Topology Optimization Guide

This article is related to a rather weird optimization technique (link). To be honest I did not know much about axiomatic design approach before reading it. And I did not like what I have seen. I will not write about what I think of axiomatic design, that is far out of my scope, and I want to be respectful. Instead we can talk about the results mentioned in the article.

The optimization is done for an automobile front subframe. The axiomatic design approach is used. It works like sizing optimization, but in a different way. There is a original subframe, and the stresses on it (at functional requirement points) are going to be reduced, while being subject to some constraints. However the boundary conditions are not appropriate for an effective FEA, defining fixed boundaries for places that are obviously nearly as elastic as the structure itself. Then stresses at critical points are measured, and are going to be reduced. After the optimization is done, the highest stress (1.13 times yield strength σy) and two lower stress points (0.25 σy) are reduced. Two other functional requirement points with stresses originally around 0.5 σy are increased to 0.8 σy. The weight is reduced by %16. There is no data about rigidity.

This study topology (or rather shape) optimization of extrusion dies were examined (link). Two aspects were optimized, reduction of dead zones and flow speed equalization. Interestingly the dead zone reduction was done by hand, in a systematic way. Flow speed equalization was carried by an evolutionary algorithm, which introduces random intrusions to the flow. The best results were optimized when they are used consecutively at each optimization step.

It is stated that extrusion die design is expert knowledge based, and optimization or simulation software are not widely used at the moment.

In this thesis (link) by Anton Olason and Daniel Tidman from CHALMERS UNIVERSITY OF TECHNOLOGY, many cases for topology optimization and shape optimization were studied, which can be a nice guide for people that want to be involved with practical structural optimization. At the end a systematic methodology is stated, which can be very useful. I did not have the time to read the work completely, so that’s all for now.

Researchers from Magna Steyr (link) investigated optimization of weld spots with respect to stiffness and fatigue. CHEXA elements were used in some runs to represent spot welds, and in some cases node to node beams were used. A cantilever was optimized and both fatigue and stiffness optimized weld distribution showed an even distribution of fatigue damage. No big difference in stiffness was observed, as the sheet metal provides almost all the stiffness in this loading mode. Another optimization was carried with a car body in white model (apparently Audi A3). All the weld spots were optimized. The design space is a rather interesting cloud of spot welds, as visualized in one of the pictures.

MKP Structural Design Associates,University of Michigan  and US Army Tank-Automotive and Armaments are developing and armor using topology optimization (link). The Function-Oriented Material Design (FOMD) methodology is used. The structure is composed of many layers, essentially a ceramic core with composite back and front plates. The back-plate is designed in this article, interpreting topology optimization results in an interesting way and making a structure with Kevlar panels sandwiching stuffers and Kevlar “tendons”. The whole structure is simulated, and found to be successful, also the back-plate is tested with actual bullets and found to be successful too. The contribution of topology optimization to its success is not clear though.

This study investigates topology optimization using Hybrid Cellular Automata (link) for blast mitigation. A metal-ceramic composite armor structure is developed, that reduces accelerations felt by the occupant. It is reported that the optimization did not converge, however still the results were satisfactory.

Felix Candela’s (link) LOMAS DE CUERNAVACA chapel is elaborated in this article. Structural efficiency of the structure is stated, and  thickness and shape optimizations were conducted. The structure is very beautiful and beyond its time. (The link was broken, now fixed)

Today I tried to integrate a Amazon aStore, there are various descriptions, all involve editing templates .ccs files etc. They suggest backing up the files. So it is a rather complex thing. But suddenly I discovered how to do it very easily, by accident. It works for me. You can see it here.

First you prepare the aStore, which is easy and lots of information can be found about it.

When you come to the step “Get Store Link” choose “Embed my store using an inline frame”

You will get a code like :
<iframe src=”http://astore.amazon.com/topologyopt-20″ width=”90%” height=”4000″ frameborder=”0″ scrolling=”no”></iframe>

Now open a new page in your WordPress, and call it Store, or what you want. Select HTML which is next to visual, and paste the code here.

Now change the width from %90 to %130. I also made height 1000 but it is not necessary. Click Publish.

Now go to pages section and click “quick edit” for your store page. In the template menu choose “One column, no sidebar” and update. Your store should be ready now.

I have the very basic theme of WordPress in this site, and it has the “One column, no sidebar” choice, other themes may not have it.