他有些美丽
designs together with Skidmore Owings 与Skidmore Owings一起设计
and Merrill unfortunately this building 而梅里尔不幸的是这座大楼
was not built yet as I understand it but 还没有按照我的理解建造，但是
I guess there's two chances for 我想有两个机会
something to come up but there are 有东西出现，但有
examples in structural engineering well 在结构工程中的例子很好
start 开始
is that were topology optimized actually 是实际上拓扑优化
we're built so to the right here we have 我们建立这样的权利在这里我们有
a structure a roof structure that was 一个屋顶结构的结构
built in Denmark we have some chairs by 建在丹麦我们有一些椅子
Dutch designers and then there's the 荷兰设计师，然后是那里的
biggest structure the biggest apology up 最大的结构最大的歉意了
to my structure I believe is the qatar 我认为我的结构是卡塔尔
national convention center and 国家会议中心和
interestingly there is a small story to 有趣的是有一个小故事
that which tells the difference between 说明两者之间的区别
architects and engineers and that is 建筑师和工程师，那就是
that this structure was optimized to 这个结构是优化的
have us so that these support things 让我们让这些支持事物
were solid material but you could 是固体材料，但你可以
imagine that that would require an 想象那将需要一个
extreme amount of concrete to build it 建造它的极端数量的混凝土
so the after the design came out as as a 所以在设计出来后就如同一个
result of the topology optimization 拓扑优化的结果
whether the structural engineers had to 无论结构工程师是否必须
modify to make it buildable oh sorry and 修改，使其可建立哦对不起
you see here they actually manufacture 你在这里看到他们实际上制造
this as a shell structure meaning that 这作为壳结构的意思
this structure is by no means optimal 这种结构绝不是最佳的
anymore so I will come back to that 了，所以我会回来给
later on how can we actually optimize 后来我们如何才能真正优化
structures that are optimal and may look 结构是最佳的，并且可能看起来
something like this but I will come back 这样的事情， 但我会回来
to that okay so this was the sort of 该好了，所以这是那种
popular introduction but let's get into 流行的介绍，但让我们进入
a little bit about the theory behind the 一点关于背后的理论
method and so the original form of 法等的原始形式
topology optimization is this a discrete 拓扑优化是一个离散的
problem so we have a design domain we 问题，所以我们有一个设计领域
have some support we have loads and the 有一些支持我们有负载和
this design domain is discretized losing 这个设计领域是离散化的
a large number of elements and 大量的元素和
essentially we want to ask the question 基本上我们想问这个问题
where which element should be filled 应填充哪个元素
with material and which should be void 与材料和应该是无效的
in order to minimize some objective 以尽量减少一些目标
function in our case so far it has been 在我们的情况下功能到目前为止
minimizing compliance of the structure 最小化结构的符合性
we have a volume constraint i should say 我应该说我们有一个数量限制
the things this is the density vector 这是密度向量
corresponding to the number of elements 对应于元素的数量
in the structure we might have some 在结构中我们可能会有一些
other structural or geometrical 其他结构或几何
constraints and then we have to satisfy 约束，然后我们必须满足
the equilibrium equations here at 平衡方程在这里
denoted as a linear system of equations 表示为线性方程组
but it could as well be some nonlinear 但它也可能是一些非线性的
systems as you will see later on so this 系统，你会在后面看到这个
is a combinatorial problem and so 是一个组合问题，所以
essentially even for very discreet or 基本上甚至对于非常谨慎或
sorry for very coarse resolutions like 对不起喜欢很粗的决议
just having 100 element discretization 只有100个元素离散化
taking 50 elements out of these to be 从中获得50个元素
filled with material then we already 然后我们已经充满了材料
have 有
astre nomicon numbers of combinations nomre nomicon数字的组合
here and we can not really that doesn't 在这里，我们不能确实没有
by now exists discrete methods that can 现在存在可以分离的方法
solve such kinds of problems so now to 现在就解决这类问题
overcome this we convert the problem 克服这一点，我们转换了问题
into a continuous problem and in that 成为一个连续的问题，并在此
way we can use gradient based methods 我们可以使用基于渐变的方法
that can maybe converge within a couple 这可能会融合在一对夫妇之中
of hundred iterations and so the idea is 百次迭代，所以这个想法是
instead of having this discrete variable 代替具有这个离散变量
will allow this design variable which we 将允许我们这个设计变量
now denote the relative density or just 现在表示相对密度或公正
the density to vary between a small 密度之间变化很小
number and one and in that way as I said 就像我说的那样
we can use a gradient calculations and 我们可以使用梯度计算和
predict and do gradient descent steps 预测并做梯度下降步骤
and converge in a much more efficient 并以更高效的方式汇聚
way now of course when you use 当然，当你使用的时候
continuous variables you might end up 连续变量，你可能会结束
with solutions that have intermediate 与中间的解决方案
values of the design variables and in 设计变量的值和in
some cases that actually doesn't happen 有些情况实际上并未发生
for some physics problems but in 对于一些物理问题，但在英国
elasticity it does happen and you could 它确实发生了弹性，你可以
interpret it as some kind of 把它解释成某种形式
microstructure but the often that would 微结构，但往往会
be expensive to manufacture so you want 制造昂贵，所以你想
to get rid of these gray regions and the 摆脱这些灰色地带和
way to do that is we make a so-called 这样做的方法是我们做一个所谓的
simp solid isotropic material with 简单的固体各向同性材料
penalisation interpolation so that's a 惩罚内插，所以这是一个
very well known method in the field and 本领域非常公知的方法和
we say that the stiffness of one element 我们说一个元素的刚度
is equal to the stiffness of solid 等于固体的刚度
material times this density raised to a 材料时间密度提高到a
power P where P is larger than 1 and 功率P，其中P大于1且
what happens now is if P is 3 we get 现在发生的是如果P是3我们得到
something like this so for density point 像这样的密度点
5 we get very little stiffness so that 5我们得到的刚度很小
means that having intermediate density 意味着具有中等密度
elements in the optimized design will be 优化设计中的元素将会是
on economic it doesn't give much 在经济上它并不多
stiffness for the amount of available 刚度为可用量
material and so in this way we penalize 材料，所以我们这样惩罚
the solution to watch 0 & 1 designs 观看0 ＆1设计的解决方案
meaning that even though we saw the 这意味着即使我们看到了
continuous problem and can use all the 连续的问题，并可以使用所有的
efficiency associated with that we end 与我们结束相关的效率
up with discrete solutions so this is a 与分立解决方案，所以这是一个
basic parameters ation of the problem 问题的基本参数
and you can go to the flowchart so you 你可以去你的流程图
would start by initializing the finite 将首先初始化有限
element procedure then you do the finite 然后你做有限元
element analysis right now its 元素分析吧
elasticity but I will compare 弹性，但我会比较
to other forms and you could also 以其他形式，你也可以
imagine having a nonlinear problem here 想象这里有一个非线性问题
and then the next step that's the most 然后是最重要的下一步
important part that's the sensitivity 这是敏感度的重要部分
analysis or gradient computation and it 分析或梯度计算和它
turns out that this can be done 事实证明这可以做到
extremely efficiently so this is the key 非常有效，所以这是关键
point to the six the key of the six 指向六个关键的六个
success of the method and so essentially 方法的成功等等
we compute so this would be the gradient 我们计算所以这将是梯度
of the objective function with respect 对目标函数的尊重
to one of the design variables and 到一个设计变量和
that's all given by things we can 这一切都是我们所能做的
compute directly so the direct 直接计算
derivative the derivative of the 衍生物的衍生物
stiffness matrix with respect to the 刚度矩阵相对于
density is simple to compute the state 密度很容易计算状态
vector which we already solve for the 我们已经为之解决的矢量
original problem here and then the 原来的问题在这里，然后
derivative of the load vector so all 所有的负载矢量的导数
these are known the only unknown is this 这些都是众所周知的唯一未知之处
a joint vector here lambda T and it 这里是一个联合向量lambda T和它
turns out it can be found from solving 事实证明它可以从解决中找到
an additional problem here which we see 这是我们看到的另一个问题
here and so essentially the low case 在这里，基本上是低的情况
it's solving a similar problem to this 它正在解决类似的问题
at least if the system matrix is 至少如果系统矩阵是
symmetric and then just with another 对称，然后与另一个
right hand side so in many cases if we 如果我们在很多情况下，右手边
actually factorize this stiffness matrix 实际上将这个刚度矩阵分解了
and it's symmetric well then we get the 它是对称的，那么我们就可以得到
sensitivities for almost free we just 我们只是几乎免费的敏感性
have to solve for one more hello case 必须再解决一个问候
but in the worst case if we are using an 但在最坏的情况下，如果我们正在使用一个
iterative solver or this system is non 迭代求解器或此系统不是
symmetric well then we have to solve one 对称好，那么我们必须解决一个
extra problem corresponding to the 额外的问题对应于
original problem but no matter how many 原来的问题，但无论多少
design variables we have even if you 即使你有设计变量
have a billion design variables the cost 有十亿个设计变量的成本
of the sensitivity analysis is 的敏感性分析是
essentially corresponding to one extra 基本上相当于一个额外的
system analysis so that's sort of the 系统分析，这是那种
key point of the success we can perform 我们可以执行的成功的关键点
gradient analysis extremely efficiently 梯度分析非常有效
now based on these great gradients we 现在基于这些伟大的渐变我们
update the design and be performed these 更新设计并执行这些
until convergence now one thing I 直到融合现在我有一件事
skipped here was this guy years of the 跳过这里是这家伙的年
regularization here and so it turns out 这里正规化，所以事实证明
that just solving it without 那只是解决它没有
regularization we get problem or we get 正规化我们遇到问题或得到
designs looking like this we call it 看起来像这样的设计我们称之为
checkerboard so alternating solid and 棋盘如此交替固体和
void elements and to avoid that so that void元素并避免这种情况
it's not well modeled by the finite 它并没有很好地被有限的模型所模拟
element model so we want to avoid that 元素模型，所以我们想要避免这种情况
and at the same time you also get mesh 同时你也可以获得网格
dependency so we want to 依赖性，因此我们要
that with mesh refinement we actually 我们实际上用网格细化
convert to a certain design such that we 转换为一定的设计，使我们
