基于无网格Galerkin方法的整体式柔性机构的多准则拓扑优化设计

基于一种新型的数值计算技术—无网格伽辽金法,提出了一种整体式柔性机构拓扑优化设计的新方法.利用移动最小二乘形函数和伽辽金的弱变分形式建立弹性问题的控制方程,用Lagrange乘子法增强本质边界条件.在优化问题中,同时综合考虑机构的柔性和结构的刚度要求,用折衷规划法建立了柔性机构拓扑优化的多准则优化模型,这样对于非凸的优化问题也能保证搜索到Pareto解集所有的有效解.基于SIMP密度函数惩罚模型和优化准则法,建立了一种设计变量的显式迭代格式.运用经典算例证明了文中方法的正确性和有效性.

A MESHLESS GALERKIN APPROACH FOR TOPOLOGY OPTIMIZATION OF MONOLITHIC COMPLIANT MECHANISMS USING OPTIMALITY CRITERIA METHOD

A novel scheme for topology optimization of monolithic compliant mechanisms is presented based on a new numerical approach titled element free Galerkin method(EFGM).The equilibrium equation for elastic problems is derived by using moving least-square(MLS) approximants and the weak form of Galerkin method,where Lagrange multipliers are employed to enforce the essential boundary conditions,To satisfy the requirement of the mechanical flexibility and structural stiffness,the multi-criteria mathematical formulation is developed,which adopts the compromise programming to find the whole set of Pareto optimum solutions with respect to non-convex optimization problems.Further,an implicit iterative algorithm for the design variables is also established based on SIMP interpolation scheme and optimality criteria method.The validity of the proposed methods is substantiated by a typical example.