Improved Coupling of Finite Shell Elements and 3D Boundary Elements

Haas, Michael; Helldörfer, Bastian; Kühn, G.

doi:10.1007/s00419-006-0037-5

Cited by 12 publications

(3 citation statements)

References 15 publications

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“…Coupling approaches can be either FEM-driven or BEM-driven. In the former, the BEM subdomain is interpreted as a macro finite element that can be assembled easily to the FEM stiffness matrix Haas, Helldörfer, and Kuhn (2006); Mouhoubi (2000) and the global matrix equation is solved as a FE system. By contrast, the latter option, the FE subdomain contribution is incorporated into a boundary element system, see Brebbia and Georgiou (1979); Zienkiewicz, Kelly, and Bettess (1977).…”

Section: Grid Reinforcement By Fem-bem Couplingmentioning

confidence: 99%

Modelling of the fatigue cracking resistance of grid reinforced asphalt concrete by coupling fast BEM and FEM

Dansou

Mouhoubi

Chazallon

et al. 2022

Road Materials and Pavement Design

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We present a computational modeling approach aimed at investigating the effect of fiber grid reinforcement on crack opening displacement and fatigue crack propagation. Grid reinforcements are modeled using elastic membrane finite elements, while the cracked concrete is treated using a symmetric boundary element method (BEM), which in particular allows easy geometrical modelling and meshing of cracks. The BEM is accelerated by the fast multipole method, allowing the handling of potentially large BEM models entailed by three-dimensional configurations hosting multiple cracks. Fatigue crack growth is modelled using the Paris law. The proposed computational approach is first verified on a reinforced cracked beam, and then applied to a three-dimensional configuration featuring a grid-reinforced asphalt pavement.

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Section: Grid Reinforcement By Fem-bem Couplingmentioning

confidence: 99%

Modelling of the fatigue cracking resistance of grid reinforced asphalt concrete by coupling fast BEM and FEM

Dansou

Mouhoubi

Chazallon

et al. 2022

Road Materials and Pavement Design

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“…The primary objective is to compromise between the requirement of computational resources and accuracy of predicted results. Within the context of linear elasticity, there have been several investigations directed towards the coupling of the conventional BEM and the standard FEM e.g., 24-26 and the coupling of the strongly singular SGBEM and the standard FEM e.g., [27][28][29][30] . It should be emphasized that the former type of coupling procedure generally destroys the desirable symmetric feature of the entire system of linear algebraic equations whereas the latter type requires special numerical treatment of strongly and hyper singular integrals e.g., 31,32 .…”

Section: Introductionmentioning

confidence: 99%

Stress Analysis of Three‐Dimensional Media Containing Localized Zone by FEM‐SGBEM Coupling

Rungamornrat

Sripirom

2011

Mathematical Problems in Engineering

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This paper presents an efficient numerical technique for stress analysis of three-dimensional infinite media containing cracks and localized complex regions. To enhance the computational efficiency of the boundary element methods generally found inefficient to treat nonlinearities and non-homogeneous data present within a domain and the finite element method (FEM) potentially demanding substantial computational cost in the modeling of an unbounded medium containing cracks, a coupling procedure exploiting positive features of both the FEM and a symmetric Galerkin boundary element method (SGBEM) is proposed. The former is utilized to model a finite, small part of the domain containing a complex region whereas the latter is employed to treat the remaining unbounded part possibly containing cracks. Use of boundary integral equations to form the key governing equation for the unbounded region offers essential benefits including the reduction of the spatial dimension and the corresponding discretization effort without the domain truncation. In addition, all involved boundary integral equations contain only weakly singular kernels thus allowing continuous interpolation functions to be utilized in the approximation and also easing the numerical integration. Nonlinearities and other complex behaviors within the localized regions are efficiently modeled by utilizing vast features of the FEM. A selected set of results is then reported to demonstrate the accuracy and capability of the technique.

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“…S IB = S IF = S IR ) and there is, of course, no distinction between a point y and its closest point projection onto one of the surfaces. The weak-form statements of the continuity conditions are then equivalent to the strong-form statements (25)- (27) and it follows that E ≡ 0. However, in the context of a numerical implementation in which the three interfaces are discretized separately, the quantity E does not in general vanish; a discussion of the error involved in discarding this term will be given further below after the numerical implementation of the method is described.…”

mentioning

confidence: 97%

SGBEM–FEM coupling for analysis of cracks in 3D anisotropic media

Rungamornrat¹,

Mear²

2010

Numerical Meth Engineering

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SUMMARYA weakly singular symmetric Galerkin boundary element method (SGBEM) is coupled with the standard finite element method (FEM) in order to establish an accurate and efficient numerical technique for analysis of fractures in three-dimensional, anisotropic, linearly elastic media. In the strategy, the weakly singular SGBEM developed by Rungamornrat and Mear (Int. J. Solids Struct. 2008; 45:1283-1301 Comput. Methods Appl. Mech. Engrg 2008; 197:4319-4332) is utilized to model a small-scale region containing the crack while the (possibly large and complex) compliment region is treated by the FEM. The coupled technique exploits the positive features of both methods; the SGBEM proves to be a convenient and highly accurate method for obtaining mixed-mode stress intensity factors along the crack front, whereas the FEM is very efficient for modeling large-scale problems in the absence of cracks. An important aspect of the formulation and implementation of the technique is that continuity of displacement and traction across the interface between the SGBEM and FEM regions is enforced in a weak sense. This allows the two regions (one modeled by the SGBEM and the other by the FEM) to be discretized independently without the need for the resulting meshes to conform on the interface separating the regions, and this flexibility in the discretization process leads to a significant reduction in the modeling effort. To demonstrate the utility and accuracy of the technique, several boundary value problems involving both embedded and surface breaking cracks are treated, and it is shown that the coupled technique yields highly accurate stress intensity factors that exhibit only a slight dependence upon mesh refinement.

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Improved Coupling of Finite Shell Elements and 3D Boundary Elements

Cited by 12 publications

References 15 publications

Modelling of the fatigue cracking resistance of grid reinforced asphalt concrete by coupling fast BEM and FEM

Modelling of the fatigue cracking resistance of grid reinforced asphalt concrete by coupling fast BEM and FEM

Stress Analysis of Three‐Dimensional Media Containing Localized Zone by FEM‐SGBEM Coupling

SGBEM–FEM coupling for analysis of cracks in 3D anisotropic media

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