can rely on our finite element analysis 可以依靠我们的有限元分析
so the idea here is to introduce some 所以这里的想法是介绍一些
kind of length scale and the first idea 一种长度规模和第一个想法
was to do some filtering so we introduce 我们要做一些过滤，所以我们介绍一下
a neighborhood of one element at its 它的一个元素的邻域
neighborhood within a certain radius and 在一定范围内的邻域
then we filter the sensitivities within 那么我们过滤内部的敏感性
this neighborhood and so this was 这附近， 所以这是
originally just a heuristic idea but it 最初只是一个启发式的想法，但它
turns out that it's actually very 事实证明，这实际上是非常
similar to a non-local elasticity theory 类似于非局部弹性理论
so we are optimizing the structures 所以我们正在优化结构
using on local elasticity theory you 利用局部弹性理论你
could say and what comes out of that is 可以说，那是什么出来的
that even with we get rid of the 即使我们摆脱了
checkerboards and with mesh refinement 棋盘格和网格细化
we get converge towards a certain 我们得到了一定的收敛
topology now this can also be done with 现在这个拓扑也可以用来完成
an other method done by Edward Reilly Edward Reilly完成的另一种方法
who is from here also on his former 谁也来自他的前任
student runs with a density filtering 学生运行密度过滤
that does almost the same and well both 这两者几乎都是一样的
of these here require that you build up 这些在这里需要你建立起来
this neighborhood for all the elements 这个社区的所有元素
and this might be expensive if you have 如果你有这可能是昂贵的
a billion elements to compute the 一十亿元计算
neighborhood for all of these elements 所有这些元素的邻域
so a more efficient method that we have 所以我们有一个更有效的方法
been working on recently is simply to 最近一直在努力工作
solve an additional but skala problem so 解决一个额外的但skala问题
it's a cheaper problem than solving the 这是一个比解决问题更便宜的问题
original problem the original elasticity 原始问题原来的弹性
problem and in this way this only the 问题，并以这种方式，这只是
Helmholtz based filtering or PDE based 基于亥姆霍兹过滤或基于PDE的
filtering so you solve a little extra 过滤，以便解决一些额外的问题
differential equation to find these 微分方程来找到这些
filtered density densities that avoid 过滤后的密度密度避免
the checkerboard issue and the mesh 棋盘问题和网格
dependency so this is essentially the 依赖关系，所以这实质上是
algorithm and it can be implemented in 算法，并可以在中实现
all kinds of ways and we have within the 各种方式，我们在内
last couple of years been doing 最近几年一直在做
different apps that can actually run on 不同的应用程序可以实际运行
your smart phone or your iPad or 你的智能手机或iPad或
whatever I'm going to talk about more 无论我要谈的更多
about this one tomorrow but I would just 关于这个明天，但我会
say sort of real time you can do to 说你可以做的实时
polity optimization on your iPhone or 政策优化在你的iPhone或iPod上
your smartphone and it's available at 您的智能手机， 它可在
our webpage so more recently we actually 我们的网页实际上更近一些
also did this in 3d and here I'm just 也在3D中做了这个，在这里我只是
going to give you a short demonstration 会给你一个简短的示范
so sometimes when I show this people 所以有时候我会展示这些人
think oh it was a cool animation you did 想想哦，这是你做的一个很酷的动画
but 但
is actually running now on my computer 现在实际上正在我的电脑上运行
real time and it would run on your smart 实时，它会运行在你的智能
phone or your laptop also and so you can 手机或你的笔记本电脑也是如此，你可以
see here this is a structure that's 在这里看到这是一个结构
supported so this is now in 3d it's 支持所以这是现在3D 是
supported to the right it has loads to 支持它正在加载的权利
the left and you see how it starts Regis 左边，你会看到它是如何启动Regis的
you viewing material and I will just 你看材料，我将只
demonstrate how I can interactively work 展示我可以如何交互式工作
with this and so I'm introducing a 有了这个，所以我介绍了一个
bridge stake here and I rotate it and I 桥桩在这里， 我旋转它和我
scale it so this would be the bridge 扩大它，这将成为桥梁
deck and I apply a load on it so now 甲板上，我现在应用一个负载
it's loaded and I change boundary 它被加载并且我改变边界
conditions or supports here I add a 条件或支持，我添加一个
little bit more material and then I 一点点材料，然后我
change the boundary conditions here to 将边界条件改为此处
impose symmetry and now you should see a 施加对称性，现在你应该看到一个
nice bridge like structure coming up 漂亮的桥梁像结构即将到来
here and we can put on the symmetry also 这里我们也可以穿上对称
so here and so now we see here that 所以现在我们在这里看到
there's a structure building up here 这里有一个建筑物
this is a bridge structure and you can 这是一个桥梁结构，你可以
play around with it to get an intuition 玩弄它来获得直觉
of what's happening when you change for 当你改变时发生的事情
example the position of the bridge stick 例如桥牌的位置
and you see here now the structure has 你现在看到这里的结构
to adapt and put the pillars in the 适应并把支柱放在中
right places and you can move the 正确的地方，你可以移动
supports here and it has also to 在这里支持，它也有
redistribute adults so you see here it 重新分配成人，让你在这里看到它
can actually be done extremely 实际上可以做得非常好
efficiently even on single laptops and i 即使在单个笔记本电脑和我也能有效地使用
believe so still this cannot be used 相信如此仍然不能使用
directly to build a bridge afterwards 之后直接搭桥
but it gives you a very nice idea of 但它给你一个非常好的想法
what's possible the method and also to 该方法可能有什么可能，还有什么
learn for students and work with it and 学习的学生，并与它合作，
keeping in mind that 17 years ago and 牢记17 年前和
ipad would have been on the top 500 list iPad将进入前500名单
of supercomputers in the world well then 当时世界上超级计算机的世界
you can imagine that it will not take 你可以想象它不会采取
many years before you can actually do 很多年才能真正做到
design real realizable design on your 设计真正的可实现的设计
lap on your ipads and stuff like that ok 搭上你的iPad和类似的东西好吧
so this was an ipad we also have and 所以这是一个我们也有的ipad
there i should say here that there's 在那里我应该说，那里是
some export facility so you can export 一些出口设施，所以你可以出口
it directly as an object file or stl 它直接作为一个对象文件或stl
file and you can print it on your 文件，你可以打印在你的
desktop 3d printer and have 桌面3D打印机和有
models in your lap within an hour or so 在一个小时左右的时间内在你的腿上模型
so I invite you all it's it's freely 所以我邀请你一切都是自由的
available and you can download it from 可用，你可以从它下载
app store or for your pc or zone so 应用商店或您的电脑或区域
architects and designers they have their 建筑师和设计师他们有他们的
favorite code they are looking with 他们正在寻找与喜爱代码
rhino and grasshopper so we have also 犀牛和蚱蜢，所以我们也有
been working on implementing a topology 一直在努力实现拓扑
optimization module there and our 优化模块和我们的
friends in the architecture they build 他们建造的建筑中的朋友
all kinds of funny structures I don't 各种有趣的结构， 我不知道
remember if I have I don't have a case 记得如果我有我没有案件
of that here but anyway this is also an 在这里，但无论如何，这也是一个
option for people interested in working 为有兴趣工作的人选择
with it okay so apart from these things 除了这些事情之外 ，它还可以
we also have published civil computer 我们也出版了民用电脑
codes on our web page many of you may 许多人可能会在我们的网页上输入代码
know this basic 99 line code so it turns 知道这个基本的99行代码，所以它转向
out in 2d you can write it very compact 在2D中你可以写得非常紧凑
in MATLAB and that's available for 在MATLAB中，这是可用的
people to to extend and work with more 人们要扩大和更多地工作
recently we made a vectorized version 最近我们做了一个矢量化版本
that works much more efficiently but 那效果更好，但是
it's also more difficult to read and 阅读和阅读也更加困难
then recently we published a paper on 那么最近我们发表了一篇论文
very efficient multiquip methods for 非常有效的multiquip方法
doing 3d problems and even more recently 甚至最近做3D问题
it's still on line first but we 它仍然在线，但我们
published a pizza base coat for 发表了一份比萨基础外套
large-scale computations that I will 我将会进行大规模的计算
talk about more in just a few minutes 在几分钟内谈论更多
okay so it seems like we are mall is 好吧，好像我们是商场是
done here we have a design method we can 在这里完成我们有一个我们可以设计的方法
do all what we want but it turns out we 做所有我们想要的，但事实证明我们
still have challenges and goals in this 在这方面仍然有挑战和目标
fields so we are not unemployed yet and 所以我们现在还没有失业
so we are looking into several 所以我们正在研究几个
improvements of the methods we're 我们正在改进的方法
looking into manufacturing limitations 研究制造限制
feature control adaptive to an additive 特征控制适应于添加剂
adaption to additive manufacturing super 适应超级增材制造
large scale problems so this is on the 大规模的问题，所以这是关于
method development side and also on the 方法开发方面也在
application side we work on different 我们应用方面的工作不同
extremal material design cases 极值材料设计案例
nonlinearities multiphysics wave 非线性多物理波
propagation and multis game and I will 传播和多人游戏， 我会的
get through some of these things in the 通过一些在这些事情中得到解决
next half hour whatever we have left so 接下来的半小时，我们已经离开了
let me start with something with the 让我从这件事开始
link scale control in robustness and so 链接比例控制鲁棒性等
everything look very well but when you 一切看起来都很好，但是当你
start applying this idea to new 开始将这个想法应用于新的
concepts and you run into problems and 概念和你遇到问题和
so one of them I will demonstrate on 所以我会演示其中的一个
mechanism design and in particular micro 机构设计，特别是微型
electromechanical system design so this 这样的机电系统设计
slide shows a so called thermoelectric 幻灯片显示所谓的热电
thermomechanical actuator and so the 热机械致动器等等
idea is well you see it on the animation 想法很好，你在动画中看到它
here if you add an electric field over 这里如果你添加一个电场
these two here you will have heating 这两个这里你会有暖气
where the structure is sin the heating 那里的结构是加热的罪
causes thermal expansion and eventually 导致热膨胀并最终
you can cause movement of a gripping 你可以引起夹子的移动
device and in the lower right corner you 设备，并在右下角你
see here so the people we work with 看到这里，我们一起工作的人
wanted to manipulate carbon nanotubes so 想要操纵碳纳米管
you have a carbon nanotube here that's 这里有碳纳米管
on a substrate you want to break it off 在你想要分解的衬底上
and do manipulation with it and it 并用它来操纵它
turned out that their intuitive design 原来他们的直观设计
