Topology optimization applied to 2D elasticity problems considering the geometrical nonlinearity

Abstract

Topological Optimization (TO) of structures in plane stress state with material elastic-linear behavior, but taking into consideration the geometrical nonlinearities, was performed and the results are presented herein. For this process, an evolutionary heuristic formulation denominated SESO (Smoothing Evolutionary Structural Optimization) associated with a finite element method was applied. SESO is a variant of the classic evolutionary structural optimization (ESO) method, where a smoothing process is applied in the “hard-kill” process of element removal – that is, their removal is done smoothly, reducing the values of the constitutive matrix of the element as if it were in the process of damage. It has been demonstrated that this non-linear geometric phenomenon clearly influences the final optimized topology when compared to an optimum configuration obtained with the equilibrium equations written at an undeformed position. Some numerical examples from literature are presented in order to show the differences in the final optimal topology when linear and non-linear analyses are used, allowing the verification of the importance of correctly analyzing the final optimum topology and as such, demonstrate the advantages of SESO as a structural optimization method.