Continuum structural topological optimization with dynamic stress response constraints

This paper proposes a methodology for the topology optimization of continuum structures subject to dynamic stress response constraints under stochastic loads. The topology optimization model is built, where the objective function is the structural weight, and the dynamic stress constraints are applied. In order to greatly reduce the computational cost of dynamic stress responses and prevent stress concentration phenomenon, the P-norm aggregation function is adopted to replace the dynamic stress response constraints. To solve the defined topology optimization problem, a method with varying dynamic stress response limit is presented, and the sensitivities of the equivalent dynamic stress response constraints with respect to the reciprocal design variables is derived so as to form the explicit approximate functions for structural equivalent dynamic stress response constraints. Then, based on dual theory, an algorithm by using nonlinear programming method with simple trust regions is introduced to solve the optimization problem. Finally, the results of several numerical examples are given to demonstrate the validity and effectiveness of the proposed approach.