Integrated topology and boundary shape optimization of 2-D solids

Abstract This study is concerned with the development of an integrated procedure for the computation of the optimal topology as well as the optimal boundary shape of a two-dimensional, linear elastic body. The topology is computed by regarding the body as a domain of the plane with a high density of material and the objective is to maximize the overall stiffness, subject to a constraint on the material volume of the body. This optimal topology is then used as the basis for a shape optimal design method that regards the body as given by boundary curves. For this case the objective is to minimize the maximum value of the Von Mises equivalent stress in the body, subject to an isoperimetric constraint on the area as well as a constraint on the stiffness. The solution procedures for the shape design are based on variational formulations for the problems and the results of a variational analysis are implemented via finite element discretizations. The discretization grids are generated automatically by an elliptical method for general two-dimensional domains. Computational results are presented for the design of a fillet, a beam and a portal frame.

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