Structural rigidity optimization with an initial design dependent stress field. Application to thermo-elastic stress loads

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This paper presents a compliance optimization methodology considering an initial stress field. Assuming a local dependency of the initial stress with the optimization parameters, the obtained numerical procedure is composed of finite element stress calculations and local minimization problems that are solved analytically or using a simple bisection procedure. This optimization algorithm is then found to be numerically very efficient. Two optimization problems that fall in the scope of the proposed methodology are considered: topology optimization of the isotropic mixture of two isotropic linear elastic materials (one of the material possibly being void) and orientational optimization (i.e. distribution of anisotropy) with an orthotropic linear elastic material. Numerical examples illustrating the optimization methodology in the case of thermo-elastic stress loads are presented.