复变量法求解拓扑优化敏度分析研究

Sensitivity Analysis of Topology Optimization Based on Complex Variable Method

研究复变量法对拓扑优化问题敏度分析的有效性和可行性,在现有的经典理论为基础,通过使用无网格伽辽金法离散问题域而求得结构场位移为例,使用O.Sigmund的经典拓扑优化方法,利用复变量来求解出目标函数的导数,然后比较复变量法和直接法某些点敏度分析的误差以及最后拓扑图形的异同,结果显示复变量法和直接法的误差极小,最后通过实际例子结果的总结归纳,能够得出复变量法比较简便易行、精度高的结论。

The effectiveness and feasibility of complex variable method is studied for sensitivity analysis in topology optimization problem. Based on the existing classical theory , EFGM discrete displacement field of structure is solved using the complex variable out of the derivative of the objective function and O.Sigmund classical topology optimization method. Then the error of the topology graph,sensitivity analysis error of the complex variable and direct method,are compared. The comparison of theoretical and practical examples proves that the complex variable method is more simple and more precise.