基于Logistic函数改进插值模型拓扑优化

Research on Topology Optimization of Improved Interpolation Model Based on Logistic Function

针对传统插值模型在中间密度删除难以抉择而导致的拓扑构型出现灰色区域的问题,提出了一种基于logistic函数改进插值模型的拓扑优化方法。推导了二维结构拓扑优化的敏度公式和更新迭代公式,并验证了柔度函数在原点的一阶连续性;此插值模型在中间密度的极化问题上具有显著的二分类特性,极大的减少了拓扑构型中的中间密度区域;此外,探讨了插值模型中的参数取值问题。通过两个典型的数值算例验证了本方法的可行性和有效性。

Aiming at the problem that the traditional interpolation model has gray areas in the topological configuration caused by the difficulty of intermediate density deletion, a topological optimization method based on logistic function to improve the interpolation model is proposed. Sensitivity formulas and updated iteration formulas for the topology optimization of 2D structures were deduced, and the continuity of the first derivative of the flexibility function at the origin was verified;this interpolation model has a significant dichotomous characteristics in the polarization of intermediate density, greatly reduces the intermediate density area in the topological configuration. In addition, the value of the parameters in the interpolation model is discussed. The feasibility and effectiveness of the proposed method are verified by two typical numerical examples.