Micro shape optimization for minimizing microstructural thermal-stress considering heat conduction - Torisaki, Mihiro; Shimoda, Masatoshi; Ali, Musaddiq Al (International journal of mechanical sciences, 2024)
•A novel shape optimization method for reducing thermal stress of porous structures.•Introduced homogenization method considering heat conduction and thermal elasticity.•Derived the sensitivity function theoretically for a multiscale shape design problem.•Achieved smooth pore design using the H1 gradient method, a non-parametric method.•Total volume can be properly distributed into the plural microstructures. In this paper, we propose a shape optimization method to minimize the maximum thermal stress induced in the microstructures of a multiscale structure by heat conduction and thermal expansion. The weak- coupling problem is solved by applying the temperature distribution, obtained by solving the heat conduction problem, to the thermoelastic problem to find the maximum thermal stress caused by thermal expansion. The homogenization method is used to bridge the macrostructure and the porous microstructures, in which the elastic tensor, the tensor of the coefficients of thermal expansion, the thermal conductivity tensor and the thermal transfer coefficient are homogenized. The local thermal stress in the porous structure is minimized by shape optimization. The difficulty posed by non-differentiability of the local maximum stress is avoided by introducing a Kreisselmeier-Steinhauser function. It is assumed that the macrostructure consists of multiple subregions, in which the homogenized coefficients can be independently defined. This problem is formulated as a distributed-parameter optimization problem subject to a volume constraint, including all the microstructures. The shape gradient function for this design problem is derived for each subregion using the Lagrange multiplier method, the material derivative method and the adjoint method. The H1 gradient method is used to determine the optimal shape of the porous unit cell while reducing the objective function and maintaining smooth design boundaries. The effectiveness of the proposed method for minimizing the microstructural thermal stress of porous structures is confirmed by the numerical examples presented. [Display omitted]