Radial Basis Collocation Method for Nearly Incompressible Elasticity

Abstract

Strong form collocation using radial basis functions approximation, which is called the radial basis collocation method, is an efficient method for solving partial differential equations or integral equations because it has implementation simplicity and exponential convergence. In this work, the radial basis collocation method is introduced in conjunction with a least-squares scheme to suppress the volumetric locking in nearly incompressible elastic problems. Radial basis approximation, which possesses infinite continuity, is rich enough to ensure the divergence-free condition. Modal analysis proves that all the nonphysical locking modes can be removed, which eliminates the locking effect. Numerical studies validate the good performance of the proposed method. Exponential convergence is obtained as expected, and no pressure oscillation is observed.