平面弹性问题的位移-应力混合重心插值配点法  

Barycentric interpolation collocation method based on mixed displacement-stress formulation for solving plane elastic problems

作　　者：王兆清[1] 张磊[1] 徐子康 李金[2] 

机构地区：[1]山东建筑大学力学研究所,济南250101 [2]山东建筑大学理学院,济南250101

出　　处：《应用力学学报》2018年第2期304-308,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金面上项目(51379113);山东省省属优青项目(ZR2016JL006)

摘　　要：提出数值分析平面弹性问题的位移-应力混合重心插值配点法。将弹性力学控制方程表达为位移和应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。使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,应用最小二乘法求解过约束方程组,得到平面弹性问题位移和应力数值解。数值算例结果表明,重心Lagrange插值方法的计算精度可达到10^(-10)量级。位移-应力混合重心插值配点法的计算公式简单、程序实施方便,是一种高精度的无网格数值分析方法。Barycentric Interpolation Collocation Method based on mixed displacement-stress formulation for solving plane elastic problems is proposed. The governing equations of elastic theory are expressed as a coupled system of partial differential equations with displacements and stresses variables. Both displacements and stresses are approximated via tensor-product type barycentric Lagrange interpolation. The matrix-vector form expressions of the governing equations for plane elasticity problem are obtained by using barycentric interpolation differentiation matrices. Discrete boundary conditions of the displacements and stresses are obtained by barycentric interpolation. The additional method is applied to impose boundary conditions, and an over-constrained linear system of algebraic equations for elastic plane problem is constructed. Numerical solutions of displacements and stresses for plane elasticity problem are solved by using least-square method. Some numerical examples are given to verify the effectiveness and accuracy of the proposed method. The numerical results indicate that the computational errors of Lagrange interpolation method would be smaller by 10^(-10) order of magnitude.

关 键 词：弹性力学问题 重心Lagrange插值 微分矩阵 位移-应力混合公式 配点法 

分 类 号：O343.1[理学—固体力学]