PolyDyna: a Matlab implementation for topology optimization of structures subjected to dynamic loads

We present a Matlab implementation for topology optimization of structures subjected to dynamic loads. The code, which we name PolyDyna, is built on top of PolyTop-a Matlab code for static compliance minimization based on polygonal finite elements. To solve the structural dynamics problem, we use the HHT-alpha method, which is a generalization of the classical Newmark-beta method. In order to handle multiple regional volume constraints efficiently, PolyDyna uses a variation of the ZPR design variable update scheme enhanced by a sensitivity separation technique, which enables it to solve non-self-adjoint topology optimization problems. We conduct the sensitivity analysis using the adjoint method with the "discretize-then-differentiate" approach, such that the sensitivity analysis is consistently evaluated on the discretized system (both in space and time). We present several numerical examples, which are explained in detail and summarized in a library of benchmark problems. PolyDyna is intended for educational purposes and the complete Matlab code is provided as electronic supplementary material.