Topology optimization of compliant mechanisms considering strain variance
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RESEARCH PAPER
Topology optimization of compliant mechanisms considering strain variance Bin Niu 1
&
Xiaolong Liu 1 & Mathias Wallin 2 & Eddie Wadbro 3
Received: 23 January 2020 / Revised: 9 April 2020 / Accepted: 12 May 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, compliant mechanisms are designed by using multi-objective topology optimization, where maximization of the output displacement and minimization of the strain are considered simultaneously. To quantify the strain, we consider typical measures of strain, which are based on the p-norm, and a new class of strain quantifying functions, which are based on the variance of the strain. The topology optimization problem is formulated using the Solid Isotropic Material with Penalization (SIMP) method, and the sensitivities with respect to design changes are derived using the adjoint method. Since nearly void regions may be highly strained, these regions are excluded in the objective function by a projection method. In the numerical examples, compliant grippers and inverters are designed, and the tradeoff between the output displacement and the strain function is investigated. The numerical results show that distributed compliant mechanisms without lumped hinges can be obtained when including the variance of the strain in the objective function. Keywords Topology optimization . Effective strain . Compliant mechanism . Multi-objective optimization . Strain uniformity
1 Introduction Compliant mechanisms comprise a class of mechanical systems that replaces conventional hinge mechanisms by compliant members (Her and Midha 1987). Many advantages of compliant mechanisms, including fewer parts, reduced assembly, elimination of lubrication at joints, and the ability to be miniaturized, have resulted in a rapid growth of interest in compliant mechanisms (Howell et al. 2013). Several methods are available for the design of compliant mechanisms, such as the rigid-body replacement method (Howell and Midha 1994; Howell et al. 1996), the building blocks method (Kim et al. Responsible Editor: Fred van Keulen * Bin Niu [email protected] 1
Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of Education, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, People’s Republic of China
2
Division of Solid Mechanics, Lund University, Box 118, SE-221 00 Lund, Sweden
3
Department of Computing Science, Umeå University, SE-901 87 Umeå, Sweden
2006; Kim et al. 2008; Krishnan et al. 2012), and the topology optimization method (Sigmund 1997; Nishiwaki et al. 1998; Chen and Wang 2007; Hasse and Campanile 2009; Zhu and Zhang 2012). Topology optimization has become particularly popular because of its ability to design complex geometries (Zhu et al. 2020). Optimization driven design of mechanisms can be formulated by the solid isotropic material with penalization (SIMP) method (Sigmund 1997), homogenization method (Nishiwaki et al. 1998), ground structure method (Hasse and Campanile
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