Topology optimization of members of flexible multibody systems under dominant inertia loading

The topology optimization of members of flexible multibody systems is considered for energy-efficient lightweight design, where the gradient calculation has an essential role. In topology optimization of flexible multibody systems, where the function evaluations are very time consuming, the gradient information is necessary to accelerate the optimization process. Different approaches have been introduced and tested for the gradient calculation in the fully coupled topology optimization of flexible multibody systems. However, the computation and implementation costs of these methods are high, which limits the optimization size and the possible number of design variables. In this work, we present a modified gradient calculation based on the equivalent static load (ESL) method, which combines the time efficiency of gradient calculation of the ESL method with the higher accuracy of gradient calculation in the fully coupled methods. This modified approach, which takes into account the linear dependencies of inertial loads on acceleration, is tested on the application example of a flexible slider-crank mechanism, and the results are compared with the weakly coupled ESL method and a fully coupled optimization where gradients are calculated using the adjoint variable method.