Discrete variable topology optimization for compliant mechanism design via Sequential Approximate Integer Programming wi
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RESEARCH PAPER
Discrete variable topology optimization for compliant mechanism design via Sequential Approximate Integer Programming with Trust Region (SAIP-TR) Yuang Liang 1 & Kai Sun 1 & GengDong Cheng 1 Received: 5 May 2020 / Revised: 7 July 2020 / Accepted: 15 July 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The discrete variable topology optimization method based on Sequential Approximate Integer Programming (SAIP) and Canonical relaxation algorithm demonstrates its potential to solve large-scale topology optimization problem with 0–1 optimum designs. However, currently, this discrete variable method mainly applies to the minimum compliance problem. The compliant mechanism design is another widely studied topic with distinguishing features. First, the objective function for the compliant mechanism design is non-monotonic with the material usage. Second, since de facto hinges always occur, the minimum length scale control is indispensable for manufacturability. These two issues are well studied in the SIMP approach but bring great challenges when topology optimization problems are formulated in the frame of discrete variables. The present paper generalizes this discrete variable method for the compliant mechanism design problems with minimum length scale control. Firstly, the sequential approximate integer programming with trust region (SAIP-TR) framework is proposed to directly restrict the variation of discrete design variables. Different from the continuous variable optimization, the non-linear trust region constraint can be formulated as a linear constraint under the SAIP framework. By using a merit function, two different trust region adjustment strategies that can self-adaptively adjust the precision of the sub-problems from SAIP-TR are explored. Secondly, a geometric constraint to control the minimum length scale for the material phase and void phase in the framework of discrete design variables is proposed, which suppresses de facto hinges and reduces stress concentration in optimum design. The related issue of feasibility of sub-problem is discussed. By combining the SAIP-TR framework with the geometric constraint, some different hinge-free compliant mechanism designs are successfully obtained. Keywords Discrete variable topology optimization . Compliant mechanism . Minimum length scale . Canonical relaxation algorithm . Trust region
1 Introduction Different from rigid-like mechanisms, a compliant mechanism transfers the load or displacement through elastic deformation without a hinge. The compliant mechanism can be manufactured by one integrated part. Thus, wear, friction, and backlash can be reduced. Hence, compliant mechanisms Responsible Editor: Emilio Carlos Nelli Silva * GengDong Cheng [email protected] 1
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, People’s Republic of China
are increasingly prevalent in the biomedical area and MEMS—microelectromecha
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