不规则区域平面弹性问题的正则区域重心插值配点法

将不规则区域嵌入到规则的矩形区域，在矩形区域上将弹性平面问题的控制方程采用重心Lagrange插值离散，得到控制方程矩阵形式的离散表达式。在边界节点上利用重心插值离散边界条件，规则区域采用置换法施加边界条件，不规则区域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，采用最小二乘法进行求解，得到整个规则区域上的位移数值解。利用重心插值计算得到不规则区域内任意节点的位移值，计算精度可到10^-14以上。数值算例验证了所建立方法的有效性和计算精度。

A regular domain collocation method based on barycentric interpolation for solving plane elastic problems in irregular domains

By embedding the irregular domain into a rectangular domain,the governing equations of plane elasticity problems in a rectangular domain are discretized by the differentiation matrices based on barycentric Lagrange interpolation to form a system of algebraic equations.Using barycentric interpolation to discrete boundary conditon on the boundary nodes,the regular boundary conditions are imposed by replacement method,and the irregular boundary conditions are imposed by additional method to form an over-constrainted linear system of algebriac equations.The least-squares method is applied to obtain the displacements on the regular domain.Any nodal displacements in the irregular region can be evaluted by interpolating with barycentric interpolation.The errors of the presented method are calculated in irregualar region.The numerical examples demonstrate that the proposed method has advantages of simple computational formulations,being easy to program and high precision.