基于CA的结构拓扑优化中变量更新规则研究

针对连续体结构拓扑优化中数值不稳定问题,借鉴控制系统中反馈控制和误差放大器的原理,构建了一种无梯度约束的变量更新规则,以结构应变能密度均匀分布为优化目标,建立了基于元胞自动机的拓扑优化模型,进行了二维连续体结构的拓扑优化设计,得到材料在设计域内的最优分布。通过求解三个经典的算例,探讨了不同的误差放大系数对优化结果的影响,试验结果表明,该更新规则能够有效地抑制棋盘格和网格依赖性问题。

Updating rule of variables for structural topology optimization based on CA

In order to suppress numerical instability problems in topology optimization of continuum structures,a new local control rule is proposed by using the principle of error amplifier and feedback control in control system for reference.This control rule is a new kind of updating rule for variables without gradient constraints.The topology optimization model for continuum structures is established basing on the theory of Cellular Automata(CA).The optimization objective is referred to as the uniform strain density distribution.Topology optimization design of continuum structures in two dimensions is accomplished and the optimal material distribution in the design domain is thus obtained.The effect of different error amplification factors to optimizing results is discussed using three typical numerical examples.The analysis results illustrate the updating rule can avoid numerical stability problems such as checkerboard patterns and mesh dependency effectively.