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.

Automated summary

The study introduces a Matlab implementation for topology optimization of structures under dynamic loads, using various methods and techniques to address structural dynamics problems and solve non-self-adjoint topology optimization problems. Several numerical examples are presented with detailed explanations and summarized in a benchmark problem library.