On the mechanical inconsistency of symmetrization of unsymmetric coupling matrices for BEFEM discretizations of solids

SUMMARYIn the present paper, a scheme is developed for the coupled FE/BE analysis of a plate-foundation interaction problem, in which the boundary element equations of the foundation are not explicitly assembled with the finite element equations of the plate, but instead an iterative procedure is proposed to obtain the final coupled solution. This iterative scheme preserves the nature of the BE and FE approaches and the coupled procedure can be easily implemented within an integrated FEMjBEM software environment. The scheme also reduces the computer storage requirement and avoids the error introduced by symmetrization of the BE equations. In addition, some important issues related to the scheme, such as convergence conditions and parameter se!ection, are discussed. A numerical example is provided to illustrate pthe benefits of the scheme. It is noted, however, that the overall performance of the proposed scheme when compared with the conventional direct solution of the unsymmetric equations arising from the explicit coupling of the FE and BE equations, depends on the choice of a free parameter and a matrix contained in the scheme.

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“…The corresponding step in the incremental form becomes R,AU, = -AR, + aRLAU,-l (14) with AU-= 0; while the other steps remain unchanged.…”

Section: Untilmentioning

confidence: 99%

Iterative Solution of Coupled Fe/Be Discretizations for Plate-Foundation Interaction Problems

Feng

Owen

1996

Int. J. Numer. Meth. Engng.

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“…In the practical implementation of this approach, the inverse of N A 11 is required to be computed at each step. In order to perform this in a computationally efficient way, we can compute and store the LU decomposition of N A 11 and obtain the solutions for N A 01 N A 1 11 N A 10 and N A 01 N A 1 11 r 1 by forward and backward substitution whenever required. Algorithm (1) details the monolithic solution approach including the Schur complement calculations.…”

Section: Solution Proceduresmentioning

confidence: 99%

“…Domain decomposition techniques improvements also include:iterative coupling [25][26][27] and overlapping domain decomposition [28]. The stability of the coupled numerical systems was investigated in [11,29,30].The research significance of coupling BEM and FEM can be demonstrated through non-linear applications where the BEM domain is a linear elastic sub-domain and the FEM is a sub-domain susceptible to a localized non-linearity. For illustration, consider a large elastic domain with localized points of stress concentrations introducing localized non-linear behaviour such as fracture process zones [31,32].…”

mentioning

confidence: 99%

Adaptive modeling of damage growth using a coupled FEM/BEM approach

Mobasher

Waisman

2015

Numerical Meth Engineering

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SUMMARYWe propose a coupled boundary element method (BEM) and a finite element method (FEM) for modelling localized damage growth in structures. BEM offers the flexibility of modelling large domains efficiently, while the non-linear damage growth is accurately accounted by a local FEM mesh. An integral-type nonlocal continuum damage mechanics with adapting FEM mesh is used to model multiple damage zones and follow their propagation in the structure. Strong form coupling, BEM hosted, is achieved using Lagrange multipliers. Because the non-linearity is isolated in the FEM part of the system of equations, the system size is reduced using Schur complement approach, then the solution is obtained by a monolithic Newton method that is used to solve both domains simultaneously. The coupled BEM/FEM approach is verified by a set of convergence studies, where the reference solution is obtained by a fine FEM. In addition, the method is applied to multiple fractures growth benchmark problems and shows good agreement with the literature.

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“…The response at any level of the structure can be obtained by standard techniques, i.e., through a FEM discretization of the structure, in terms of the total motion at the foundation level. Early attempts to symmetrize BEM matrices have not been successful (Mang et al 1989). (37).…”

Section: Dynamics Of Foundationsmentioning

confidence: 99%