Solving stress constrained problems in topology and material optimization

Authors:
Michal Kočvara;Michael Stingl
Affiliations:
School of Mathematics, University of Birmingham, Birmingham, UK B15 2TT and Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Praha 8, Czech Republic 18208;Applied Mathematics II, University of Erlangen-Nuremberg, Erlangen, Germany 91052
Venue:
Structural and Multidisciplinary Optimization
Year:
2012

Citing 7
Cited 2

On stiffness maximization of variable thickness sheet with unilateral contact

Quarterly of Applied Mathematics
Free material optimization via mathematical programming

Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations

SIAM Journal on Optimization
Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

SIAM Journal on Optimization
Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications

Mathematical Programming: Series A and B
Arrival Rate Approximation by Nonnegative Cubic Splines

Operations Research
A Sequential Convex Semidefinite Programming Algorithm with an Application to Multiple-Load Free Material Optimization

SIAM Journal on Optimization

Stress constrained topology optimization

Structural and Multidisciplinary Optimization
Stress-constrained topology optimization: a topological level-set approach

Structural and Multidisciplinary Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

This article is a continuation of the paper Ko驴vara and Stingl (Struct Multidisc Optim 33(4---5):323---335, 2007). The aim is to describe numerical techniques for the solution of topology and material optimization problems with local stress constraints. In particular, we consider the topology optimization (variable thickness sheet or "free sizing") and the free material optimization problems. We will present an efficient algorithm for solving large scale instances of these problems. Examples will demonstrate the efficiency of the algorithm and the importance of the local stress constraints. In particular, we will argue that in certain topology optimization problems, the addition of stress constraints must necessarily lead not only to the change of optimal topology but also optimal geometry. Contrary to that, in material optimization problems the stress singularity is treated by the change in the optimal material properties.