连续体结构拓扑优化的节点独立连续映射法

Node-based Independent Continuous Mapping Method for Topological Optimization of Continuum Structures

提出基于节点拓扑变量的独立连续映射连续体结构拓扑优化方法,将常规ICM中基于单元拓扑变量描述改进为基于节点拓扑变量描述,通过单元形函数插值保证了拓扑变量场的连续性。引入拓扑变量和设计变量倒数关系,根据复合函数链式求导法则,推导了各类结构响应量的敏度分析公式。以位移约束问题为例,遵循ICM法建模方式建立了连续体结构拓扑优化模型。基于数字图像处理过滤技术,提出两种改进的过滤方式以消除数值不稳定性现象。最后通过二维拓扑优化数值算例证明方法和模型的可行性和有效性。

A new node-based independent continuous mapping method for topological optimization of continuum structures is presented.Modifying the previous ICM method,the element-based topological variables is replaced by node-based topological variables which illustrate the features of every element.Continuity of topological variables is ensured by interpolation of shape functions in an element.Reciprocal relationship between topological variables and design variables are introduced.According to the principle for partial derivative of compound function,the derivatives of different kinds of structural responses and weight are deduced.The procedure of formulating and solving the topological optimization model of continuum structure is illustrated by the example with displacement constraints.Two different image-filter methods are developed to eliminate numerical instabilities in topology optimization,such as checkerboard patterns and mesh-dependence problems.The validity of the proposed methods is substantiated by some two-dimensional examples.