基于平面问题的位移压力混合配点法

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.

Mixed Displacement-Pressure Collocation Method for Plane Elastic Problems

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.