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
On Topology Optimization with Elliptical Masks and Honeycomb Tessellation with Explicit Length Scale Constraints
TL;DR: In this paper, a sequence for length scale (SLS) methodology is proposed wherein solutions are sought by specifying only the minimum and maximum length scales with volume fraction getting determined systematically, and it is demonstrated that solutions by-and-large satisfy the length scale constraints though the latter may get violated at certain local sites.
Journal ArticleDOI
Exploiting Lagrange duality for topology optimization with frictionless unilateral contact
TL;DR: In this paper, a tractable reformulation of topology optimization problems of structures subject to frictionless unilateral contact conditions is presented, where stiffness maximization problems of trusses and continua are considered.
Multigrid Implementation of Cellular Automata for Topology Optimisation of Continuum Structures with Design Dependent loads
TL;DR: The multigrid accelerated CA algorithm is demonstrated to be a powerful tool for solving topology optimisation problems compared to other algorithms based on finite element analysis.
Proceedings ArticleDOI
Topology optimization designing and performance testing of micro-clamp using meshless method
Yixian Du,Junjian Fu,Wei Wang +2 more
TL;DR: In this paper, a nonlinear optimization method for designing micro-clamps is presented by combining the theory of element-free Galerkin method (EFGM) and topology optimization.
Journal ArticleDOI
Fast and accurate nonlinear hyper-elastic deformation with a posteriori numerical verification of the convergence of solution: Application to the simulation of liver deformation.
Farah Saidi,Abed Malti +1 more
TL;DR: In this article, the authors proposed a new method to reduce the computational complexity of calculating the tangential stiffness matrix in a nonlinear finite element formulation by partially updating the stiffness matrix during a classic Newton-Raphson iterative process.
References
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Book
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.
Journal ArticleDOI
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.