A New Nodal-Integration-Based Finite Element Method for the Numerical Simulation of Welding Processes

Abstract

This paper aims at introducing a new nodal-integration-based finite element method for the numerical calculation of residual stresses induced by welding processes. The main advantage of the proposed method is to be based on first-order tetrahedral meshes, thus greatly facilitating the meshing of complex geometries using currently available meshing tools. In addition, the formulation of the problem avoids any locking phenomena arising from the plastic incompressibility associated with von Mises plasticity and currently encountered with standard 4-node tetrahedral elements. The numerical results generated by the nodal approach are compared to those obtained with more classical simulations using finite elements based on mixed displacement–pressure formulations: 8-node Q1P0 hexahedra (linear displacement, constant pressure) and 4-node P1P1 tetrahedra (linear displacement, linear pressure). The comparisons evidence the efficiency of the nodal approach for the simulation of complex thermal–elastic–plastic problems.

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

“…Compared with the reference solution (Q2 element), the nodal-integrationbased FEM exhibits a behavior a little too flexible. But, despite the increase of the matrix bandwidth it leads [18], the nodal-integration-based FEM gives a CPU time significantly less than the ones obtained with Q1P0 and P1P1 elements for a problem gathering the same number of nodes. This is related to the elastoplastic resolutions that are performed at the elements integration points with the Q1P0 and P1P1 meshes and at the nodes (which are much less numerous than the integrations points) with the nodal-integration-based FEM.…”

“…Ce method has been extended for 3D thermo-mechanical applications by Jia et al [18]. In this paper, we present several benchmark tests by comparing the results obtained with the nodal-integration-based finite element method as proposed by Jia et al [18] with those coming from more classical finite element solutions. All the simulations are performed using SY SW ELD T M software.…”

“…The combined use of the Finite Element Method with the SCNI technique has been developed in 2D on the basis of triangular meshes by Qual et al [16] and Canales et al [17]. Ce method has been extended for 3D thermo-mechanical applications by Jia et al [18]. In this paper, we present several benchmark tests by comparing the results obtained with the nodal-integration-based finite element method as proposed by Jia et al [18] with those coming from more classical finite element solutions.…”

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

“…The second and third computations are based on the NIFEM depicted in Jia et al [20]; the second does not use the special procedure of Section 2 for nodes belonging to the free surface, whereas the third does. The mesh used in both simulations, shown in Figure 2, consists of the same 98,578 nodes as in the mesh of Figure 1, but now 540,000 linear 4-node tetrahedral elements, obtained by splitting each hexahedron into six tetrahedra.…”

“…Such an approach may elegantly be combined with the FEM, by defining the subvolume containing a given node in relation to the finite elements containing it [18,19]. A comparison, and a proof of the equivalence, of some of the techniques proposed for evaluation of nodal strains was very recently provided by Jia et al [20].…”