A new discontinuous Galerkin method for Kirchhoff–Love shells

Noels, Ludovic; Radovitzky, Raúl

doi:10.1016/j.cma.2008.01.018

Cited by 55 publications

(89 citation statements)

References 31 publications

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“…The discontinuous Galerkin method was proposed in the seventies of the previous century in [42] and constant development of the method has been observed since the time, see [9,13,19,34,44] and its application to many problems, such as analysing plates and shell [17,36], elastic wave propagation [6,7] or fluid floats [3,32]. The present paper constitutes another step towards developing the DG method, with particular attention to the DGFD method.…”

Section: Introductionmentioning

confidence: 95%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

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The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

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Section: Introductionmentioning

confidence: 95%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

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“…Γ I = Γ IU , can be derived by following exactly the path set for other elliptic problems [52,59]. However although the second set of equations (66) is linear, the first set of equations (65) is not and the properties rigorously hold in the linearized form only.…”

Section: Numerical Propertiesmentioning

confidence: 99%

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

Becker

Noels

2014

Computer Methods in Applied Mechanics and Engineering

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One current challenge related to computational fracture mechanics is the modeling of ductile fracture and in particular the damage to crack transition. On the one hand, continuum damage models, especially in their non-local formulation which avoids the loss of solution uniqueness, can capture the material degradation process up to the localization of the damage, but are unable to represent a discontinuity in the structure. On the other hand cohesive zone methods can represent the process zone at the crack tip governing the crack propagation, but cannot account for the diffuse material damaging process.In this paper we propose to combine, in a small deformations setting, a non-local elastic damage model with a cohesive zone model. This combination is formulated within a discontinuous Galerkin finite element discretization. Indeed this DG weak formulation can easily be developed in a non-local implicit form and naturally embeds interface elements that can be used to integrate the traction separation law of the cohesive zone model. The method remains thus consistent and computationally efficient as compared to other cohesive element approaches.The effects of the damage to crack transition and of the mesh discretization are respectively studied on the compact tension specimen and on the double-notched specimen, demonstrating the efficiency and accuracy of the method.

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“…This can be overcome by discretizing the director field or introducing rotational degrees of freedom [29,30,31], or by considering more elaborate variational formulations such as in discontinuous Galerkin methods [32,33]. Instead, here we focus on methods relying on smooth basis functions.…”

Section: Introductionmentioning

confidence: 99%

Phase-field modeling of fracture in linear thin shells

Amiri

Millán

Shen

et al. 2014

Theoretical and Applied Fracture Mechanics

285

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We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximumentropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes.

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A new discontinuous Galerkin method for Kirchhoff–Love shells

Cited by 55 publications

References 31 publications

Very high order discontinuous Galerkin method in elliptic problems

Very high order discontinuous Galerkin method in elliptic problems

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

Phase-field modeling of fracture in linear thin shells

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