seen here was not strong enough to break 看到这里没有足够强大的突破
it off the substrate so we did topology 它离开基板，所以我们做了拓扑
optimization and we got this structure 优化，我们得到了这个结构
here that had an order of magnitude 这里有一个数量级
larger forces and you see down here that 更大的力量，你在这里看到
it was actually able to break as a 它实际上能够打破
carbon Eddie nanotubes so this all looks 碳埃迪纳米管，所以这一切看起来
good but let's get a little bit behind 好，但让我们稍微落后一点
the curtain here and look at the 在这里的窗帘，看看
mechanism issue and manufacturing 机制问题和制造
problems that be enforced or encountered 该强制执行或遇到的问题
so i will switch to a very very simple 所以我会切换到一个非常简单的
mechanism design problem so now we have 现在我们有机制设计问题了
we assume we have an input force here 我们假设我们在这里有一个输入力量
that's pressing towards the right and we 这是朝着我们正确的方向发展
want this point to move backwards so 希望这一点向后移动
it's a force inverter and this is one of 这是一个强制逆变器，这是其中之一
the favorite test examples for mechanism 最喜欢的机制测试例子
designed using topology optimization and 采用拓扑优化设计
just to show you the design would look 只是为了向您展示设计的外观
something like this so you can see here 像这样的东西， 所以你可以看到这里
when you press here it goes back in the 当您按下这里可以追溯到在
other direction and i should say i used 其他方向， 我应该说我用过
symmetry here so you could imagine that 在这里对称，所以你可以想象得到
you could mirror it around around the 你可以参照它周围环绕
upper horizontal line here so now this 上面的水平线在这里现在这个
looks on paper it looks good but it 在纸上看起来不错，但它
turns out if we just use the filtering 原来，如果我们只是使用过滤
methods that i showed in the beginning 我在开始时展示的方法
well then using the sensitivity 那么使用灵敏度
filtering method we did something like 过滤方法我们做了类似的事情
this and the density filtering method 这和密度过滤方法
like this and we see there are some 像这样，我们看到有一些
issues partly we have this great 问题部分我们有这个伟大的
transition which is too weak to this 过渡对此太弱了
smoothing that be 平滑即是
enforced by the filtering and partly so 由过滤强制执行，部分强制执行
we would like to have in many cases a 我们希望在许多情况下，
sharp boundary to modern physics well 现代物理学的尖锐边界
and partly we have these hinge regions 部分我们有这些铰链区域
so essentially this mechanism ones just 所以基本上这个机制就是这样
to have like rigid body hinges here but 在这里有像刚体铰链，但
we wanted to be compliant it has to be 我们希望遵守它必须是
etched out of one a piece of material so 如此蚀刻出一块材料
we don't really like these hinges and 我们不太喜欢这些铰链和
obviously they are very very 显然他们非常非常
manufacturing sensitive and essentially 制造敏感和本质上
they're due to bad finite element 他们是由于坏的有限元素
modeling we don't really capture the 建模我们并没有真正捕捉到
stress situation here with our finite 这里用有限的压力情况
element modeling so how do we get rid of 元素建模，所以我们如何摆脱
these two issues well the first thing 这两个问题很好的第一件事
with the gray scale is we could do the 与灰度是我们可以做的
thresholding and so essentially we take 阈值和基本上我们采取
the design method we had before before 我们之前有过的设计方法
we had the design variables we did the 我们有我们所做的设计变量
filtering we got these great transition 过滤我们得到了这些巨大的转变
regions and then you could say now we 地区，然后你可以现在说我们
cut at a certain filter density scale 在一定的过滤器密度等级下切割
and then put everything below 20 and 然后把一切放在20以下
everything about 21 this is not good for 关于21这一切都不好
gradient based algorithm so we do it 基于梯度的算法，所以我们这样做
with a smooth heavy side projection so 如此平滑的重边投影
this is essentially a heavy side 这实质上是一个沉重的一面
projection where beta is sharpness of 投影，其中贝塔是锋利的
the projection and so if we hear 投影，所以如果我们听到了
selected at a half so we threshold at 选择一半，所以我们的门槛在
the half density we would get something 半密度我们会得到一些东西
that gets rid of the grayness but we 摆脱了灰色，但我们
still see that way we have hinges and so 仍然看到我们有铰链等方式
we can try with different thresholding 我们可以尝试不同的阈值
values here and to see what happens with 价值观，并看看会发生什么
the designs and so if we start in the 设计，所以如果我们开始在
top if you threshold at one well then we 如果你在一个很好的门槛，然后我们
see here we have sort of a machining 看到这里我们有一种加工
tool we don't have any details in the 工具我们没有任何细节
structure or any avoid regions in the 在结构或任何避免区域
structure that are smaller than this 比这小的结构
filter size so it means here that you 过滤器的大小，所以这意味着你在这里
could machine this structure but you can 可以加工这种结构，但你可以
still have these very tiny solid regions 仍然有这些非常微小的固体区域
that would be very sensible to 这将是非常明智的
manufacturing errors now if we do the 如果我们这样做，现在制造错误
opposite so threshold at zero here we 我们在这里零点对面
have the opposite thing so here we could 在这里我们可以有相反的事情
say it's a deposition tool so we have no 说它是一种沉积工具，所以我们没有
solid solid part of the structure is 结构坚固的部分是
smaller than the filter size but we can 小于过滤器尺寸，但我们可以
have very small void regions which again 再次具有非常小的空隙区域
are not very nicely manufacturable so 所以不是很好制造
none of this really works and if we 没有一个真的有效，如果我们
threshold at point five we get neither 在第五点的门槛，我们都没有
dang scale on the void or the solid dang在虚空或固体上缩放
regions so that led to the idea why not 所以导致这个想法为什么不这样做
optimize the worst case as these three 优化这三个最糟糕的情况
cases so say we optimize the output 我们可以这么说，我们优化了产出
displacement for the worst case of these 对于这些最坏情况的位移
three realizations so now our 现在我们三个认识
optimization problem becomes a min max 优化问题成为最小最大值
problem somewhat more complicated and we 问题有点复杂，我们
have to solve three finite element 必须解决三个有限元
problems for each iteration so it 每次迭代都会有问题
becomes quite expensive but on the other 变得相当昂贵，但另一方面
hand the outcome is very nice as you 结果是非常好的，因为你
will see in the next slide here so you 将在接下来的幻灯片，你在这儿看
could see this as sort of an over-under 可以看到这是一种过度的下
etching thing so when you threshold the 蚀刻的东西，所以当你的门槛
different levels you're sort of shrink 不同的水平，你有点缩小
or you expand the structure and so we 或者你扩大结构，所以我们
are saying we optimized for the worst 我们说我们对最坏的情况进行了优化
case of wrong etching or you could say 错误蚀刻的情况下，或者你可以说
worst case of errors in the 在最坏的情况下的错误
manufacturing process and so what comes 制造过程等等
out of it is that this year that we 这是我们今年的事
would call the blueprint design looks 会称之为蓝图设计
now like this you see that there are no 现在像这样，你看到没有
hinges anymore it's nice distributed 铰链不再分布
compliant mechanism and even if we over 兼容的机制，即使我们结束
etch it or make it thinner it's still an 蚀刻它或使它更薄，它仍然是一个
integrated mechanism that would work and 整合的机制，将工作和
even if you under etch it it becomes 即使你在蚀刻它，它成为
thicker it's also a mechanism that would 较厚它也是一种机制 ，
work so in that way we include 我们以这种方式工作
manufacturing errors in the design 制造设计中的错误
process and get some designs that are 处理并获得一些设计
very nice both black and white and also 非常好的黑色和白色，也
where we have full control of the 在那里我们完全控制了
minimum length scale here and so this 最小长度尺度在这里等等
method is something we are very fond of 方法是我们非常喜欢的
these days and many of the examples you 这些天和许多例子你
will see in the coming slides are based 将在未来的幻灯片中看到
on this ensuring that we can take 在此确保我们可以采取
designs directly out of the topology 直接从拓扑结构设计
optimization process and feed them into 优化过程并将其输入
a 3d printer and get devices that 一台3D打印机，并获得设备
actually act just like we predicted so 实际上就像我们预测的那样行事
just one example here this is from 这只是一个例子
electrostatic actuator design so the 静电致动器设计等等
design so you all know if you put if you 设计，所以你都知道如果你把你的话
have two electrodes and you put an 有两个电极，你把一个
electric field over them there will be 他们会有电场超过他们
electrostatic actuation or attraction 静电致动或吸引力
forces and these forces they a 部队和这些力量他们
proportional to one over the distance 与距离成正比
squared between these two plates so 这两个平板之间的平方
really when you try to optimize a 当你尝试优化一个
topology optimize something like that 拓扑优化类似的东西
and you try to maximize the output 并尝试最大化输出
displacement or force at this point here 位移或力量在这里
well then it will try to make this gap 那么它会试图弥补这个差距
as small as possible to get the largest 尽可能小， 以获得最大的
possible actuation force and so this 可能的驱动力等等
problem specifically has 问题具体有
electrodes here and there and the ground 电极在这里和那里以及地面
here and the question is how do we 这里和问题是我们如何
distribute the material here such that 在这里分发这些材料
we get this actuation that I pointed so 我们得到了这个我指出的驱动
we want to move upwards here when we 我们想在这里向上移动
turn on the power and what comes out if 打开电源，如果出现
we just do the standard approach we see 我们只是做我们看到的标准方法
something like this you recognize the 像这样的事情你认识到了
force inverter from before but then you 强制变频器从之前，但然后你
see here this is the gap here this is 在这里看到这是这里的差距
where the electrostatic forces are 静电力的地方
working and essentially they correspond 工作和基本上他们相对应
to just one element in the mesh here and 到这里和网格中的一个元素
obviously this is bad modeling we don't 显然这是不好的建模，我们没有
capture the physics of this problem very 非常捕捉这个问题的物理
well however if we introduce this robust 不过，如果我们引入这个强大的
design approach we get a beautiful hour 设计方法让我们有一个美好的时光
or we get a structure looking like this 或者我们得到一个像这样的结构
it's cleaned up compared to this one and 它和这个相比已经被清理了
it has a well-defined gap here that 它在这里有一个明确的差距
actually makes the physics reliable for 实际上使得物理学可靠
this simulation here and just to 这个模拟在这里，只是为了
demonstrate so these would be animations 证明这些将是动画
of two devices and inverter and the 两个设备和逆变器的
gripping mechanism and you see how these 抓地力机制，你看这些如何
