SUMMARYThis paper proposes a Generalized Finite Element Method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off-line and stored in memory in the form of a computational vademecum so that they can be used on-line with negligible cost. This renders a more efficient computational method than traditional Finite Element Methods (FEM) at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing Proper Generalized Decompositions (PGD). Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics which depend on many parameters, such as welding. After introducing the V-GFEM formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes.

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A new efficient updated-Lagrangian strategy for numerical simulations of material forming processes is presented in this work. The basic ingredients are the in-plane-out-of-plane PGD-based decomposition and the use of a robust numerical integration technique (the Stabilized Conforming Nodal Integration). This strategy is of general purpose, although it is especially well suited for plateshape geometries. This paper is devoted to show the feasibility of the technique through some simple numerical examples.

Friction Stir Welding (FSW) is a welding technique the more and more demanded in industry by its multiple advantages. Despite its wide use, its physical foundations and the effect of the process parameters have not been fully elucidated. Numerical simulations are a powerful tool to achieve a greater understanding in the physics of the problem. Although several approaches can be found in the literature for simulating FSW, all of them present different limitations that restrict their applicability in industrial applications. This paper presents a new solution strategy that combines a robust approximation method, based on natural neighborhood interpolation, with a solution separated representation making use of the Proper Generalized Decomposition (PGD), for creating a new 3D updated-Lagrangian strategy for addressing the 3D model while keeping a 2D computational complexity