TY - RPRT

T1 - A hierarchical method for structural topology design problems with local stress and displacement constraints

AU - Stolpe, Mathias

AU - Stidsen, Thomas K.

PY - 2005

Y1 - 2005

N2 - 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 modeled 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 solves 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 neighborhood optimization method is used to solve 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.

AB - 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 modeled 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 solves 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 neighborhood optimization method is used to solve 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.

KW - topology optimization, convex mixed integer programming, local branching, neighborhood search

M3 - Report

T3 - Mat-Report

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

ER -