Barycentric rational interpolation collocation method (BRICM) for solving plane elasticity problems with high accuracy is presented. The plane elasticity problems on a circular or rectangular domain can be solved directly by BRICM. Embedded the irregular domain into a regular (circular or rectangular) domain, the governing equations of plane elasticity on regular domain are discretized by the differentiation matrices based on barycentric rational interpolation to form a system of algebraic equations. Discrete boundary conditions are obtained using barycentric rational interpolation. The irregular boundary conditions are imposed by the additional method to form an over‐constraint linear system of algebraic equations. Numerical experiments are presented to illustrate the efficiency and high computing precision of proposed method.

中文翻译：

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重心有理插值搭配法和正则域法求解平面弹性问题

提出了重心有理插值配点法（BRICM），可以高精度地求解平面弹性问题。圆形或矩形区域上的平面弹性问题可以通过BRICM直接解决。将不规则域嵌入到规则（圆形或矩形）域中，基于重心有理插值的微分矩阵将规则域上平面弹性的控制方程离散化，从而形成一个代数方程组。使用重心有理插值获得离散边界条件。附加方法施加不规则边界条件，以形成代数方程组的过度约束线性系统。数值实验表明了该方法的有效性和较高的计算精度。