Currently, I am working on a problem in which I need to use MILP to model equilibrium equations in a lightweight structure. Although this is an application based question, I wondered if there is a good reference in the literature discussing the mathematical modeling of such an application based on statical concepts.

A brief discussion of structural optimization is given in chapter 15 of Linear Programming: Foundations and Extensions, by Robert J. Vanderbei.

Structural optimization is the general name that researchers use for a wide range of research topics in the literature, i.e., Shape optimization, Size optimization and also Topology optimization.

  • $\begingroup$ "use MILP to model equilibrium equations" Are those complementarity conditions? $\endgroup$ Jul 15, 2019 at 17:52
  • $\begingroup$ Actually, there are two different approaches to model this kind of problems. I use the plastic form in which the forces in each joint should be in equilibrium and also the moments if the joints are welded. Those conditions are not complementarity conditions. $\endgroup$ Jul 15, 2019 at 17:58
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    $\begingroup$ Given the emphasis on engineering modeling, you might have better luck at scicomp.stackexchange.com which also has a lot of optimization stuff. $\endgroup$ Jul 15, 2019 at 18:00
  • $\begingroup$ @MarkL.Stone Thanks for the great suggestion, I haven’t asked my question there yet but I believe I will find good answers for my structural questions there. As you mentioned there are lots of questions covering both optimization and mechanical concepts. $\endgroup$ Jul 16, 2019 at 3:57

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You should have a look at the work of Mathias Stolpe. He has done a lot of modelling for structural optimization problems with integer constraints. See for example his PhD thesis. As you already written, the topic comes from a more continuous direction. See the nice book by Martin Bendsoe and Ole Sigmund for a really good overview. You can also have a look at the website of this chair.

If you provide more information on your problem I can adjust my answer to guide you to more relevant papers.


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