actually work in practice okay so let me 实际上在实践中工作好，所以让我
proceed with so this is something that 继续这样做是这样的
we use in many of our applications so 我们在许多我们的应用程序中使用
now let me proceed with a couple of 现在让我与一对夫妇的继续
other extensions that we have done 我们已经完成的其他扩展
recently just to show where we are sort 最近只是为了展示我们在哪里排序
of hitting at and so the first one is 打在和所以第一个是
what we call flux inflexible void areas 我们称之为通量不灵活空隙区域
or the blop methods and the concept is 或者blop方法和概念是
here that in many design cases so from 在很多设计案例中都是如此
the initial phase of the topology 拓扑的初始阶段
optimization we define a design domain 优化我们定义一个设计领域
and we define non design domains and so 我们定义非设计领域等等
for the bridge here we would say there 对于这里的桥梁我们会在那里说
can be no material here for the front of 在这里可以没有任何材料的前面
the trains to to run underneath it or 火车要在它下面跑
structural engineer could say I want a 结构工程师可以说我想要一个
window here but what would be the 窗口在这里，但会是什么
framing structure that would optimize it 框架结构，将优化它
or for some reason we could have a 或者出于某种原因，我们可以有一个
circular void domain and then the 圆形无效域然后是
topology optimization would try to adapt 拓扑优化会尝试适应
the structure around this fixed boy to 围绕这个固定的男孩的结构
mean however in many cases for 意味着在许多情况下
architects or others they don't really 建筑师或其他他们并不真的
care about the exact shape so maybe they 关心的确切形状，所以也许他们
don't care about this window being 不关心这个窗口
rectangular here maybe they say we just 这里的矩形也许他们说我们只是
want a certain amount of light coming 想要一定量的光线来
into the room we don't care we put more 进入房间我们不在乎我们放更多
weight on the optimality of the 体重的最优性
structure then on actually enforcing 结构然后实际执行
this square window and so what could we 这个广场的窗口，因此我们能做
do to make this 做这个
the shape of the window be a variable 窗口的形状是一个变量
but have a certain area well we do a 但是我们有一定的领域
tooth design variable approach now so we 牙齿设计变量的方法现在让我们
have the original design variables the 有原始的设计变量
density variables but then we introduce 密度变量，然后我们介绍
a second field that models the void 模拟虚空的第二个领域
region here and we say that the now the 地区在这里，我们说现在的
physical density is now the original 物理密度现在是原来的
density times one minus is a new 密度乘以一减是一个新的
variable that we introduced essentially 基本上我们引入的变量
saying if there's void governed by this 说这是否有虚空
well then we have zero density and now 那么我们现在有零密度
this here we update by a pseudo level 这里我们更新伪级别
set approach that we only allow it to 设置方法，我们只允许它
change shape at the boundaries and 改变边界处的形状和
popularly said we say that it changes 俗话说我们说它改变了
the shape of this void inclusion such 这种空隙包含物的形状如此
that it disturbs the the stiffness least 它至少干扰了刚度
possible so it sort of adapt it moves 可能会让它适应移动
away from highly stressed regions and 远离高度紧张的地区和
goes to other regions where it doesn't 去其他地区没有
disturb so much and so just to 打扰这么多， 只是为了
demonstrate that this was a circular 证明这是一个通告
hole example we start with a circular 我们以圆形开始
void and now we just say it the area of 无效，现在我们只是说它的区域
this void has to be constant but we 这个空白必须是恒定的，但我们
don't care about the shape and what we 不关心形状和我们的东西
will see here is so you see here there 将在这里看到是你在这里看到的
now this is the Conte the fixed wide 现在这是Conte的固定宽度
area and you can see how the void sort 区域，你可以看到如何无效排序
of adapts and disturbs structures as 适应和扰乱结构的
little as possible and just to do it on 尽可能少，只是为了做到这一点
the bridge example here also we see here 这里的桥梁例子也在这里看到
so the first the upper part here is a 所以这里的第一个上部是a
bridge with a fixed boil domain and the 具有固定沸腾域和桥的桥
lower part has this blob approach or so 下半部分有这个blob方法左右
the flexible block fixable void to me 灵活的块固定空白给我
and you will see here in the beginning 你会在开始时看到这里
of the iterations they look very much 他们看起来非常重要
alike but then slowly this year is 但今年缓慢
adapting and sort of becoming a nicer 适应和变得更好
looking structure and so this idea here 看起来结构，所以这个想法在这里
will be in the next version of the 2d 将在2d的下一个版本中
app also to play with ok so that was one 应用程序也玩好，这是一个
extension another one is you all know 延伸另一个是你都知道
additive manufacturing I think everybody 添加剂制造我想每个人
has a 3d printer by now in his office on 现在在他的办公室里有一台3d打印机
not everybody but it's getting towards 不是每个人，但它正在走向
that and so we are also getting into 那我们也正在进入
that and we have a lot of the activities 那我们有很多的活动
I will just talk about one of them here 我会在这里谈谈其中的一个
and so this is inspired by three cases 所以这受到三种情况的启发
here so the first one is a work 这里所以第一个是一个工作
from a couple of years ago from I 从几年前我从
believe Stanford where they did the 相信斯坦福在哪里做过
world's lightest material and the idea 世界上最轻的材料和想法
was that they took a polymer bath then 当时他们接受了聚合物浴
they shine a laser light into it and 他们将激光照射进去
they solidified it and get sort of a 他们巩固了它，并得到了一个
very small scale a lattice structure 非常小规模的格子结构
made in polymer then they take is a 在聚合物制成，然后他们采取的是
lattice structure and they evaporate 晶格结构， 它们蒸发
metal on it and so they get a nanometer 金属，所以他们得到纳米
thick surface putting in put on the top 厚的表面放在顶部
of this lattice structure and then they 这个格子结构然后他们
dissolve or burn away the polymer 溶解或烧掉聚合物
structure and what they have left is a 结构和他们留下的是一个
very very thin shell like structure and 非常非常薄的壳状结构和
since they can make the wall so thin 因为它们可以使墙变得如此薄
they actually were able to put it on top 他们实际上能够把它放在最前面
of this this flower here so obviously 这个花这么明显
this is not optimal I believe it's the 这不是最佳的我相信它是最好的
world light is so far but we could 世界之光是如此之远，但我们可以
optimize it further and get better 进一步优化并且变得更好
properties if we could topology optimize 属性，如果我们可以拓扑优化
it the other thing is with 3d printing 另一件事是3D打印
we often see you so if you just send 如果你只是发送，我们经常会看到你
your structure to your 3d print it will 你的结构到你的3D打印它会
cheat you right so it will actually it 欺骗你，所以它会实际上
will do the surface solid but if you 会做表面是固体，但如果你
stop in the middle of the process you 停止在你的过程中
will see that it doesn't fill material 会看到它不填充材料
inside the structure to save material 在结构内部节省材料
and so this is called infill and for 所以这被称为infill和for
structural optimizer it makes you think 结构优化器让你思考
well maybe we could use this infill to 好吧， 也许我们可以使用这个infill来
our advantage and two structures that 我们的优势和两个结构
automatically have poor structure inside 内部结构自动不好
and get in again and mechanical 并再次进入和机械
advantage for that and of course nature 这当然有利于自然
knows that so if you look at bone 知道，所以如果你看着骨头
structure it has a closed outer wall 结构它有一个封闭的外壁
here so you don't write the muscle and 在这里，所以你不写肌肉和
you get a smooth surface and inside it 你会得到一个光滑的表面，并在里面
has this spongy tissue here so nature 自然界中有这种海绵组织
already knows and so the question is 已经知道，所以问题是
could be devised a topology optimization 可以设计一个拓扑优化
procedure that makes it possible to 程序，使之成为可能
design also the interface so assuming 设计也是如此假设的界面
that we want to to control the 我们想要控制的
properties of the interface and control 界面和控制的属性
the properties of the inside of the 内部的属性
structure and so to do that it requires 结构，这样做是需要的
some extension of the interpolation 插值的一些扩展
scheme i will just outline it with this 我只是简单介绍一下这个方案
slide here so in this case if we start 如果我们开始的话，请在这里滑动
with the usual design variables then we 与通常的设计变量，然后我们
do the filtering 做过滤
we have done so far also and then we do 我们迄今也做了，然后我们做了
with reg holding and so a projection as 与reg持有等投影为
we saw before and that's what gives us 我们之前看到过，这就是给我们的
the structure however now we add extra 现在我们增加额外的结构
steps on it so now we do a second 现在我们做了第二步
filtering with another filter radius and 用另一个过滤器半径过滤和
we compute the norm of the gradient of 我们计算梯度的范数
that so that would give us something 那样会给我们一些东西
that detects the boundaries where the 检测到的边界
density changes and then we project that 密度变化，然后我们预测这一点
to a discrete solution and then at the 到分立的解决方案，然后在
end we say that the stiffness is now a 最后我们说刚度现在是a
function of the projected field here and 这里投影场的功能和
this boundary detection field here and 这边界检测字段在这里和
in that way we can do a due to polity 这样我们可以做一个由于政治
optimization where we have an internal 我们有一个内部优化
part with one density or one mass or 部分具有一个密度或一个质量或
whatever and stiffness and it's coded 无论什么和刚度，它的编码
with a certain thickness of our material 与我们的材料的一定厚度
here so looks a bit complicated but it 这里看起来有点复杂，但它
actually works very efficiently and just 实际上工作非常有效和公正
show use of this convergence study so 展会使用这种融合的研究，以便
you can actually control here you have a 你实际上可以在这里控制你有一个
certain stiffness inside and then this 一定的硬度，然后这个
differ outside on the structure and we 外部的结构和我们不同
can control by varying the different 可以通过改变不同来控制
filter radii we can control the 滤波半径我们可以控制
thickness of the outer layer here so so 这里的外层厚度如此如此
far we only did this for two dimensions 远远我们只做了两个维度
so this is another case where we have 所以这是我们拥有的另一个案例
supports here and we have a load here so 在这里支持，我们在这里负载
this would be with the interface or 这将与接口或
coded structure approach this would be 这将是编码结构的方法
with the usual approach turns out into 用通常的方法变成
the stiffness optimization we actually 我们实际上的刚度优化
don't get a higher stiffness of this 不要有更高的刚度
structure but you can imagine if you 结构，但你可以想象，如果你
computed the buckling value the buckling 计算屈曲值的屈曲
