Hybrid stress analysis of boundary and finite elements by a super-element method

Kohno, Kazukiyo; Tsunada, Tomohiro; Seto, Hideyuki; Tanaka, Michio

doi:10.1016/0168-874x(91)90043-x

Cited by 6 publications

(2 citation statements)

References 2 publications

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“…The earliest recorded implementations of the coupled BEM‐FEM systems were presented by Zienkiewicz and Brebbia . Since then, many contributions have been recorded on the deployment of BEM‐FEM for the solution of linear elasticity and other potential‐type problems e.g. heat conduction and fluid flow .…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

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

Mobasher

Waisman

2015

Numerical Meth Engineering

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“…89, 90, 98, 176. Different procedures were proposed to different specific purposes, mainly for BEM applications to problems in which symmetry represents a feature of paramount importance, like BEM/FEM coupling, Refs 90,. 176 (Sec.…”

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confidence: 99%

Symmetric Galerkin boundary element method for quasi-brittle-fracture and frictional contact problems

Maier

Novati

Cen

1993

Computational Mechanics

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This review concerns a methodology for solving numerically, to engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form; the discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager's sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions, some quadratic forms have a clear energy meaning, variational properties characterize the solutions and other results, invalid in traditional boundary element methods, enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, computer implementations. Areas and aspects which at present require further research are identified and comparative assessments are attempted with respect to traditional boundary integral-element methods.

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Numerical solution of the flow of thin viscous sheets under gravity and the inverse windscreen sagging problem

Hunt

2002

Numerical Methods in Fluids

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The slumping of a thin sheet of very viscous liquid glass is used in the manufacture of windscreens in the automotive industry. The governing equations for an asymptotically thin sheet with variable viscosity are derived in which the vertical coordinate forms the centre‐line of the sheet. The time‐dependant equations have been solved numerically using the backward Euler method to give results in both two and three dimensions. The flow of an initially flat sheet falls freely under gravity until it becomes curved and the flow becomes very slow in the ‘slumped’ phase. Finally the sheet freefalls as the thickness becomes small at the boundaries. The inverse problem in which the viscosity profile is to be determined for a given shape can be solved as an embedding problem in which a search is made amongst the forward solutions. Possible shapes in the two‐dimensional problem are very restrictive and are shown to be related to the sheet thickness. In three dimensions the range of shapes is much greater. Copyright © 2002 John Wiley & Sons, Ltd.

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Hybrid stress analysis of boundary and finite elements by a super-element method

Cited by 6 publications

References 2 publications

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

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

Symmetric Galerkin boundary element method for quasi-brittle-fracture and frictional contact problems

Numerical solution of the flow of thin viscous sheets under gravity and the inverse windscreen sagging problem

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