基于显式函数的位移约束板结构拓扑优化方法

TOPOLOGICAL OPTIMIZATION METHOD FOR PLATE STRUCTURES UNDER DISPLACEMENT CONSTRAINTS USING EXPLICIT FUNCTIONS

显式函数优化模型被认为可以极大地提高计算效率,显式近似是结构优化建模的追求目标。在应变能灵敏度分析和渐进结构优化方法(evolutionary structural optimization,ESO)的基础上,提出板结构位移约束下的显式函数拓扑优化方法。在优化过程中,首先将单元修改引起的位移变化转变为结构应变能灵敏度。其次将位移约束通过功能互等原理转化为结构应变能的约束,从而将灵敏度指标与优化指标统一起来,都变成结构单元修改的显式函数。最后根据结构应变能与目标的差值,根据ESO方法的思想,按一定的比率将灵敏度小的单元伪删除(单元厚度设为很小的值),修改后的结构采用精度控制的重分析方法进行快速求解,反复迭代达到满足要求的稳定结构,最后将厚度最小的单元从最终结构中删除。将所提的方法应用于板结构的拓扑优化中,数值算例表明,仅用18次迭代即可以达到稳定的目标,大大加快了求解的速度,表明所提出的方法是有效的。

As the explicit functions can greatly improve the solution efficiency of a optimize process,the goal of optimization modeling is to explicit approximate expression of the objective and constraints.Based on strain energy sensitivity analysis and evolutionary structural optimization（ESO）,a topological optimization method for plate structures under displacement is presented. Firstly,the displacement changes caused by deletion of elements are converting to that of strain energy.Secondly,the displacement constraint is converting to strain energy constrains according to conservation of energy.As a result,both objective and constrains are the same explicit express of strain energy.Finally,the elements are modified according to the scaling error strain energy between the real structure and the goal,that is,the elements with low strain energies are deleted（in order that it can recover in the next step,the thickness of those elements are set to very small value）,an iterative reanalysis method is presented to solve the modified structures rapidly,repeating the above step until an stationary status reached.The elements with small thickness are removed from the final result to form the optimal design.The presented method are implement onto the computer and cooperated with the commercial general finite element analysis software,and an example is given,result show that only 18 iterations are need to find the optimal design,while hundreds of iterations are need by other method for the similar demo,it is show that the presented method is efficient.