基于节点独立连续映射方法的变上限周长控制

Perimeter Control with Variational Upper-Bound Based on Nodal Independent Continuous Mapping Method

为克服连续体结构拓扑优化中的数值不稳定性问题如棋盘格现象、网格依赖性问题和灰色区域等,提出变上限周长控制方式.在每轮优化迭代步中,根据当前结构周长值确定周长上限值,从而避免基于数值实验的周长上限确定过程.基于节点变量建立了连续体结构的独立连续映射拓扑优化模型,根据链式求导法则推导了周长敏度表达式并采用一阶泰勒展开近似表达周长约束方程.数值实验表明,该方法具有较好的优化迭代收敛性并能获得消除各类数值不稳定现象的清晰结果.

In order to overcome numerical instabilities such as checkerboards, mesh-dependence and gray regions in the topological optimization of continuum structures, a perimeter-constrained version of the nodal independent continuous mapping method with variational upper-bound is proposed. In order to avoid the determination of value of the perimeter constraint by experiments, an upper-bound perimeter is determined automatically in every optimization iteration. A topological optimization model with nodal variables of continuum structure is developed in independent continuous mapping. According to calculations for the partial derivative of compound function, derivatives of perimeter are deduced. Perimeter constraint is approximately formulated based on first-order Taylor expansion. Numerical examples show that good convergent solution and clear topological configuration can be obtained by the proposed method.