Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
The Enriched Modified Local Green’s Function Method applied to static fracture mechanic problems
Submission Author:
Ramon Macedo Corrêa , PR , Brazil
Co-Authors:
Ramon Macedo Corrêa, Marcos Arndt, ROBERTO Dalledone Machado
Presenter: Ramon Macedo Corrêa
doi://10.26678/ABCM.COBEM2023.COB2023-0112
Abstract
The Modified Local Green’s Function Method (MLGFM) is an integral method hybrid of the Boundary Element Method (BEM) and the Finite Element Method (FEM). Unlike BEM, the MLGFM does not require a known expression of a Green Function or a fundamental solution to solve the integral form of the problem. The MLGFM creates discrete projections of the Green’s function solving an auxiliary domain problem, and this problem can be achieved, for example, by the FEM formulation. The main characteristic of the MLGFM is to present good convergence for displacement in all the domain and for the tractions on the boundary. Although most research in MLGFM uses the FEM to obtain the discrete projections of the Green’s functions, any method based on finite elements can be used. In this paper the Generalized Finite Element Method (GFEM) will be used to achieve this goal. The GFEM uses the Partition of Unity Method idea to bring previous knowledge about the solution of the problem to enrich the traditional FEM approximation space with appropriate functions. The GFEM is widely used for fracture mechanic problems because allows the creation of discontinuous elements through the enrichment using Heaviside functions in the crack interface and functions with asymptotic derivatives to describe the stress fields around the crack tip. These two enrichments allow us to describe with more precision the stress in the tip region and to monitor the crack evolution without the need of remeshing. The idea of this paper is to bring the GFEM enrichment techniques to the MLGFM in order to describe the displacement field and the stress fields of 2D static crack problems.
Keywords
Green Functions, Generalized Finite Element Method, Boundary Element Method, Fracture Mechanics
