二维单域弹性问题虚边界无网格伽辽金法分析

Analysis of two-dimensional single-domain elastic problem based on virtual boundary meshless Galerkin method

使用加权残值法中的伽辽金法,并利用无网格法中的径向基函数法插值虚边界上的虚拟源函数,形成了虚边界无网格伽辽金法,具有边界元法和无网格法的共同优点。且该方法的加权值为位移或面力的偏导数,数值意义明确,形成的方程具有对称性。详细推导了单域虚边界无网格伽辽金法的具体数值离散格式,便于其他学者编程、研究。数值实例为文献中的三峡水利枢纽中的双排列输水孔实例,计算虚、实边界不同距离,单元上不同高斯点数,虚拟源函数的不同虚节点径向基函数插值的影响,结果均说明单域虚边界无网格伽辽金法的可行性与精确性。

Using Galerkin method of weighted residual method, and the radial basis function in meshless method to interpolate the virtual source function on the virtual boundary, the Virtual Boundary Meshless Galerkin Method(VBMGM)is formed. VBMGM has both the advantages of boundary element method and meshless method. And the weighted value is the partial derivative displacement or surface force, whose numerical meaning is clear. Equation formed is of symmetry. The specific numerical scheme of VBMGM is deduced in detail. It is easily programmed and researched by other scholars.Numerical example is the water holes dual arrangement of Three Gorges Project in the literature. The results reveal the feasibility and the accuracy of VBMGM, by computing different distances of virtual boundary and real boundary,different Gauss points on each element, and different virtual nodes on virtual boundary to interpolate the virtual source function.