物质点拓扑变量法在柔性机构设计中的应用
Topology Optimization for Compliant Mechanism Using Material Point Topological Variable
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摘要: 为克服柔性机构拓扑优化设计中的各类数值不稳定性问题,提出一种以物质点拓扑变量为设计变量的拓扑优化方法.物质点拓扑变量可视为节点密度概念的进一步拓展,基于修正网格无关性过滤函数提出了新的拓扑变量场插值形函数.基于弹簧模型,建立了柔性机构的多约束拓扑优化模型,推导了常见结构响应量的敏度表达式,采用移动渐进线法进行优化求解.最后通过二维数值算例验证了文中方法的可行性和有效性.Abstract: To overcome various kinds of numerical instabilities in topology optimization for compliant mechanisms,a method using material point topological variables as design variables is proposed.The material point topological variable can be viewed as natural extension of the nodal density.Based on a modified mesh-independent filtering scheme,a new interpolation function used to construct the topological variable field is presented.The mathematical model of topology optimization for compliant mechanisms is established based on spring model,in which some structural responses are taken as constraint functions.The analytical expressions of various structural responses sensitivity are deduced.The method of moving asymptotes is adopted in the optimization algorithm.The feasibility and generality of the method are demonstrated by some numerical examples.