An ANSYS APDL code for topology optimization of structures with multi-constraints using the BESO method with dynamic evo
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EDUCATIONAL PAPER
An ANSYS APDL code for topology optimization of structures with multi-constraints using the BESO method with dynamic evolution rate (DER-BESO) Haidong Lin 1 & An Xu 1,2 & Anil Misra 2 & Ruohong Zhao 1 Received: 10 February 2020 / Revised: 22 March 2020 / Accepted: 27 March 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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. Keywords Topology optimization . BESO method . Dynamic evolution rate . ANSYS APDL
1 Introduction Topology optimization is a mathematical method that optimizes material layout within a given design space for a given set of loads, boundary conditions, and constraints with the goal of maximizing the performance of the system. Different from shape optimization and size optimization, topology optimization can attain any shape within the design space, instead of dealing with predefined configurations (Bendsoe and Kikuchi 1988; Bendsoe 1989). Topology optimization has a Responsible Editor: Raphael Haftka * An Xu [email protected] 1
Guangzhou University-Tamkang University Joint Research Center for Engineering Structure Disaster Prevention and Control, Guangzhou University, Guangzhou, China
2
Civil, Environmental and Architectural Engineering Department, Bioengineering Research Center (BERC), University of Kansas, 1530 W. 15th Street, Learned Hall, Lawrence, KS 66045-7609, USA
wide range of applications in aerospace, mechanical, biochemical, and civil engineering, mostly at the concept level of a design process. With the development of computer technology and finite element analysis method, topology optimization has been investigated extensively in the past decades (Rozvany 2009). It has been applied to structural optimization with s
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