Time-Dependent Structural Topology Optimization Using a Continuous Adjoint Formulation

A new time-dependent topology optimization methodology is presented based on a time-dependent continuous adjoint approach. The main advantage is its non-intrusiveness which allows us not to interfere with the discretization scheme of the finite-element or finite-volume topology optimization software. The discretization of the differential adjoint equations can be different from the discretization of the structural equations. The objective is to minimize the time-average compliance of a structure subject to a volume-based constraint. A gradient-based optimization algorithm is used. The sensitivity derivatives of a time-average compliance function with respect to the topology design parameters are computed using a time-dependent adjoint formulation. The self-adjoint feature is first presented for discrete time-dependent topology optimization and then extended to the continuous case. The proposed methodology is demonstrated using the topology optimization of a two dimensional and a three dimensional structure under time-dependent excitations.