基于平面问题的位移压力混合配点法

doi:10.19596/j.cnki.1001-246x.7585

计算物理 ›› 2018, Vol. 35 ›› Issue (1): 77-86.DOI: 10.19596/j.cnki.1001-246x.7585

基于平面问题的位移压力混合配点法

王兆清, 徐子康

山东建筑大学力学研究所, 济南 250101

收稿日期:2016-11-17 修回日期:2017-02-25 出版日期:2018-01-25 发布日期:2018-01-25
作者简介:王兆清(1965-),男,博士,副教授,从事工程数值分析方法研究,E-mail:sdjzuwang@126.com
基金资助:
国家自然科学基金面上项目（51379113）及山东省自然科学基金重点项目（ZR2016JL006）资助

Mixed Displacement-Pressure Collocation Method for Plane Elastic Problems

WANG Zhaoqing, XU Zikang

Institute of Mechanics, Shandong Jianzhu University, Jinan 250101, China

Received:2016-11-17 Revised:2017-02-25 Online:2018-01-25 Published:2018-01-25

摘要/Abstract

摘要： 引入压力变量，将弹性力学控制方程表达为位移和压力的耦合偏微分方程组，采用重心插值近似未知量，利用重心插值微分矩阵得到平面问题控制方程的矩阵形式离散表达式.采用重心插值离散位移和应力边界条件，采用附加法施加边界条件，得到求解平面弹性问题的过约束线性代数方程组，采用最小二乘法求解过约束方程组，得到平面问题位移数值解.数值算例验证了所提方法的有效性和计算精度.

关键词: 弹性平面问题, 位移压力混合公式, 重心Lagrange插值, 配点法, 无网格

Abstract: Introducing a pressure variable, governing equations of elasticity are expressed as displacements and pressure coupled system of partial differential equations. Barycentric interpolation is applied to approximate unknown functions. Matrix-vector forms of discrete expressions of governing equations for plane elastic problems are obtained by using barycentric interpolation differentiation matrices. Discrete boundary conditions of displacements and pressure are obtained by using barycentric interpolation. Boundary conditions are imposed by additional method to form an over-constrained linear algebra equation system of plane elastic problem. Numerical solutions of displacement for plane elastic problem are solved with least-square method. Numerical examples illuminate efficiency and computing precision of the method.

Key words: plane elastic problem, mixed formula of displacement and pressure, barycentric Lagrange interpolation, collocation method, meshless method

中图分类号:

O343.1

王兆清, 徐子康. 基于平面问题的位移压力混合配点法[J]. 计算物理, 2018, 35(1): 77-86.

WANG Zhaoqing, XU Zikang. Mixed Displacement-Pressure Collocation Method for Plane Elastic Problems[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(1): 77-86.

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基于平面问题的位移压力混合配点法

Mixed Displacement-Pressure Collocation Method for Plane Elastic Problems

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