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Using artificial reaction force to design compliant mechanism with multiple equality displacement constraints

机译：利用人工反作用力设计具有多个等位移约束的柔性机构

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摘要

Monolithic compliant mechanisms are elastic workpieces which transmit force and displacement from an input position to an output position. Continuum topology optimization is suitable to generate the optimized topology, shape and size of such compliant mechanisms. The optimization strategy for a single input single output compliant mechanism under volume constraint is known to be best implemented using an optimality criteria or similar mathematical programming method. In this standard form, the method appears unsuitable for the design of compliant mechanisms which are subject to multiple outputs and multiple constraints. Therefore an optimization model that is subject to multiple design constraints is required. With regard to the design problem of compliant mechanisms subject to multiple equality displacement constraints and an area constraint, we here present a unified sensitivity analysis procedure based on artificial reaction forces, in which the key idea is built upon the Lagrange multiplier method. Because the resultant sensitivity expression obtained by this procedure already compromises the effects of all the equality displacement constraints, a simple optimization method, such as the optimality criteria method, can then be used to implement an area constraint. Mesh adaptation and anisotropic filtering method are used to obtain clearly defined monolithic compliant mechanisms without obvious hinges. Numerical examples in 2D and 3D based on linear small deformation analysis are presented to illustrate the success of the method.
机译：整体顺应机构是弹性工件，其将力和位移从输入位置传递到输出位置。连续体拓扑优化适合于生成此类顺应性机制的优化拓扑，形状和大小。已知在体积约束下用于单输入单输出顺应性机制的优化策略是使用最佳性标准或类似的数学编程方法来最佳实现的。以这种标准形式，该方法似乎不适用于受多种输出和多种约束的顺应性机构的设计。因此，需要一个受多个设计约束的优化模型。关于受多个等价位移约束和面积约束约束的顺应性机构的设计问题，我们在此提出一种基于人工反作用力的统一灵敏度分析程序，其中关键思想是基于拉格朗日乘数法。由于通过此过程获得的灵敏度表达式已经影响了所有等式位移约束的效果，因此可以使用一种简单的优化方法（例如最佳性标准方法）来实现面积约束。网格自适应和各向异性过滤方法用于获得明确定义的整体顺应性机制，而无需明显的铰链。给出了基于线性小变形分析的2D和3D数值例子，说明了该方法的成功。

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  • 来源
    《Finite elements in analysis & design》 |2009年第9期|555-568|共14页
  • 作者

    Zhenyu Liu; Jan G. Korvink;

  • 作者单位

    State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences, Changchun, Jilin 130033, China;

    Laboratory for Simulation, Department of Microsystems Engineering (IMTEK), and Freiburg Institute of Advanced Studies (FRIAS), University of Freiburg, 79110 Freiburg, Germany;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    topology optimization; compliant mechanism; equality constraint; reaction force; mesh adaptation;

    机译：拓扑优化;顺应机制;平等约束反作用力网格自适应;

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