基于径向基函数的局部边界积分方程方法

LOCAL BOUNDARY INTEGRAL EQUATION METHOD BASED ON RADIAL BASIS FUNCTIONS

将基于径向基函数构造的具有插值特性的逼近函数应用于弹性力学问题的局部边界积分方程,推导出相应离散方程的计算公式,建立基于径向基函数的局部边界积分方程方法。与原有的局部边界积分方程方法相比,该方法不需要虚拟节点变量,而是采用节点变量的真实解作为基本未知量,是局部边界积分方程无网格法的直接解法。由于形函数及其导数的构造相对简单,并且满足Delta函数性质,故该方法具有计算量小、精度高,可以像有限元法一样直接施加边界条件等优点。算例证明了该方法的有效性。

The interpolation function, which is of delta function property and constructed on the basis of radial basis functions, is applied in the local boundary integral equation of elasticity, the discretized equations of 2D elasticity are obtained, then the local boundary integral equation method based on radial basis functions is presented. Comparing with the conventional local boundary integral equation method, the present method need not the unknown virtual nodal quantities, the basic unknown quantities are the real solutions of the nodal variables. The present method is a direct numerical method of local boundary integral equation. The implementation procedure is simpler and the computation cost is much lower because of the simple interpolation, the corresponding derivatives and the delta function property. In addition, the essential boundary conditions can be implemented easily as in the finite element method. Some numerical results to demonstrate the efficiency of the present method are presented.