On the use of Cartesian grid finite element code in structural optimization

The structural shape optimization is an iterative process built up by a higher level, which proposes the geometries to analyze, and a lower level which is in charge of analyzing, numerically, their structural response, usually by means of the Finite Element Method (FEM). These techniques normally report notorious advantages in an industrial environment, but their high computational cost is the main drawback. The efficiency of the global process requires the efficiency of both levels. This work focuses on the improvement of the efficiency of the lower level by using a methodology that uses a 2D linear elasticity code based on geometry-independent Cartesian grids, combined with FEM solution and recovery techniques, adapted to this framework. This mesh type simplifies the mesh generation and, in combination with a hierarchical data structure, reuses a great calculus amount. The recovery technique plays a double role: a) it is used in the Zienkiewicz-Zhu type error estimators allowing to quantify the FEM solution quality to guide the h-adaptive refinement process which minimizes the computational cost for a given accuracy; and b) it provides a solution, more accurate than the FEM one, that can be used. The numerical results, which include a comparative with a commercial code, show the effect of the proposed methodology improving the efficiency in the optimization process and in the solution quality. (C) 2012 CIMNE (Universitat Politecnica de Catalunya). Published by Elsevier Espana, S.L. All rights reserved.