基于Heaviside投影和进退法的结构拓扑优化方法

Optimization Method of Structural Topology Based on Heaviside Projection and the Method of Advance and Retreat

针对二分法对部分结构无法收敛和收敛速度较慢的问题,本文提出一种基于Heaviside投影和进退法的结构拓扑优化方法.该方法首先以柔度最小为目标建立拓扑优化模型;其次,通过固体各向同性材料惩罚(SIMP)法和材料属性有理近似(RAMP)法计算单元的弹性模量;然后,使用Heaviside投影函数对所求单元密度进行过滤;最后,使用改进的进退法对目标函数进行计算.通过建立拓扑优化模型验证所提方法的有效性,并将其结果与二分法计算结果进行对比分析.结果表明:改进的进退法计算所用时间少于二分法,迭代数相对于二分法减少了约40%,并能较好地解决二分法计算无法收敛的问题.

The dichotomy is a method of one-dimensional search,which is widely used in the field of topology optimization,however,the dichotomy is slower in computing efficiency and cannot converge on the calculation of complex problems.Aiming at the problems that the dichotomy cannot converge on some structures and the convergence speed is slower,A structural topology optimization method based on the Heaviside projection and the method of advance and retreat.Firstly,a topological optimization model with the goal of minimum flexibility is established..Secondly,the Young's modulus of the unit by the method of solid isotropic material punishment(SIMP)and the method of material property rational approximation(RAMP)is calculated.Meanwhile,the Heaviside projection function is used to filter the resulting element density.Finally,the improved step-back method is adopted to calculate the objective function.The effectiveness of the proposed method is verified by establishing a topology optimization model,and the results are compared with the calculation results of the dichotomy.Simulations show that the improved step-by-step method takes less time of calculation than the dichotomy,and the number of iterations is reduced by about 40%relative to the dichotomy.In addition,for the problem that the binary method of computation cannot converge,the improved method of advance and retreat can solve it better.