Dynamic topology optimization of continuum structures considering moving mass excitations

Abstract

The structures excited by the moving mass are widely existed in nature and engineering. The dynamic loads are related to time and space and greatly affect structural performances. However, the moving mass problems have not been considered in the topology optimization design of continuum structures. Therefore, this paper proposes a novel dynamic topology optimization method to design the continuum structures considering moving mass excitations. Firstly, the finite element formulation is established to solve the dynamic responses for the moving mass excitations by using the HHT-α method. Secondly, in the density-based framework, the dynamic topology optimization problem is formulated to minimize the mean strain energy constrained with the total volume, whose interpolation scheme is the rational approximation of material properties. Thirdly, the sensitivities of the optimization problem are derived by using the adjoint variable method in the discretize-then-differentiate scheme. Finally, numerical examples demonstrate the effectiveness of the proposed method and the influence of the moving mass excitations on the topological structures.