Three types of meshless finite volume method for the analysis of two-dimensional elasticity problems

This paper presents three schemes of 2D meshless finite volume (MFV) method, referred to as MFV with overlapping control volumes (MFV1), MFV with irregular non-overlapping control volumes (MFV2) and MFV with regular non-overlapping control volumes (MFV3). The methods utilize the local symmetric weak form of system equation and the interpolation functions constructed using the weighted multi-triangles method (WMTM) which is recently developed by the present authors. The proposed formulation involves only integrals over the boundaries of control volumes. The performance of the proposed schemes is studied in three benchmark problems. A comparative study between the predictions of the above MFV schemes and finite element method (FEM) shows the superiority of WMTM-based MFV1 and MFV2 over FEM.