基于随机摄动有限元的连续体随机拓扑优化设计

摘要

提出了连续体结构随机拓扑优化设计(STOD)的概念.假定连续体的随机参数满足正态分布,根据随机参数的均值和方差,利用随机摄动有限元理论(SFEA)求出连续体单元应力的均值和方差,利用线性同余法(LCGs)产生伪随机数,得到单元应力的伪随机数值,继而以单元应力的欧氏距离为判别标准,利用K邻近算法(KNN)对连续体结构进行拓扑优化设计,最后给出了计算示例.%A concept of STOD of continuum structure was proposed. Assuming the random parameters of the continuum to meet normal distribution, according to the mean and variance of random parameters, by using method of stochastic perturbation finite element analysis (SFEA), the unit stress' s mean and variance were calculated. Using linear congruential random number generators (LCGs) , the pseudo -randoms of unit stress were obtained. The unit stress Euclidean distance was used to be as the criterion, and the stochastic topology optimization of continuum structure was gotten by K nearest neighbor (KNN). Finally, the numerical examples were given.