A new constraint of variance of principal stress direction for improving structural strength in topology optimization

The present study proposes a simplified topology optimization method to improve structural strength. Topology optimization considering structurally nonlinear behavior is one of the important topics. However, most of those methodologies request the complicated analytical derivation of sensitivity analysis and also high computational costs to obtain the optimal solution. This is the reason why the optimal design method based on linear structural analysis is still common approach in practice. However, optimal layouts based on linear structural analysis may lose the structural stability under larger or uncertain load. From this background, we propose a method of practical and simplified topology optimization to improve structural buckling behavior with much lower computational costs than that of optimal design based on complicated nonlinear structural analysis. Finally, we discuss the setting of the optimization problem improving the structural strength and demonstrate the accuracy and performance of the proposed method by a series of numerical examples.