The robust fail-safe topological designs based on the von Mises stress

For large-scale equipment, e.g. aerospace and architecture industry, it is valuable to guarantee that one structure could survive partial damages. Due to the location of the damage is unknown in prior, results in a high number of failure scenarios to be calculated when considering fail-safe requirement in topology optimization. In this article, we propose an efficient continuum topology optimization method on the basis of the design philosophy of robust fail-safe structure. A number of patches with predefined shapes are used to simulate the material failure. The material properties of damaged models are interpolated by von Mises stress to construct the well-posed optimization model. The damaged compliance for the worst failure case is set as the optimization objective, and the KS function is adopted to approximate the non-differentiable max-operator. A computationally efficient sensitivity formulation is derived via the adjoint method. To suppress the highly nonlinear stress behavior and the phenomenon of optimization oscillation, an extended variable update scheme within the framework of Optimality Criteria (OC) method is developed. Representative benchmarks show that the presented strategy has the effectiveness at yielding the fail-safe structure by using acceptable computational cost.