Journal ArticleDOI
A 99 line topology optimization code written in Matlab
TLDR
It is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem and by adding three additional lines, the program can solve problems with multiple load cases.Abstract:
The paper presents a compact Matlab implementation of a topology optimization code for compliance minimization of statically loaded structures. The total number of Matlab input lines is 99 including optimizer and Finite Element subroutine. The 99 lines are divided into 36 lines for the main program, 12 lines for the Optimality Criteria based optimizer, 16 lines for a mesh-independency filter and 35 lines for the finite element code. In fact, excluding comment lines and lines associated with output and finite element analysis, it is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem. By adding three additional lines, the program can solve problems with multiple load cases. The code is intended for educational purposes. The complete Matlab code is given in the Appendix and can be down-loaded from the web-site http://www.topopt.dtu.dk.read more
Citations
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Journal ArticleDOI
Topology optimization approaches: A comparative review
Ole Sigmund,Kurt Maute +1 more
TL;DR: An overview, comparison and critical review of the different approaches to topology optimization, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
Journal ArticleDOI
Morphology-based black and white filters for topology optimization
TL;DR: In this article, the physical stiffness of an element is based on a function of the design variables of the neighboring elements, and a new class of morphology-based restriction schemes that work as density filters is introduced.
Journal ArticleDOI
Achieving minimum length scale in topology optimization using nodal design variables and projection functions
TL;DR: In this paper, a methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described, where nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology.
Journal ArticleDOI
Efficient topology optimization in MATLAB using 88 lines of code
TL;DR: The paper presents an efficient 88 line MATLAB code for topology optimization using the 99 line code presented by Sigmund as a starting point, and a considerable improvement in efficiency has been achieved, mainly by preallocating arrays and vectorizing loops.
Journal ArticleDOI
Topology optimization of continuum structures: A review*
Hans A. Eschenauer,Niels Olhoff +1 more
References
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Journal ArticleDOI
Generating optimal topologies in structural design using a homogenization method
Martin P. Bendsøe,Noboru Kikuchi +1 more
TL;DR: In this article, the authors present a methodology for optimal shape design based on homogenization, which is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i.i.
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The method of moving asymptotes—a new method for structural optimization
TL;DR: In this article, a new method for non-linear programming in general and structural optimization in particular is presented, in which a strictly convex approximating subproblem is generated and solved.
Journal ArticleDOI
Optimal shape design as a material distribution problem
TL;DR: In this article, various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable are described. But none of these methods can be used for shape optimization in a general setting.
Journal ArticleDOI
Material interpolation schemes in topology optimization
Martin P. Bendsøe,Ole Sigmund +1 more
TL;DR: In this article, the authors analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials, and derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design.
Journal ArticleDOI
Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima
Ole Sigmund,Joakim Petersson +1 more
TL;DR: The current knowledge about numerical instabilities such as checkerboards, mesh-dependence and local minima occurring in applications of the topology optimization method are summarized and the methods with which they can be avoided are listed.