正交各向异性弹性力学平面问题的样条虚边界元法

采用域外奇点技术并根据问题的边界条件,建立了正交各向异性弹性力学平面问题的非奇异虚边界积分方程,然后采用性态优越的B样条函数去逼近未知虚荷载函数,并采用性能稳定的最小二乘边界子段法去消除边界余量,据此获得积分方程的数值解.数值算例表明:该方法具有相当高的精度和良好的数值稳定性,且计算工作量少.文中引言部分还对域外奇点法的发展作了系统的评述.

Elastic Analysis of Orthotropic Plane Problems by the Spline Fictitious Boundary Element Method

Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.