New method for controlling minimum length scales of real and void phase materials in topology optimization
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RESEARCH PAPER
New method for controlling minimum length scales of real and void phase materials in topology optimization Xuanpei Rong1,2 · Jianhua Rong1,3 · Shengning Zhao1,3 · Fangyi Li1,3 · Jijun Yi1,3 · Luo Peng1,3 Received: 21 September 2019 / Revised: 28 November 2019 / Accepted: 6 January 2020 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Minimum length scale control on real and void material phases in topology optimization is an important topic of research with direct implications on numerical stability and solution manufacturability. And it also is a challenge area of research due to serious conflicts of both the solid and the void phase element densities in phase mixing domains of the topologies obtained by existing methods. Moreover, there is few work dealing with controlling distinct minimum feature length scales of real and void phase materials used in topology designs. A new method for solving the minimum length scale controlling problem of real and void material phases, is proposed. Firstly, we introduce two sets of coordinating design variable filters for these two material phases, and two distinct smooth Heaviside projection functions to destroy the serious conflicts in the existing methods (e.g. Guest Comput Methods Appl Mech Eng 199(14):123–135, 2009). Then, by introducing an adaptive weighted 2-norm aggregation constraint function, we construct a coordinating topology optimization model to ensure distinct minimum length scale controls of real and void phase materials for the minimum compliance problem. By adopting a varied volume constraint limit scheme, this coordinating topology optimization model is transferred into a series of coordinating topology optimization sub-models so that the structural topology configuration can stably and smoothly changes during an optimization process. The structural topology optimization sub-models are solved by the method of moving asymptotes (MMA). Then, the proposed method is extended to the compliant mechanism design problem. Numerical examples are given to demonstrate that the proposed method is effective and can obtain a good 0/1 distribution final topology. Keywords Structural topology optimization · Minimum length scale · Manufacturability · Coordinating density filter · Heaviside projections · Void phase
1 Introduction Topology optimization has become one of the important research topics [1–7] in the structural optimization community in recent years. A large effort has been done and
* Jianhua Rong [email protected] 1
School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410076, People’s Republic of China
2
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, People’s Republic of China
3
Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle of Hunan Province, Changsha University of Science and Technology, Changsha 410114
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