Journal ArticleDOI
Topology optimization of non-linear elastic structures and compliant mechanisms
T.E. Bruns,Daniel A. Tortorelli +1 more
TLDR
In this paper, the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities to resolve the non-existent solution to the solid void topology problem.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2001-03-16. It has received 1125 citations till now. The article focuses on the topics: Topology optimization & Optimization problem.read more
Citations
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Journal ArticleDOI
Parametric studies and manufacturability experiments on smooth self-supporting topologies
TL;DR: In this paper, the effects of optimisation parameters (the filter radius, mesh size, and target volume fraction) on the compliance and manufacturability of smooth self-supportin...
Journal ArticleDOI
Game theory approach to robust topology optimization with uncertain loading
Abstract: The paper concerns robustness with respect to uncertain loading in topology optimization problems. Using a game theoretic framework we formulate problems, or games, defining generalized Nash equilibria. In each game a set of topology design variables aim to find an optimal topology, while a set of load variables aim to find the worst possible load. Several numerical examples with uncertain loading are solved in 2D and 3D. The games are formulated using global stress, mass and compliance as objective functions or constraints.
Journal ArticleDOI
Explicit level set and density methods for topology optimization with equivalent minimum length scale constraints
TL;DR: A minimum length scale is imposed by adopting geometric constraints that have been recently proposed for density-based topology optimization with projections filters that provide a computationally inexpensive solution for the instabilities which often appear in level set XFEM topological optimization.
Journal ArticleDOI
On the solution of the checkerboard problem in mixed-FEM topology optimization
TL;DR: In this paper, an alternative formulation for the classical topology optimization problem of getting structures with minimum compliance with constraint on volume, relying on the adoption of a mixed finite element discretization scheme instead of a common displacement-based one using mixed methods not only displacements are main variables but also stresses enter the formulation.
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Achieving stress-constrained topological design via length scale control
TL;DR: Stress-constrained topology optimization is posed as a minimum compliance problem with additional treatment of the length scale with high-quality trade-offs between compliance, stress and volume.
References
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The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
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.
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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.