A hierarchical method for discrete structural topology design problems with local stress and displacement constraints

• Published in: International journal for numerical methods in engineering Vol. 69; no. 5; pp. 1060 - 1084
• Main Authors: Stolpe, Mathias, Stidsen, Thomas
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 29.01.2007; Wiley
• Subjects: Computational techniques; convex mixed integer programming; Displacement; Exact sciences and technology; Fundamental areas of phenomenology (including applications); local branching; Mathematical methods in physics; Mathematical models; neighbourhood search; Numerical analysis; Optimization; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Stresses; Structural and continuum mechanics; Topology; topology optimization; Branching; Geometrical shape; Refinement method; local branching; Optimization method; Global optimum; Topology; Automatic mesh generation; Modeling; Adaptive method; Convex programming; Weight; Finite element method; Local structure; neighbourhood search; convex mixed integer programming; topology optimization; Mesh generation; Non convex analysis; Structural analysis
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1800

In this paper, we present a hierarchical optimization method for finding feasible true 0–1 solutions to finite‐element‐based topology design problems. The topology design problems are initially modelled as non‐convex mixed 0–1 programs. The hierarchical optimization method is applied to the problem of minimizing the weight of a structure subject to displacement and local design‐dependent stress constraints. The method iteratively treats a sequence of problems of increasing size of the same type as the original problem. The problems are defined on a design mesh which is initially coarse and then successively refined as needed. At each level of design mesh refinement, a neighbourhood optimization method is used to treat the problem considered. The non‐convex topology design problems are equivalently reformulated as convex all‐quadratic mixed 0–1 programs. This reformulation enables the use of methods from global optimization, which have only recently become available, for solving the problems in the sequence. Numerical examples of topology design problems of continuum structures with local stress and displacement constraints are presented. Copyright © 2006 John Wiley & Sons, Ltd.