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
Approximate Reanalysis in Topology Optimization
TL;DR: In this paper, the authors apply the so-called nested approach where optimization is performed in the design variables only and where the equilibrium equations are treated as function calls, which can substantially reduce the number of required factorizations of the stiffness matrix, and thus removing a significant portion of the computational effort.
Journal ArticleDOI
Topology optimization of hyperelastic bodies including non-zero prescribed displacements
TL;DR: In this paper, the authors consider topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements and show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimisation based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used.
Journal ArticleDOI
Topology optimization design of crushed 2D-frames for desired energy absorption history
TL;DR: In this article, a quasi-static nonlinear finite element solution is obtained with an implicit backward Euler algorithm, and the analytical sensitivities are computed by the direct differentiation method.
Design of Nonlinear Springs for Prescribed Load-Displacement
TL;DR: A generalized nonlinear spring synthesis methodology that synthesizes a spring for any prescribed nonlinear load-displacement function and generates designs having distributed compliance, and introduces a design parametrization that is conducive to geometric nonlinearities.
Journal ArticleDOI
Concurrent aerostructural topology optimization of a wing box
TL;DR: In this paper, a multidisciplinary framework for performing shape and topology optimization of a flexible wing structure is presented, where both the aerodynamic shape and the structural topology are optimized concurrently using gradient-based optimization.
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.
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.