Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity

Abstract

SUMMARYThe coupling of Finite Element Method (FEM) with a Boundary Element Method (BEM) is a desirable result that exploits the advantages of each. This paper examines the e$cient symmetric coupling of a Symmetric Galerkin Multi-zone Curved Boundary Element Analysis method with a Finite Element Method for 2-D elastic problems. Existing collocation based multi-zone boundary element methods are not symmetric. Thus, when they are coupled with FEM, it is very di$cult to achieve symmetry, increasing the computational work to solve the problem. This paper uses a fully Symmetric curved Multi-zone Galerkin Boundary Element Approach that is coupled to an FEM in a completely symmetric fashion. The symmetry is achieved by symmetrically converting the boundary zones into equivalent &macro "nite elements', that are symmetric, so that symmetry in the coupling is retained. This computationally e$cient and fast approach can be used to solve a wide range of problems, although only 2-D elastic problems are shown. Three elasticity problems, including one from the FEM-BEM literature that explore the e$cacy of the approach are presented.

Impedance of flexible suction caissons

“…However, as an alternative a coupling of an FE shell model with the so-called symmetric Galerkin boundary-element method (SGBEM) may be applied [33]. An extensive review of the developments regarding the SGBEM can be found in the work by Ganguly et al [34,35].…”

Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral

“…Indeed, FE method is appropriate for structural analysis, whereas BE method is well-suited to linear elastic problems involving unbounded domains. Nevertheless, the coupling of FE and collocation BE method may involve problems concerning the lack of symmetry of the coefficient matrix in BE formulations and difficulties in the imposition of interface conditions; an extensive overview is given in [5]. The first difficulty can be removed by adopting Symmetric Galerkin BEM-FEM coupling procedures, see e.g.…”

A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics

“…/j.ijsolstr.2006 The first type essentially treats the subdomain BEM as a macro-finite element (super-element). The displacement-traction equations governing the boundary element subdomain are transformed into displacement-force equations and assembled with those of the finite element method (Wearing and Sheikh, 1988;Ganguly et al, 2000;Aour, 1997;Aour et al, 2005). Conversely, the BEM approach treats the FE subdomain Rice's integral [K] stiffness matrix K I stress intensity factor for mode I N number of boundary elements N i (n) shape functions n i unit direction normal r distance between the field point and the source point R distance from the crack-tip S integration contour for evaluation of J-integral {t n } vector containing the nodal tractions t x , t y traction components in the x-and y-directions, respectively T superscript indicating transpose of a matrix {u n } vector containing the nodal displacements U strain energy density u, v displacement components in the x-and y-directions, respectively u i (x f ), u i (x s ) displacements at field and source points, respectively W work done by external loads x, y…”