Plane elasticity problems by barycentric rational interpolation collocation method and a regular domain method

Abstract

SummaryBarycentric 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.

Barycentric Interpolation Collocation Method for Solving Fractional Linear Fredholm-Volterra Integro-Differential Equation

“…Therefore, this method has been applied to solve various equations, such as heat conduction equation [36], generalized Poisson equation [37], fractional differential equation [38], and fractional reaction-diffusion equation [39]. At the same time, the BICM is also utilized to solve some engineering problems, such as the plane elasticity problem [40], the bending problem of elliptic plate [41], and the numerical approximation of Darcy flow [42].…”