Stress-constrained multiscale topology optimization with connectable graded microstructures using the worst-case analysis

This article proposes a stress-constrained multiscale topology optimization approach with connectable graded microstructures. The proposed method includes two stages. In the first stage, the shape interpolation method is first employed to generate a series of connectable unit cells. Then the effective elasticity tensors are calculated by the numerical homogenization and XFEM. Besides, the worst-case analysis and stress correction factor are employed to predict the maximum microscopic stress of the unit cells under arbitrary loading conditions. Furthermore, reduced-order models for the stress correction factor and effective elasticity tensor are built to efficiently predict the mechanical properties of the unit cell with any specified volume fraction. In the second stage, stress-constrained topology optimization is employed to find the distribution of microstructures by using established reduced-order models. Except for applying approaches commonly used in the traditional stress-constrained topology optimization, the moving Heaviside function is also proposed to include the void material into optimization. Finally, a threshold projection scheme is performed to realize the design of multiscale structures. Two numerical examples are presented to validate the proposed method. In addition, because the worst-case analysis overestimates the structural stress, an evolutionary discrete optimization is employed to further explore the potential of the multiscale structures.