Three-dimensional radial point interpolation meshfree method and its application to consolidation analysis

ZHANG Yan; PENG Chong; LI Xing

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Three-dimensional radial point interpolation meshfree method and its application to consolidation analysis

更新时间：2026-06-25

- Three-dimensional radial point interpolation meshfree method and its application to consolidation analysis
- Vol. 32, Issue 6, (2011)
- 作者机构：
  
  1. 中国电力科学研究院,北京,100192
  2. 清华大学水沙科学与水利水电工程国家重点实验室,北京,100084
  3. 河北理工大学轻工学院,河北,唐山,063000
- 作者简介：
- 基金信息：
- DOI：
  CLC： TB115
- Online First：21 June 2011，
  
  Published：2011
- 稿件说明：
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ZHANG Yan, PENG Chong, LI Xing. Three-dimensional radial point interpolation meshfree method and its application to consolidation analysis[J]. 2011, 32(6).
DOI：

ZHANG Yan, PENG Chong, LI Xing. Three-dimensional radial point interpolation meshfree method and its application to consolidation analysis[J]. 2011, 32(6). DOI：

摘要

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

Abstract

The radial point interpolation method (RPIM) is a new-style meshfree method. As its shape functions have the Kronecker delta functions property

essential boundary conditions can be enforced as easily as in the finite element method. The basic principle of RPIM is introduced; and the basic formulas of RPIM are derived. Based on the variational principle and Biot’s consolidation theory

the basic equations and numerical integration method of RPIM are proposed; and the corresponding calculation program is developed. Numerical examples of 3D cantilever beam and 1D consolidation problem are given to verify the validity and availability of the RPIM to the 3D elastic problem and consolidation problem

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