item value well then this would be 项目的价值，那么这将是
better because the cross sections are 更好，因为横截面是
bigger and hence buckling would be 更大，因此会屈曲
better properties so this was actually 更好的属性，所以这实际上是
accepted for publication and right now 现在接受发布
we're working on extending it to 3d and 我们正在努力将其扩展到3D和
i said earlier with this approach we 我之前用这种方法说过我们
should be able to actually come up with 应该能够真正拿出
a real optimal structure that is also 一个真正的最佳结构也是
manufacturable as a shell structure when 可制造成壳体结构时
we when we can do that in fiji ok so now 我们什么时候可以在斐济这样做， 现在就这样
to the efficiency of this so everything 这样做的一切效率
looks very nice here but i would say 在这里看起来很不错，但我会说
that we are still suffering from what 我们还在遭受什么
called the Duke Blue proper problem so 所以叫公爵蓝问题
I'm from Denmark you all know Lego 我来自丹麦， 你们都知道乐高
bricks I guess maybe some of you will 砖块，我想也许你们中的一些人会
play with the duplo bricks as babies and 像婴儿和宝宝一样玩耍
certainly if you see this would be the 当然，如果你看到这将是
disco time structure you can see this is 迪斯科时间结构，你可以看到这是
an airplane but it's not really bad 一架飞机，但它不是很糟糕
modeling of it it you don't get really 它的建模，它你没有得到真正的
the right details so what we want to get 正确的细节，所以我们想要得到什么
over is to get out of childhood and go 过去就是摆脱童年而去
to well at least teenager would and do 以及至少少年会做和做
much more detailed design I don't know 更详细的设计我不知道
if you can see in the back but this is 如果你可以看到后面，但这是
still illegal airplane but you hardly 仍然是非法飞机，但你很难
see the structural details here right so 这里请看结构细节
we want to go from baby to a teenager 我们想要从婴儿走向少年
and work with the real Lego bricks and 并与真正的乐高积木一起工作
so this can be transferred to the 所以这可以被转移到
topology optimization community so you 拓扑优化社区让你
see lots of nice 2d designs but when you 看到很多漂亮的2D设计，但是当你
go to 3d we are limited by the 去3d我们受限于
resolution so we are still on the duke 决议，所以我们仍然在公爵
blue stage there we want to get too much 我们想要得到太多的蓝色舞台
higher resolutions in order to be able 为了能够更高的分辨率
to solve full airplane wing and wings 解决完整的飞机机翼和机翼
and much larger structures so we have 和我们拥有的更大的结构
been working on that recently and this 一直在努力，最近这一点
year is a structure so I guess it so the 一年是一个结构，所以我想它是如此
record high resolution so this has 记录高分辨率，所以这一点
something like 120 million elements and 大约有1.2亿个元素和
again there's no post-processing here 这里再也没有后期处理
but the discretization is sophie vine 但离散化是苏菲藤
it's still with these voxel elements but 它仍然与这些体素元素，但
you hardly see it and you get much more 你很难看到它，你会得到更多
structural detail here and so this is 结构细节在这里，所以这是
actually published also in an open 实际上也公开发表
software so it's based on the Pepsi 因此它基于百事可乐软件
framework that's provided by the argonne 由argonne提供的框架
national lab so it's a portable 国家实验室，所以它是一个便携式
extensible toolkit for scientific 可扩展的科学工具包
computations and we build topology 计算和我们构建拓扑
optimization on top of that and so the 最重要的优化，等等
the code that you can download from our 您可以从我们的网站下载的代码
web page shelves essentially this 网页基本上就是这样
problem here and it includes the 这里的问题，它包括
optimizer and filters and input/output 优化器和过滤器以及输入/输出
stuff and like that so i invite you to 东西，所以我邀请你
test this so it gets quite exciting with 测试这个，所以它变得非常令人兴奋
the level of detail you can do here so 你可以在这里做的详细程度如此
in other case is this so this is a pic 在其他情况下是这样的， 所以这是一个图片
so you have supports in the corners and 所以你有角落和支持
you have adjusted to the load on the top 你已经调整到顶部的负载
we get a structure looking like this if 我们得到一个像这样的结构
you cut off that 你切断了
out of it you will see a very intricate 在它之外你会看到一个非常复杂的
pattern of struts and walls and stuff 支柱和墙壁和东西的模式
like that and so I think it really can 这样，所以我认为它确实可以
give structural engineers a new insight 给结构工程师一个新的见解
into optimal structures when you have 当你拥有最佳结构时
this extreme level of detail so we also 这个极端的细节，所以我们也是
tried to solve an analytical problem so 试图解决一个分析问题
we see that anything also paulina has 我们看到任何东西也是保利娜
this model in his office so Michele 100 这个模特在他的办公室如此Michele 100
years ago came up with these designs so 多年前就提出了这些设计
if you have to a torsional load here and 如果你要在这里扭转载荷和
you want to transfer it from the left 你想从左边转移它
hand to the right hand well then you 然后右手向右转
need this grillage like structure or 需要这个架构或格架
sort of a ball that is made up of this 由此组成的一种球
frame like structure and so we tried 像结构框架，所以我们尝试了
that and we got disappointed we got an 我们失望了，我们得到了一个
egg we didn't get this frame or this 鸡蛋，我们没有得到这个框架或这个
cage-like structure and so what's wrong 笼状结构等等有什么不对
here well nothing is wrong it turns out 这里没有什么是错误的结果
that actually Michelle assume that it 实际上米歇尔假定它
had to be a crazy Dyke structure so the 不得不说是一个疯狂的戴克结构，所以
real optimum is actually an eggshell 真正的最佳实际上是一个蛋壳
that's much more stiff and so it's you 这更僵硬，所以这就是你
have to introduce other things to get 必须介绍其他的东西才能得到
rid of this egg shell structure like 摆脱这种蛋壳结构
thing and so if you introduce a length 事情，所以如果你引入一个长度
scale that is larger than the thickness 比厚度大的比例尺
that is allowed by the air volume 这是空气量所允许的
fraction well then you can come up with 分数好，然后你可以想出
structures that look like this which 看起来像这样的结构
actually take this part here so it means 实际上这部分在这里，所以它的意思
that optimal 3d structures are usually 最佳的三维结构通常是
closed wall and you have to add other 封闭的墙，你必须添加其他
criteria to get open walls so this is 准则得到开放的墙壁，所以这是
also interesting for the structural 结构也很有趣
designer so I think because they 设计师，所以我想是因为他们
probably want windows in the house so 可能要在房子里的窗户
they have to do something else than just 他们必须做别的事情，而不仅仅是
pure 3d topology optimization for 纯三维拓扑优化
stiffness okay and well just to point 僵硬没关系，只是为了指出
that what we're working on now is to try 我们现在正在努力的是尝试
to design the whole airplane wing and so 设计整个飞机机翼等等
we are aiming at running this on one 我们的目标是一举成立
with 1 billion elements and so the only 有10亿个元素，因此是唯一的
thing missing is the computer right now 缺少的东西是现在的计算机
the code scales and we need access to a 代码缩放，我们需要访问一个
computer with 16,000 course and so we 计算机有16,000课程，所以我们
are applying for that for the some 正在为一些人申请
European computers to do that but I 欧洲电脑这样做，但我
think it will be exciting to see what 想想看什么会让人兴奋
comes out with this extreme level of 出来这个极端的水平
detail with 1,000,000,000 elementium 具有10 亿个元素的细节
okay so still lots of things to talk 好的，还有很多事要说
about so I'm 关于我是如此
to give you a couple of different 给你几个不同的
applications here so the first one in is 这里的应用程序是第一个应用程序
in material design so you can imagine so 在材料设计中你可以想象得如此
far spoke about structures but you can 远谈到结构，但你可以
also scale this down to designing the 也缩小到设计的范围
periodic material structure and so the 周期性的材料结构等等
first case which is actually something i 第一种情况实际上是我的事情
did in my PhD work many years ago back 很多年前我在博士学位工作
in 95 and that wants the question my 在95，并希望我的问题
advisors post can you use to polity up 顾问后，你可以用它来政体起来
to my station to make a material that 到我的工作站做一个材料
has negative poisson's ratio so in other 在其他地方有负泊松比
words if you press a compress it 如果你按压它的话
horizontally can you make it compress 水平地可以使它压缩
also compress also vertically and so 也垂直压缩等等
essentially i took out one basil assume 基本上我拿出一个罗勒假设
periodicity and a little bit like the 周期性和一点点像
mechanism design i said when i press 机械设计我说，当我按下
here it has to compress in the other 这里它必须压缩在另一个
direction or actually I did it by an 方向或实际上我做了一个
inverse homogenization approach and what 逆均匀化方法和什么
comes out of that is this structure so 出来的就是这样的结构
you can see the sort of a fishbone like 你可以看到类似鱼刺
structure and you can imagine when you 结构，你可以想象当你
compress it horizontally these triangles 水平压缩这些三角形
will contract in the other direction and 将在另一个方向收缩
so I can operate it here I think and you 所以我可以在这里操作它，我想和你在一起
see here when I compress horizontally it 当我水平压缩它时，请看这里
also contracts vertically and so this is 也垂直收缩，所以这是
a negative person for a tube behavior so 一个管人行为的负面人物如此
this was back in 95 since then computers 这是从95年以来的计算机
have allowed us to do quite detailed 让我们做得相当详细
designs in three dimensions so this is a 三维设计，所以这是一个
block manufactured block in the in 3d 块中制造的块在3d中
printing based on I think 4 x 4 x 10 打印基于我认为4 x 4 x 10
unit cells and actually it turned out so 单元格，实际上它是如此
with this robust manufacturing 有了这个强大的制造
constraints that i spoke about earlier 我谈到了早先的制约，
we could just take the design directly 我们可以直接采取设计
out of the optimization and then send it 脱离优化，然后发送它
to the manufacturing and get actually 到制造和实际上
the expected negative possums way to 预期的负面后果方式
behavior so now you could ask the 行为，所以现在你可以问
question so what happens for finite 问题所以有限的情况会发生
strains on this structure here so this 在这个结构上的应变就是这样
would be the unit cell that i just 将是我刚刚的单元格
designed so it's isotropic for small 设计使其对小的各向同性
deformations but now if you subject is 变形，但现在如果你的主题是
too large deformation so 所以变形太大
thirty percent strain here well then 那么百分之三十的压力就在那里
what we see is initially but it is 我们看到的是最初的，但它是
isotropic but it immediately becomes an 各向同性，但它立即成为一个
isotropic so what songs r age 12 and 21 各向同性，12岁和21岁的歌曲
become different so it behaves different 变得不同，所以它表现不同
