随机结构弹性屈曲的递推求解方法

采用随机收敛的非正交的多项式展式表示未知的随机屈曲特征值和屈曲模态,利用摄动技巧,建立了随机结构弹性屈曲的递推求解方法。算例表明,和基于泰勒展开的摄动随机有限元方法相比,方法的结果能在较宽的随机涨落范围内更好地逼近蒙特卡洛模拟结果,即使只采用前四阶非正交多项式展式,逼近的结果仍然较好。

ELASTIC BUCKLING ANALYSIS OF RANDOM STRUCTURES BASED ON RSFEM

The analysis of elastic buckling of random structures using recursive stochastic finite element method(RSFEM)is presented.Buckling eigenvalues and eigenvectors of random structures are expressed as non-orthogonal polynomial expansions that are randomly convergent.Utilizing perturbation technique,a set of deterministic recursive equations are set up.Statistic buckling eigenvalues of structures are obtained by iteratively solving the deterministic equations.It is found in numerical examples that compared with perturbation stochastic finite elements method based on Taylor expansion,the results of RSFEM are more close to those of Monte-Carlo simulation in large range of random fluctuation.The examples also show that acceptable results can still be obtained using RSFEM with only the first four orders of non-orthogonal polynomial expansions.