Abstract:

Based on the continuum structural topology optimization, the element-free Galerkin method was applied to design large-displacement compliant mechanisms with geometrical nonlinearities.The multi-criteria mathematical formulation was developed using the SIMP（solidisotropic material with penalization）interpolation scheme and compromise programming,in which the mechanical flexibility and structural stiffness were both considered as the prescribed performances to be optimized. The optimization formulation was solved by optimality criteria method. The element-free Galerkin method was employed to discretize the design domain with the aim of avoiding the undesired mesh distortion caused by adopting finite element methods to deal with geometrical nonlinear problems.Numerical examples have been presented to demonstrate the effectiveness of the proposed approaches by analyzing the results derived from linear and nonlinear cases,respectively.

Key words: compliant mechanism；topological optimization, meshless method;geometrical nonlinearity;optimality criteria

摘要：

基于连续体结构的拓扑优化理论，将无网格伽辽金数值方法引入分布式大变形柔性机构拓扑优化设计，并解决了优化中的几何非线性问题。在优化问题中，基于各向同性固体材料惩罚模型（solidisotropic material with penalization,SIMP)和折衷规划法，同时考虑结构的柔性和刚度要求，建立了柔性机构拓扑优化的多准则优化模型，并利用优化准则法求解。采用无网格伽辽金法将求解域离散成节点，避免了有限元方法在处理大变形问题时由于使用网格而产生网格畸变等问题。求解经典算例，与基于线性理论的优化结果相比较分析，说明了该方法的正确性和有效性。

关键词: 柔性机构, 拓扑优化, 无网格法, 几何非线性, 优化准则