An ANSYS APDL code for topology optimization of structures with multi-constraints using the BESO method with dynamic evolution rate (DER-BESO)

This paper presents a 390-line code written in ANSYS Parametric Design Language (APDL) for topology optimization of structures with multi-constraints. It adopts the bi-directional evolutionary structural optimization method with the proposed dynamic evolution rate strategy (DER-BESO) to accelerate the iteration convergence. The complete APDL program includes the modules of finite element modeling, element sensitivity calculation, Lagrange multiplier updating, and the element updating module using DER-BESO method. It allows users to conduct the finite element analysis and optimization iterations just in one platform without having to switch repeatedly between the finite element analysis software and the optimization program. Through a cantilever example, the evolution procedure of DER-BSEO is compared to the primary BESO method to show its better performance in convergence speed. Different constraint cases are also considered to examine the robustness of the DER_BESO program. Example extensions for 3D structures and periodic structures with geometric restraints are also presented and discussed. Since ANSYS is a powerful finite element analysis platform, the given code has a perspective of extending to the optimization of large-scale structures or more complicated optimization problems that consider nonlinear or buckling effects.