Achieving minimum length scale in topology optimization using nodal design variables and projection functions
Achieving minimum length scale in topology optimization using nodal design variables and projection functions
复制标题
DOI：
10.1002/nme.1064
复制
发表时间：
2004-09-14
影响因子：
2.9
通讯作者：
Belytschko, T
中科院分区：
文献类型：
--
作者：
Guest, JK;Prévost, JH;Belytschko, T
描述了离散拓扑优化问题中构件最小长度尺度的一种方法。节点变量被实现为设计变量，并被投影到元素空间上，以确定传统上定义拓扑结构的元素体积分数。投影是通过基于最小长度尺度的网格独立函数进行的。研究了一种简单的线性投影格式和一种利用正则Heaviside阶跃函数实现近0-1解的非线性格式。该方法在最小柔度问题上进行了验证，并采用流行的SIMP方法对中间体积分数单元的刚度进行了补偿。解决方案显示满足用户定义的长度尺度标准，没有额外的约束，惩罚函数或灵敏度滤波器。没有观察到网格依赖或棋盘图案的实例。版权所有：John Wiley Sons， Ltd. 2004
A methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described. Nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology. The projection is made via mesh independent functions that are based upon the minimum length scale. A simple linear projection scheme, and a non-linear scheme using a regularized Heaviside step function to achieve nearly 0-1 solutions are examined. The new approach is demonstrated on the minimum compliance problem and the popular SIMP method is used to penalize the stiffness of intermediate volume fraction elements. Solutions are shown to meet user-defined length scale criterion without additional constraints, penalty functions or sensitivity filters. No instances of mesh dependence or checkerboard patterns have been observed. Copyright (C) 2004 John Wiley Sons, Ltd.