Example extensions for 3D structures and periodic structures with geometric restraints are also presented and discussed. Different constraint cases are also considered to examine the robustness of the DER_BESO 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. 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. 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 adopts the bi-directional evolutionary structural optimization method with the proposed dynamic evolution rate strategy (DER-BESO) to accelerate the iteration convergence. This paper presents a 390-line code written in ANSYS Parametric Design Language (APDL) for topology optimization of structures with multi-constraints.
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