in the two directions and we also see as 在两个方向，我们也看到
the strain becomes thirty percent we 我们的压力变得百分之三十
don't have any negative persons way to 没有任何负面的人的方式
affect any more it's up to zero puzzles 再次影响到零谜题
Rachel so this is not what we intended 瑞秋，所以这不是我们的意图
at least if we want to unless the 至少如果我们想，除非
structure undergo large deformations so 结构经历大的变形
we extended the idea to include 我们将这个想法扩展到了包含
geometrical non-linearity so first we 几何非线性首先我们
drop the isotropic constraints so this 降低各向同性约束
would be the microstructure obtained for 将获得的微观结构
the linear case you see still it goes 你看到的线性情况仍然存在
towards zero crossings ratio for large 向零个交叉比率为大
deformations but now with a non linear 变形但现在具有非线性
deformation theory we get this structure 变形理论我们得到这个结构
here that is sort of more intricate but 这里有点复杂，但是
you see it has a nice constant Poisson 你会发现它有一个不错的恒泊松
ratio of minus point eight over a very 减去八分之一的比例
large deformation span so essentially 大变形范围如此基本
using this method we can design any kind 使用这种方法我们可以设计任何种类
of material properties in using for our 的材料特性用于我们的
finite deformations and essentially what 有限变形，基本上是什么
we do is to obtain this is that we 我们所做的就是获得这是我们
specify a number of points on this 在此指定一些点数
deformation curve and then we optimize 变形曲线再进行优化
the difference between the realized 实现的区别
deformations and what we wanted so my 变形和我们想要的东西，所以我的
stew one of my students is in a tower to 炖我的一个学生是在一座塔楼里
visiting Jennifer Lewis's lab and so he 拜访珍妮弗刘易斯的实验室，所以他
is using her 3-d or 3-d printing 正在使用她的三维或三维打印
possibilities to actually build these 实际建立这些的可能性
materials and so far we have just 材料和迄今为止我们刚刚
manufactured them but we are going to 制造他们，但我们会去的
measure them all soon and we can make a 尽快测量他们，我们可以做一个
series of materials with constant large 系列材料恒定大
deformation for some great use for 4 变形为一些伟大的使用4
minus point eight point six point four 减点八点六点四
and up two plus point four so we hope to 和两个加四点，所以我们希望
publish that soon another interesting 尽快发布另一个有趣的
problem no sorry we also do it in three 问题没有抱歉，我们也在三个
dimensions and you see this is linearly 尺寸，你看到这是线性的
optimized that sort of locks at some 优化了某种类型的锁
point and the negative the optimized or 点和负面的优化或
sorry that large deformation theory 对不起，大变形理论
optimized one remains negative over a 优化的仍然是负面的
large fan here so this was one kind of 这里的大粉丝，这是一种
extreme material property the other one 极端物质财产的另一个
is designing materials when negative 负面时正在设计材料
thermally expand 热膨胀
in coefficient and so in this case you 在这个例子中你是系数
have you need three material phases and 你需要三个物质阶段吗？
so we have one blue material face that 所以我们有一个蓝色的材质脸
has a certain stiffness and the low 具有一定的刚度和低
thermal expansion but still positive and 热膨胀但仍然是积极的
we have another material phase that has 我们有另一个物质阶段
the same stiffness but a higher positive 相同的硬度，但更高的积极性
thermal expansion coefficient and so we 热膨胀系数等等
now have to design variables per element 现在必须为每个元素设计变量
so 1 a 1 design variable still 所以1个1设计变量仍然存在
determines the density of material and 决定材料的密度和
the second design variable determines 第二个设计变量确定
the type of materials or whether it's 材料的类型或是否是
the blue or the right material and so 蓝色或正确的材料等等
otherwise omit optimization runs in the 否则在运行中省略优化
similar fashion and you will see here 类似的时尚，你会看到这里
this is the outcome of it and I'm going 这是它的结果，我要走了
to to animate it in a second so right 让它在第二个如此正确的动画
now it's cooled off so you see it 现在它已经冷却，所以你看到它
protrudes outside of the design domain 突出于设计领域之外
but when I turn on the animation it will 但是当我打开它的动画
heat up and even though both the blue 升温，即使这两个蓝色
and the red face is expand well then 那么红脸就很好地展开了
effectively contracts and so you see 有效契约，所以你看到
that here it contracts by heating and 在这里它通过加热收缩
when you cool it off it expands so it 当你冷静下来时，它就会展开
has this negative so much expansion 有这么多的负面扩张
behavior and again this is something 行为，这又是一回事
it's quite late or early work by myself 这是相当晚或自己早期的工作
at it as a postdoc in Princeton but we 作为普林斯顿的博士后， 但我们
are taking this up again because now we 我们现在正在重新考虑这一点
also have the beta manufacturing 也有beta制造
technologies however we also back then 不过我们当时也有技术
try to compare this with theoretical 尝试将其与理论进行比较
bounds and so people are always worried 人们总是担心
when the dual optimization including 当双优化包括
myself do we actually reach the optimum 我自己是否真的达到最佳状态？
or are we far away from the optimum and 还是我们远离最佳状态？
so we compared to the theoretical bounds 所以我们比较理论界限
this shows the thermal expansion 这显示了热膨胀
coefficient this function of the bulk 系数这个函数的批量
modulus and we see the smaller the 模量和我们看到的越小
stiffness that larger the range of the 刚度更大的范围
thermal expansion coefficient we can get 热膨胀系数我们可以得到
and so we optimized one case minimizing 所以我们优化了一个案例最小化
for certain bulk modulus one case 对于一定的体积模量一种情况
maximizing the bulk modulus 40 thermal 最大化体积弹性模量
expansion and here maximizing the 扩张和这里最大化
thermal stress and it looked awful right 热压力，它看起来很糟糕的权利
so people teased me and said oh yeah 所以人们嘲笑我说，哦，是的
nice pictures but bad free songs right 好的照片，但不好的免费歌曲的权利
but it turned out so there were some 但事实证明，有一些
clever people at Princeton at that point 在那时普林斯顿聪明的人们
they knew well these shapur erosion 他们很清楚这些沙普的侵蚀
oisin bounds were based on old theory we oisin界限是基于我们的旧理论
have new theory called the translation 有新的理论称为翻译
method for deriving bounds so they 方法来派生界限，所以他们
improved on these bounds and then they 改善了这些界限，然后他们
managed to match the theoretical pounds 设法匹配理论磅数
almost to the numerical results so that 几乎到了数值结果
sort of shows that we can never 有种表明我们永远不会
guarantee global Optima but we can 保证全球Optima，但我们可以
certainly say that we are close to it 当然可以说我们已经接近它了
that's what I usually say okay so this 这就是我通常说的那么好
was Judy and then lately my student the 是朱迪然后最近我的学生
Eric andreasen has been doing this in 3d Ericandreasen一直在用3D做这件事
I don't know if you can see the 我不知道你能否看到
animation here but it becomes pretty 动画在这里，但它变得漂亮
fancy it's like sort of a flower pebble 想象它就像一颗花卵石
that opens when the Sun comes up and 当太阳升起时它会打开
closes again at night and so this is 在晚上再次关闭，所以这是
sort of the same effect that you see 与你看到的效果类似
here and again this actually compares 这实际上是一次比较
favorably to the theoretical bounds yep 有利于理论界限是的
so now I have a few minutes till two to 所以现在我有一个几分钟，直到两
small examples I will go through them 小例子我会通过他们
fast so one is a wave areas are both 快，所以一个是波浪区都是
civil engineering oriented so actually I 实际上我的土木工程导向
did experimental work this night so my 今晚做了实验性的工作，所以我的
hotel is close to the railway and I felt 酒店靠近铁路，我感觉
every time there was a train then 每次有火车的时候
everything was jumping so I'm very 一切都在跳跃，所以我非常
motivated to continue this project I 有动力继续这个项目我
should say so anyway when you have 无论如何你应该这样说
trains going past buildings you have 火车通过你有的建筑物
earth-based vibration transmission and 地基振动传播和
you could either improve the railway 你可以改善铁路
tracks but that's expensive or you could 轨道，但这是昂贵的，或者你可以
improve your house so you could just 改善你的房子，所以你可以
assigned Amber's in the house but people 指派琥珀在房子里但人
are not willing to do that but what you 不愿意这样做，但你是什么
could do was to put in some kind of 可以做的就是投入某种形式
passive device between the source and 源与之间的无源器件
the house in order to redirect the waves 房子为了重新引导波浪
or dampen the waves and so this project 或抑制波浪等等这个项目
is some early work on that and I will 是一些早期的工作，我会的
just go quickly through it essentially 本质上就是快速通过它
we can distribute now soil and some 我们现在可以分发土壤和一些
concrete material and we have a design 混凝土材料和我们有一个设计
domain that extends eight meters into 延伸八米的域
the ground so you could imagine you 地面，所以你可以想象你
could make some kind of sound wall in 可以制造某种音墙
the ground and just to show you examples 地面，只是为了展示你的例子
of that this would be a reference design 这将是一个参考设计
where you just will have a wall of 你只需要一堵墙
concrete in the ground and you get an 在地下混凝土，你会得到一个
insertion loss so essentially the 插入损耗基本上是这样的
damping of something like 40 be over 像40的东西的阻尼将会结束
wide frequency range 宽频率范围
if we do the topology optimization we 如果我们做拓扑优化我们
can improve that so we can have a much 可以改善， 所以我们可以有很多
higher a larger insertion does but 更大的插入但是
however only for one frequency but you 但是，只有一个频率，但你
see the mechanism here so this this 看到这里的机制，所以这个
would be the reference design here you 将成为您的参考设计
see the simple wall that sort of steps 看到简单的墙壁那种步骤
but wave still propagate here but with 但波仍然在这里蔓延，但与
this topology optimized design you see 您看到的这种拓扑优化设计
sort of you redirect the waves into the 有点你重新引导波浪进入
ground here and you can do is the same 地面在这里，你可以做的是一样的
thing for for multiple frequencies and 适用于多个频率和
so their use you get a more complicated 所以他们的使用你会变得更加复杂
structure and you see you can actually 结构，你看到你实际上可以
damp it up to 70 b or something like 将其潮湿至70b或类似的东西
that oh sorry and this would be the 哦，对不起，这将是
insertion does and you see heather has 插入，你看到石南了
actually damp it damped the vibrations 实际上它阻止了振动
very much at the house so of course this 当然这很重要
will be difficult to build but we are 将很难建立，但我们是
currently looking into how to do the 目前正在研究如何去做
trade off between the price of doing it 在做它的价格之间折衷
