A nodal position finite element method for plane elastic problems

Abstract

This paper presents a new nodal position finite element method (NPFEM) as an alternative to the existing finite element method (FEM) for plane elastic problem. The newly developed method addresses the complications of the existing FEM in dealing with dynamic problems experiencing large rigid-body motion coupled with small elastic deformation. Unlike the existing FEM that is based on nodal displacements, the new NPFEM uses nodal positions as basic variables to eliminate the need to decouple the elastic deformation from the rigid-body motion. As a result, it can avoid the accumulated errors arising from the existing FEM over a long period of time by comparing the deformed element with its undeformed status directly. This will be very useful in dynamic modeling of mechanical system where the current positions of parts are more meaningful to designers than the displacements. In addition, the new NPFEM has the potential to address the need in bridging the position based molecular dynamics (MD) to the displacement based finite element (FE) modeling in the multiscale MD/FE analysis. Thus, the NPFEM can provide a unified description in multiscale MD/FE modeling in future.