Large-scale smooth plastic topology optimization using domain decomposition

Abstract

A domain decomposition procedure based on overlapping partitions of the design domain is proposed for solving large problems of smooth topology optimization of plastic continua. The procedure enables the solution of problems with sizes exceeding the available computational and storage capacities. It takes advantage of the favorable features of the integrated limit analysis and design formulation of the smooth topology design problem. The integrated approach preserves the mathematical structure and properties of the underlying static, lower bound problem of limit analysis. In particular, the formulation is characterized by weak coupling between subproblems because it does not involve a stress–strain relationship. The decomposition strategy begins by solving a reduced design problem, using a coarse finite element mesh, followed by an iterative process using a fine discretization. At each iteration, an independent topology optimization subproblem is associated with each subdomain, considered as a substructure. The traction vectors acting on the subdomain boundaries are updated at each iteration as the overlapping partitions are switched. The numerical tests showed that as early as the first iteration, the decomposition process generates a feasible, near optimal design with a weight less than 0.1% above the direct solution.