and the damping efficiency of this the 并在此阻尼效率
very last example also just to point 最后一个例子也只是为了指出
where we are going at and now I'm 我们现在在哪里，现在我在哪里
getting into unsafe Browns so we are 进入不安全的布朗队，所以我们是
collaborating with people in the 与人合作
structural engineering lab to do a 结构工程实验室做一个
structural fire safety and so of course 结构防火安全等等当然
buildings fires every now and then and 建筑物时不时发生火灾
some of them are very catastrophic and 其中一些是非常灾难性的
this has to be taking into the building 这必须进入建筑物
codes as I understand that these days 代码，据我了解，这些天
what usually is done is that you do the 通常做的是你做的
structural design and then afterwards 结构设计，然后再进行
you do the fire protection and so if you 你做消防，所以如果你
optimize the structural design both 优化结构设计
visually and mechanically well then you 视觉和机械方面，然后你
might lose a lot of this when you're 可能会在你失去很多时候
afterwards do this fire protection and 之后做这个防火和
the structure might be much heavier and 结构可能会更重，而且
stuff like that so you want to combine 像这样的东西， 所以你想结合
these two and do a combined structural 这两个并且做一个联合结构
and fire protection topology 和防火拓扑结构
optimization and so the very initial 优化等等非常初步
work we have on that and now don't kill 我们在这方面做的工作，现在不杀人
me for that because it's it is indeed 我为此，因为它的确是
very simple but I will just show you 很简单， 但我会告诉你
some of the ideas here so for those of 这里的一些想法对于那些
you who know fire stuff you know that 你知道那些知道火的东西
there's an incipient face a growth phase 有一个初期面临增长阶段
a full burning after flashing were and 闪光后的完全燃烧是和
then IDK stage and we are just assuming 那么IDK阶段，我们只是假设
that we have a full fire here that all 我们在这里全面开火
the temperature in the room or in the 房间里或房间里的温度
structure is the same everywhere 结构到处都是一样的
second we assume a very simplified 其次我们假设一个非常简化的
degradation model so we say we have a 退化模型，所以我们说我们有一个
Young's modulus up to a certain 杨氏模量达到一定值
temperature and then it's a suddenly 温度，然后是突然的
loses stiffness so that's valid from 失去刚度，这是有效的
steel structures and other materials I 钢结构和其他材料我
guess and the idea is now so we have 猜测和现在的想法是如此我们有
this structure that is engulfed in fire 这种结构被吞没在火中
and we say now we want to maximize the 我们现在说，我们想要最大化
stiffness for this structure at the 刚度为这种结构在
service load so without the structure 没有结构的服务负载
without the fire and then after a 没有了火，然后在之后
certain time of fire exposure and in 一定时间的火灾暴露和中
this year the color scaling here means 今年这里的颜色缩放意味着
that gray region means the data 该灰色区域表示数据
structure that was above the limit here 结构超过了这里的限制
so it lost its stiffness and so just to 所以它失去了刚度，所以就这么做了
show you some very initial designs just 只是向你展示一些非常初始的设计
show you this year so this would be the 告诉你今年这样，这将是
mbb beam we saw before so if we don't 我们以前看过的mbb光束，如果我们不这样做的话
have any fire on the structure we would 我们会对结构产生任何影响
get this quite detailed structure with 得到这个相当详细的结构
the civil struts here but as we increase 这里的民间支柱，但随着我们的增加
the requirement to having stiffness 要求具有刚度
after a certain time of the fire we get 我们得到了一段时间的火之后
less and less structural detail meaning 越来越少的结构细节含义
that no smaller parts will disappear and 没有更小的部分将消失，
so I will just show it with the 所以我只会用它来展示它
animation here so this is a non 动画在这里，所以这是一个非
fireproofed structure and this is a 防火结构，这是一个
fireproof structure and you would see 防火结构，你会看到
something like this so the upper one 像这样的东西就是上面那个
here is losing its diff pneus and 这里正在失去它的差异pneus和
collapsing whereas this one is still 崩溃，而这个仍然是
standing here so I wonder going to 站在这里，所以我想知道
apologize for if there are any fire 对是否有火灾表示歉意
safety experts in the room this is 这是房间里的安全专家
extremely simple but it's our sort of 非常简单，但它是我们的排序
first initial studies into this domain 第一次初步研究到这个领域
here so this was also the Michelle 这里所以这也是米歇尔
structures with sub fire safety it 与子消防安全它的结构
doesn't look as beautiful as the 看起来不像美丽
original one year but that's another 原来的一年，但那是另一回事
story so this concludes my talk I think 故事总结了我的想法
you have seen that you can apply to 你已经看到你可以申请
polity optimization to lots of different 政体优化到很多不同的地方
areas we are at the verge of being able 我们正处于能够接近的领域
to skip post-processing because we have 跳过后处理，因为我们有
this manufacturing insensitive designs 这种制造不敏感的设计
we have lots of interesting challenges 我们有很多有趣的挑战
I've shown you and you certainly see 我向你展示了你，你一定会看到
that there's lots of work to do in the 这有很多工作在做
civil engineering examples here and also 这里也有土木工程的例子
many other areas and so 许多其他领域等等
with that I would just invite you again 我会再次邀请你
we have the top of web page where you 我们拥有您网页的顶部
can try our apps and the games and we 可以尝试我们的应用程序和游戏和我们
have some some of our recent papers here 这里有一些我们最近的论文
that could be to your reference so thank 这可能是你的参考，所以谢谢
you very much for your attention and I'm 你非常关注你，我是
happy to answer questions you would like 很高兴回答你想要的问题
to thank professor Sigmund for such an 感谢西格蒙教授这样的一个
informative presentation and also for 内容丰富的介绍和也
sharing is vision with us we appreciate 分享是我们欣赏的愿景
that very much we have a few minutes for 我们非常有几分钟的时间
questions however pay attention that the 但是问题要注意了
lecture is being videotaped if you want 讲座正在录像如果你想
to ask questions then you should use one 提出问题，那么你应该使用一个
of the microphones in the middle of the 在的中间麦克风
room so that your question will be 房间，这样你的问题就会发生
captured we have time for questions now 抓获我们现在有时间回答问题
thank you for your presentation at the 谢谢你在你的演讲
beginning you mentioned the example on 从你提到的例子开始
Qatar and the column was going to be 卡塔尔和专栏将是
concrete but then they change the Sun 然后他们改变太阳
and it was an empty element I wasn't 这是一个空洞的因素，我不是
clear about what happened that you say 清楚你说的事情
you can explain at the end that it was 你可以在最后解释它是
whenever hollow column and the other 每当空心柱和其他
question is if you are doing reinforced 问题在于你是否在加强
concrete for this and if you can combine 具体为此，如果你可以结合
two different materials in your 你的两种不同的材料
optimization and where's the future for 优化和未来在哪里
for that to material thing thank you ok 为实现这一目标物质的东西谢谢OK
i was a bit fast with the guitar example 我用吉他的例子有点快
so i guess the main thing was that the 所以我猜主要的是那个
architect used a simple topology 架构师使用简单的拓扑结构
optimization code that just assumed an 优化代码，只是假设一个
isotropic material and so he generated 他产生了各向同性的材料
these legs here which were assuming that 这些假设的腿在这里
they were solid and so he didn't really 他们是坚实的，所以他不是真的
think about concrete or anything like 想想混凝土或类似的东西
that and then realizing that this would 然后意识到这会
be way too heavy no matter what material 无论使用什么材料，都会太重
he did then he said well let's just use 他这样做，他说，让我们只是使用
this shape and make a shell structure 这个形状和做一个壳结构
that has this shape so that was 有这样的形状，以至于
essentially the idea the second thing 基本上这个想法是第二件事
was so this had nothing to do with 这与此无关
concrete or reinforced concrete but 混凝土或钢筋混凝土
there are people who are working with 有人正在合作
that I also have a couple of papers so 我也有这么几篇论文
where we both distribute to concrete 我们都分配到混凝土
itself and the 本身和
the reinforcements and so you get 增援，所以你得到
optimized designs like that and of 像这样的优化设计和
course you have the nonlinear material 当然你有非线性材料
layer where the concrete can't take 混凝土不能采取的层
tension but only compression so that's 紧张，但只有压缩，这样的
possible actually this Rhino plug-in 实际上可能是这个Rhino 插件
thing the top of software there has a 那里的软件的顶部有一个
material model that differs between 材料模型之间的差异
compression and tension and so there was 有压缩和紧张等等
a red and blue color I don't know it was 红色和蓝色我不知道它是
faster but that's actually denoting in 更快，但实际上表示在
case where it takes properties of 它需要属性的情况
concrete into account in the design 在设计中考虑具体
process yeah thank you for your 过程是啊谢谢你的
presentation my question is about 介绍我的问题是关于
redundancy it's quite appealing to have 冗余是非常有吸引力的
an optimal structure but you also 一个最佳的结构，但你也
incorporate the fact that sometimes 纳入有时候的事实
redone that redundancies are also you 重做冗员也是你
know appealing to having the in the 知道有吸引力的人
system well you could say that that 系统，你可以这么说
right now with a robust approach they 现在他们采用了一套强大的方法
are you sort of get tend to get bigger 你是否会变得越来越大？
structures that are insensitive to to 对不敏感的结构
they wouldn't die on the way so there's 他们不会死在路上，所以有
no need for for redundancy we have some 没有必要为冗余我们有一些
other cases with the fire protection 其他情况下的防火
where we instead of having the fire 我们在哪里而不是在发生火灾
everywhere we just had a localized fire 到处都是我们本地化的火灾
and there we certainly saw that there 那里我们当然看到了那里
were designs coming up that had 设计即将到来了
redundancy because it could tolerate 冗余，因为它可以容忍
that one bar one column would disappear 一栏一栏就会消失
but then reinforcing the other ones that 但随后加强其他那些
were further away from the fire so so 离火很远
depending on how you formulate you up to 这取决于你如何制定你到
my solution captain's you do see you 我的解决方案队长，你看到你
redundancy or you don't see it very nice 冗余或你看不到它很好
talk my question is more towards the 说我的问题更多的是朝向
framework that you're using you have a 你使用的框架有一个
nonlinear iterative procedure for the 非线性迭代程序
optimization and that is coupled with a 优化，这是与一个
filter process and you're using a PDE 过滤器过程，并且您正在使用PDE
