Topology optimization considering uniformity of dynamic reaction forces

Abstract The present study proposes a method to maximize structure stiffness with the constraint of even reaction forces under dynamic loading. The dynamic variance of the reaction forces at the Dirichlet boundary is introduced to evaluate the uniformity of the reaction forces. Several formulations for optimal topology design are provided by introducing the constraints of dynamic variance of reaction forces. Multi-objective optimization considering dynamic mean-compliance minimization and uniform distribution of force transmission is proposed. Sensitivity analysis is then derived based on the adjoint variable method and verified by the finite differentiation approximation (FDA). Several numerical examples prove the effectiveness of the proposed method.