Applications of a Nodal-Integration-Based Finite Element Method to Non-Linearc Problems

Abstract

In this paper, we firstly introduce a nodal-integration-based finite element method. The method allows the use of first-order tetrahedral elements without suffering from the volumetric locking problem. The most important advantage of tetrahedral meshes is that they can be automatically generated for complex geometries using existing reliable meshing tools. The method is then applied to 3 types of applications. The first application is a large displacement, large strains elastic-plastic simulation on a notched specimen. The second application is an elastic-plastic bending problem. And the last example concerns the numerical simulation of the thermo-mechanical problem. In all the cases, the solution given by the nodal-integration-based FEM is compared to more classical FEM results.

Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods

“…Although the main focus of this paper is not on comparisons of CPU times and storage requirements in the classical FEM and Jia et al's [20] NIFEM-which have already been discussed by Jia et al [20,26]-some quick remarks on the subject may be welcome. The CPU time required by the NIFEM (be it without or with the procedure of Section 2 for free surface nodes) is approximately 2.7 times larger than that required by the classical FEM (5.37 h or 5.51 h versus 2.01 h)-most probably because of the increased bandwidth of the LHS matrix in the NIFEM.…”