改进的无网格局部边界积分方程方法

Improved Meshless Local Boundary Integral Equation Method

将局部边界积分方程与改进的移动最小二乘法相结合,提出改进的无网格局部边界积分方程方法。改进的移动最小二乘法引入带权的正交基函数,可以克服现有的移动最小二乘法在构造近似函数时须要进行大量的矩阵求逆、计算量大、法方程组容易出现病态方程组的缺点。将改进的无网格局部边界积分方程方法应用于弹性力学问题,并推导出相应的离散方程。通过数值算例验证了该方法的有效性。与原有的局部边界积分方程方法相比,该方法具有计算量小、数值稳定性好并且不会出现病态方程组的优点。

Combining the local boundary integral equation with the improved moving least-square method, an improved meshless local boundary integral equation method is presented. In the improved moving least-square method, the weighted orthogonal functions are used as basis ones so that the matrix inverse at each quadrature point is avoided and the algebra equations system is not ill-conditioned. In addition, the improved meshless local boundary integral equation method is applied to linear elasticity problems, the corresponding discrete equations are derived. Some numerical results to demons trate the efficiency of the method are presented. Compared with the conventional local boundary integral equation method, the present method has higher computational efficiency and precision, and will not form ill-conditioned or singular equations.