Collocation Discrete Least Squares (CDLS) Method for Elasticity Problems and Grid Irregularity Effect Assessment

A meshless approach, collocation discrete least square (CDLS) method, is extended in this paper, for solving elasticity problems and grid irregularity effect is assessed. In the present CDLS method, the problem domain is discretized by distributed field nodes. The field nodes are used to construct the trial functions. The moving least-squares interpolant is employed to construct the trial functions. Some collocation points that can be independent of the field nodes are used to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of the residuals for the collocation points. The final stiffness matrix is symmetric and therefore can be solved directly via efficient solvers. The boundary conditions are easily enforced by the penalty method. The present method does not require any mesh so it is a truly meshless method. Numerical examples are studied in detail, which show that the present method is stable and possesses good accuracy, high convergence rate and high efficiency for both regular and irregular point distribution.