A Feasible Sequential Convex Programming Method for Free Material Optimization

S. Ertel, K. Schittkowski, C. Zillober: 8th World Congress on Structural and Multipdisciplinary Optimization, June 1-5, 2009, Lisbon, Portugal (2009)
Abstract: In free material optimization (FMO), one tries to find the best mechanical structure by minimizing the weight  or by maximizing the stiffness with respect to given load cases. Design variables are elasticity tensors or elementary material matrices, respectively, based on a given FE discretization. Material properties are as general as possible, i.e., anisotropic, leading to positive definite elasticity tensors, which may be arbitrarily small in case of vanishing material. To guarantee a positive definite global stiffness matrix for computing design constraints, e.g., displacements or stress constraints, it is required that all iterates of an optimization algorithm retain strictly positive definite tensors. We propose a modification of a sequential convex programming method (SCP). The corresponding separable and strictly convex nonlinear subproblems are expanded by additional nonlinear constraints, to guarantee positive definite elementary matrices in each iteration step. These constraints are retrieved from a sign condition of sub-determinants. The algorithm is introduced and some numerical examples based on academic test cases are presented.

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