A Finite Element-Meshless Hybrid Method (FEMLHM) of Elasticity Problem and Its Applications

In this paper, a finite element-meshless hybrid method (FEMLHM) is proposed to numerically simulate the elasticity problems. In the proposed FEMLHM, the nodal displacement components of a discrete structure are determined by the finite element method (FEM). The approximation formulations of displacement field, strain field and stress field are all developed using the radial basis point interpolation method (RPIM), which is one of the meshless approximation methods. Especially, a compactly supported and higher-order continuous radial basis function is used in the RPIM to ensure that all fields of displacement, stress and strain are continuous in the whole problem domain. Therefore, the proposed FEMLHM overcomes the limitation that both fields of stress and strain are not continuous in the FEM. In addition, the nodal displacements are calculated by FEM, which makes the proposed FEMLHM has higher computational efficiency than a meshless method. The displacement field and stress field of a cantilever beam problem are first numerically simulated to verify the proposed FEMLHM. Then it is used to numerically simulate the stress fields of a circular ring under uniform pressures. The simulation results are compared with both FEM and analytical solution to illustrate that the proposed FEMLHM can numerically simulate an elasticity problem more effectively and accurately than FEM. The proposed FEMLHM is easy to use, and has an application potential in a lot of engineering and science fields.