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1. #Matlab optimization toolbox multiple design variables update
2. #Matlab optimization toolbox multiple design variables full
3. #Matlab optimization toolbox multiple design variables software

Leveraging the modular structure of the educational code, PolyTop, we extend it to the multi-material version, PolyMat, with only a few modifications.

We introduce a Matlab implementation of topology optimization for compliance minimization on unstructured polygonal finite element meshes that efficiently accommodates many materials and many volume constraints. Here, we use this code to generate examples in both two and three dimensions that illustrate the advantage of elastic meta-materials over structures with a single length scale, i.e., those without micro-architectures. The surrogate models are also simple to implement, which we demonstrate by modifying Sigmund’s 99-line code to solve a three-dimensional, multiscale compliance design problem with spatially varying relative density.

#Matlab optimization toolbox multiple design variables full

These surrogate models are relatively accurate over the full range of relative densities, in contrast to analytical models in the literature, which we show lose accuracy as relative density increases. Instead, we provide simple, accurate surrogate models of the homogenized linear elastic response of the isotruss, more » the octet truss, and the ORC truss based on high-fidelity continuum finite element analyses. Unfortunately, concurrent design of both the micro-scale and the macroscale is computationally very expensive when the former can vary spatially, particularly in three dimensions. The introduction of such architecture, which is increasingly able to be fabricated due to advances in additive manufacturing, expands the design domain and enables improved design, from the most complex multi-physics design problems to the simple compliance design problem that is our focus. We are including this updated version of the code to allow the reader to understand exactly what changes must be made to a “standard” topology optimization code to implement the surrogate models and thus multiscale design = ,Įlastic meta-materials are those whose unique properties come from their micro-architecture, rather than, e.g., from their chemistry. Sigmund’s 2001 paper describes the implementation line-by-line.

#Matlab optimization toolbox multiple design variables software

The code’s primary function is as a pedagogical tool rather than as a finished software product. We plan to include the full source code in an Appendix in this paper. The development of these surrogate models and their implementation is described in a journal article we intend to submit. What is new in this code is our implementation of simple surrogate models for several truss micro-architectures, which converts this code to a multiscale design tool, whereas the original code is single-scale.

This functionality is identical to, or the simplest possible extension from 2D to 3D of, a 99-line Matlab code released in 2001 in a journal article by Sigmund.

#Matlab optimization toolbox multiple design variables update

It uses a simple linear elastic finite element solver to solve the equilibrium equations, and the optimality criterion (00) method to update the design iteratively. This Matlab script implements a simple topology optimization algorithm that minimizes the compliance of a structure within a 3D prismatic design domain.