Using New Hp-Cloud Approximate Function in Meshless Finite Volume Method for Solving 2D Elasticity Problems

Abstract

In this paper, a novel Hp-Cloud approximate function with Kronecker delta property, named herein as HPCK, is utilized in a meshless finite volume method for two-dimensional elasticity problems. Using the enrichment parts in the HPCK approximate functions leads to excessive unknowns corresponding to nodal points. Therefore, the obtained equations from the ordinary finite volumes method (FVM) are underdetermined. We tackled this problem by proposing an algorithm that considers more control volumes (CVs), known as enrichment CVs (ECVs), inside the main CVs. Following the fulfillment of the equilibrium equations on these ECVs, sufficient equations are obtained to solve the unknowns. In the proposed FVM with HPCK approximate function, the boundary conditions are easily and directly enforced due to Kronecker delta property of HPCK. Moreover, the proposed method leads to a fast convergence and highly accurate results for the studied test problems. In addition, unlike approximation functions like MLS, this method does not involve matrix inversions, which leads to low computational costs and CPU usage while achieving desirable accuracy levels.