based filter and as I understand your 根据我的理解你的
filter is a diffusion reaction type 过滤器是一种扩散反应型
equation you have a second order term 方程中有一个二阶项
there in a zeroth order term there so 那里有一个零阶的术语
it's a linear filter yeah so are you 这是一个线性过滤器耶，你也是
using filter at the end of every 在每个结尾使用过滤器
nonlinear iteration and what is the 非线性迭代和什么是
implication of using a linear filter in 在线使用线性滤波器的含义
an otherwise nonlinear iterative process 否则非线性迭代过程
the filter is only to determine the 过滤器只是确定的
material properties so you could say if 材料属性，所以你可以说如果
your material properties change on the 你的材料属性会改变
way you would have to do the filtering 你将不得不做的过滤
also so if you had some non local 所以如果你有一些非本地的话
material law you would have to do that 物质法你必须这样做
but for now we are just assuming that 但现在我们只是假设这一点
it's that the Youngs modulus is given 这是杨氏模量给出
from the filter up front so you do the 从前面的过滤器，所以你做的
filtering and then you do that analysis 过滤然后你做那个分析
and then you do without my say-so the 然后你没有我的话就这么做了
filter will change the value will change 过滤器会改变值会改变
the value of Young's modulus yeah from 杨氏模量是从的值
step to step but considering that is a 一步一步，但考虑到这是一个
linear filter what is the relation 线性过滤器是什么关系
between the filtered value from step n 来自步骤n的过滤值之间
to n plus 1 or how is in a nonlinear n加1或非线性如何
process can we just change the value on 过程只能改变价值
the spot without recourse to its 现场无追索权
previous values yeah because it's an 以前的价值是因为它是一个
optimization well as long as you don't 只要你不这样做，优化就会很好
have some history dependent material 有一些历史依赖材料
door then it's fine because it's an 那么门是好的，因为它是一个
optimization that determines what the 优化决定了什么
material properties are so so it doesn't 材料属性是如此，所以没有
need to have any connection to what was 需要与之前有任何联系
happening before but your butt yeah even 发生之前，但你的屁股是的，甚至
though you don't need that because even 尽管你不需要，因为即使
if you have a history dependent material 如果你有一个历史依赖材料
or you have you a material distribution 或者你有一个物质分配
from the onset before you start the 从你开始之前的发病开始
nonlinear procedure and that will would 非线性程序，那会
then develop according to the material 然后根据材料开发
or so so no you wouldn't have to include 左右，所以没有你不必包括在内
the filtering in the non linear modeling 非线性建模中的过滤
step I guess we need to discuss it in 我想我们需要讨论它
more detail but I just want you to get 更多的细节，但我只是想让你得到
it clarified for the students you know 它向你认识的学生澄清
we can talk about it later also but if 我们以后也可以谈论它，但如果
the material evolves material evolution 材料演变材料演变
by itself is a nonlinear process let's 本身就是一个非线性过程
say let's not talk about the geometric 说我们不要谈论几何
part if we look at the material part and 的一部分，如果我们看一下材料部和
the way to solve an non-linear evolution 解决非线性演变的方法
problem for the material we need to use 我们需要使用的材料的问题
with what we do is consistent 我们所做的是一致的
linearization yeah and we solve a 线性化是啊，我们解决了一个问题
sequence of linearized problems so they 线性化问题的顺序如此他们
are linearized problems but then they 是线性化的问题，但他们
are not linear sequence of linear 不是线性的线性序列
problems they are linearized and the 他们被线性化的问题和
word linearized means that the state at 字的线性化意味着状态在
next step is going to inherit the 下一步将继承
information that it had at step n minus 它在步骤n减去的信息
1 and n minus 2 and so on especially if 1 和n减2等特别是如果
the material is nonlinear then I think 我认为材料是非线性的
there could be some issues there no no 那里可能有一些问题没有
no so I hope I can explain it so you 不，所以我希望我能解释它，所以你
should see the optimization process is 应该看到优化过程是
just going from one design to another 从一个设计到另一个设计
design to a third design and so on and 设计到第三个设计等等
these designs there they are not related 这些设计与他们没有关系
physically they are just new a new 身体上他们只是一个新的
generation or a new structure right so 一代或一个新的结构是如此
it means that the new structure coming 这意味着新的结构即将到来
out of the optimization process has no 退出优化过程没有
physical relation to the previous 与之前的物理关系
iteration also in that way if i was 如果我是这样，迭代也是这样
using some kind of evolution law to 使用某种进化规律来进行
develop if it was some mechanical or 发展，如果它是一些机械或
some face change thing there a society I 有些人面对改变这个社会的事情
end on the old one but here it's just a 结束旧的，但这里只是一个
new design and you start start your 新的设计， 你开始开始你的
modeling all over so they're not 一切都建模，所以他们不是
connected and okay so there is no 连接好，所以没有
conservation law no don't lie not 守恒定律不是不说谎
between design iterations yeah well I 在设计迭代之间耶，我很好
thank you for exceptionally clear and 非常感谢你的明确和
impressive presentation one of the 令人印象深刻的介绍之一
questions I had was what are people 我的问题是人是什么
doing in terms of the dynamic response 在动态反应方面做了些什么
of structures because the airplane that 因为飞机的结构
you showed a lot of the problems we're 你展现了很多我们遇到的问题
not just static but also considering the 不仅仅是静态的，还要考虑到
dynamic response and I wonder how you 动态的反应，我不知道你是如何
could incorporate that into the analysis 可以将其纳入分析
well I would say with a with the next to 好吧， 我会与旁边的一个说
last example with the wave propagation 波浪传播的最后一个例子
so you can see we can include it so if 所以你可以看到我们可以包含它，所以如果
you know the dynamic loads on the 你知道在动态负载
airplane there you can insert them as 飞机那里你可以插入它们
boundary conditions either you can try 你可以尝试边界条件
to maximize fundamental icon frequencies 最大化基本图标频率
or if you have a time history of your 或者如果你有你的时间历史
loading then you can add that to your 加载然后你可以添加到你的
optimization problem and minimize the 优化问题并尽量减少
overall vibration energy or whatever so 整体振动能量或任何如此
as soon as you can model this behavior 只要你能模拟这种行为
and you can point a quantify what you 你可以指出一个量化你的东西
want to minimize so the maximum 想要最大限度地减少
deflections or something like that and 偏转或类似的东西
we can include it an optimization 我们可以将其包含在内优化
problems and people do that I guess most 问题和人们这样做，我猜最
of the loads that one would consider for 人们会考虑的负载
example on airplanes and other 例如在飞机和其他
structures and we're particularly 结构，我们特别
interested in earthquake and wind loads 对地震和风荷载感兴趣
here at the University of Illinois are 在伊利诺伊大学这里
stochastic in nature and so you don't 在自然界是随机的，所以你不这样做
have it 有它
mystic representation to include in has 神秘主义的代表性包括在内
anybody done work in that particular 任何人在那个特定的工作
area no but you did you know no well 地区没有，但你是否知道不好
what should I say if you could in 如果你能参加，我该怎么说
principle if you have a number of 原则上，如果你有一些
different loading situations you could 不同的加载情况，你可以
do the whole time integration part and 做整个时间的整合部分和
for the sensitivity analysis is that 对于灵敏度分析就是这样
just implies that you have to go 只是意味着你必须去
backwards in time to introduce their 及时向后介绍他们的
joints and stuff so people are doing 关节和东西，所以人们正在做
that we have done pulse propagation 我们已经完成了脉冲传播
problems and stuff like that so there's 问题和类似的东西， 所以有
nothing hindering doing it the question 没有什么阻碍做这个问题
is can you do it more efficiently so 你能更有效地做到吗？
what about just tailoring the frequency 那裁剪频率怎么样？
response or something like that so if 反应或类似的东西，如果
you will for you do a frequency sweep 你会为你做频率扫描
and you make sure that you don't have 你确定你没有
some very big vibration or empty two 一些非常大的振动或空的两个
peaks or something like that so I would 高峰或类似的东西， 所以我会
attack it in a simpler fashion just 只是以更简单的方式攻击它
looking at the frequency response rather 而是看频率响应
than doing the full time history of the 比做全职的历史
full earth weight or something like that 全土重量或类似的东西
but it's in yeah so people are doing it 但它是在，所以人们正在这样做
we and we could include it here also if 我们和我们也可以在这里包括它，如果
needed and wanted well we really 需要，我们真的很想
appreciate all the interactions and all 欣赏所有的互动和所有
the discussions and I may suggest that 讨论和我可能会建议
you don't go away you stay here and then 你不离开你留在这里然后
as soon as you finish you go to the 一旦你完成你去了
reception and then you can talk to ollie 接待，然后你可以谈谈奥利
and continue all these exciting 并继续所有这些令人兴奋的
discussions like to do two things now 讨论喜欢现在做两件事
before your two things just I summer you 在你的两件事情之前，我只是在夏天你
know i'm giving a second talk tomorrow 知道我明天再次发言
and I'm actually not fully I haven't 而我其实并不完全我没有
fully planned what I'm going to talk 完全计划了我要说的话
about so if someone you think I was too 如果有人认为我也是
fast on some of this stuff and you want 快速的这些东西， 你想要的
to get me more into detail about that or 让我更详细地了解这个或那个
you think i left out something to you 你以为我给你留下了一些东西
read that i've been written up up wished 读我已经写了希望
then feel free to come to me i will 然后随时来找我，我会的
still be jet lag tomorrow morning so i 我明天早上仍然是时差
can get up early and prepare the lecture 可以早起，准备演讲
thank you all of this was one of the two 谢谢你们所有这一切都是其中之一
ok and the this the second one is we 好的，这第二个是我们
have one more activity to do here and I 在这里和我有更多的活动
would like to pass the floor back to my 想把我的地板传回给我
colleague professor are made 同事教授做成
that was a great talk thank you very 这是一个非常棒的演讲，非常感谢你
much so we have a little gift to 所以我们有一点点礼物
Professor segment and you like to 教授部分，你喜欢
present to me right away I'm sure this 马上给我介绍我确定这一点
is like an amorphous crystal if that 就像一个非晶体晶体
make sense to you but it's it just has 对你有意义，但它只是它
the name of Professor segment and 教授的名字和
recognize the origination and for him as 承认起源和为他
a speaker of the distinguished newmarket 可分辨的新市场的扬声器
lecture for this 这个讲座