Speaker
Description
The Finite Element Method (FEM) is one of the most powerful stretegies to solve boundary value problems in solid mechanics. It comes out, however, not without drawbacks, especially when dealing with complex geometries and discontinuities. Over time, several advanced FEMs have been developed to overcome the aforementioned limitations by eliminating or reducing the rigid reliance on the finite elements. These approaches include: (i) Meshless Methods (MMs), which represent the domain of a problem only by a set of arbitrarily distributed nodes; (ii) enriched Finite Element Methods (e-FEMs), which use any a priori knowledge of the solution to improve the finite element approximation space in a continuous Galerkin framework; (iii) the Virtual Element Method (VEM), which allows polytopal discretisation (polygons in 2-D or polyhedra in 3-D) of the geometry; (iv) Isogeometric Analysis (IGA), which exploits Non-Uniform Rational B-Splines (NURBS) as shape functions to blend FEM into CAD. To the best of the authors’ knowledge, a comparative survey of these FEM approaches seems to have drawn a limited attention. The aim of this study relies on an engineering perspective to the aforementioned advanced FEMs, comparing their accuracy and computational performance. Further, we discuss the advantages and disadvantages of the selected models through investigating their interplay with conventional FEM.
References
[1] Zienkiewicz O. C., Taylor R. L., Zhu J., (2005). "The Finite Element Method", Elsevier.
[2] Bathe K. -J., (1996). "Finite Element Procedures", Prentice-Hall.
[3] Liu W.K., Li S., Park H.S. (2022). "Eighty Years of the Finite Element Method: Birth, Evolution, and Future", Arch Computat Methods Eng 29, 4431–4453.