Journal ArticleDOI
Achieving minimum length scale in topology optimization using nodal design variables and projection functions
TLDR
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.Abstract:
A methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described. Nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology. The projection is made via mesh independent functions that are based upon the minimum length scale. A simple linear projection scheme and a non-linear scheme using a regularized Heaviside step function to achieve nearly 0–1 solutions are examined. The new approach is demonstrated on the minimum compliance problem and the popular SIMP method is used to penalize the stiffness of intermediate volume fraction elements. Solutions are shown to meet user-defined length scale criterion without additional constraints, penalty functions or sensitivity filters. No instances of mesh dependence or checkerboard patterns have been observed. Copyright © 2004 John Wiley & Sons, Ltd.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
A survey of structural and multidisciplinary continuum topology optimization: post 2000
TL;DR: Topology optimization is the process of determining the optimal layout of material and connectivity inside a design domain this paper, which is the same as the problem of finding the optimal configuration of a set of components.
Journal ArticleDOI
On projection methods, convergence and robust formulations in topology optimization
TL;DR: It is shown that simple projection methods do not ensure localMesh convergence and a modified robust topology optimization formulation based on erosion, intermediate and dilation projections is proposed that ensures both global and local mesh-convergence.
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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.
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
A 99 line topology optimization code written in Matlab
TL;DR: 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.
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.