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径向基函数点插值无网格法(radial point interpolation method,RPIM)是一种新型的无网格法,其形函数具有插值特性,且形式简单,易于施加本质边界条件。文中介绍了径向基函数点插值无网格法的基本原理,推导了三维情况下点插值无网格法的基本公式。从变分原理出发,结合比奥固结理论,建立了流-固耦合的三维点插值无网格法基本方程和数值积分方法,并开发了相应计算程序。通过三维悬臂梁和单向固结问题的数值试验,验证了该方法对三维弹性问题和流-固耦合问题的适用性和有效性。
Radial point function interpolation (RPIM) is a new type of meshless method, its shape function is interpolated and simple in form, so it is easy to apply essential boundary conditions. In this paper, the basic principle of meshless method for radial basis function point interpolation is introduced and the basic formula of point interpolation meshless method is derived. Based on the principle of variational principle and combining with the theory of Biot consolidation, a flow-solid coupling method of three-dimensional meshless point-free meshless method and numerical integral method is established and the corresponding calculation program is developed. The numerical experiments of three-dimensional cantilever beams and unidirectional consolidation problems verify the applicability and effectiveness of this method to three-dimensional elastic problems and fluid-solid interaction problems.