Topology Optimization Of Continuum Two-Dimensional Structures Under Compliance And Stress Constraints.

Abstract

This paper presents the problem of volume minimization of two-dimensional
continuous structures with compliance and stress constraints. Problems are solved by a
topology optimization technique, formulated as finding the best material distribution into the
design domain. Discretizing the geometry into simpler pieces and approximating the
displacement field, equilibrium equations are solved through the finite element method. A
material parametrization method is used to represent the fictitious constant material
distribution into each finite element. Sequential Linear Programming is used to solve the
optimization problem. For both compliance and stress constrained problems, an analytical
sensitivity analysis for elastic behavior is derived, and for this last problem, Von Mises
equivalent stress is the failure criteria considered. A first neighborhood filter was
implemented to minimize the effects of checkerboard patterns and mesh dependency, two
common problems associated to topology optimization. Stress constrained problems have a
further difficulty, the stress singularity, which may prevent the algorithm to reach a feasible
solution. To overcome this problem, the feasible domain is modified using a mathematical
perturbation technique, the epsilon-relaxation.