平面弹性力学充要的随机边界元

A Sufficient and Necessary Stochastic Boundary Integral Formulation for Plane Elasticity Problems

将平面弹性力学确定性的充分必要的边界积分方程推广到含材料常数随机的不确定问题中去，给出了位移的均值以及偏差的充分必要的边界积分方程。数值计算结果表明，和确定性的积分方程一样，习用的随机边界积分方程在退化尺度附近，无论是均值还是偏差都存在巨大的误差。

This paper develops the sufficient and necessary integral equations of the deterministic problem in plane elasticity to undeterministic problem including the randomness of material parameters, the sufficient and necessary boundary integral equations of the mean and deviation concerning displacement is presented. Numerical analyses show the conventional stochastic boundary integral equations obtain wrong results when the scale in the fundamental solution approaches its degenerate scale values. Meanwhile, the sufficient and the necessary stochastic integral equations are in good agreement with analytical solutions.