2-D infinite element modeling for elastostatic problems with geometric singularity and unbounded domain

Liu, D. S.; Chiou, D. Y.

doi:10.1016/j.compstruc.2005.03.009

Cited by 9 publications

(5 citation statements)

References 18 publications

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“…However, other approaches reported in the literature such as the infinitely small element method (ISEM) of Go & Lin (1990) and the infinite-element method (IEM) of Liu & Chiou (2005), which also employ a self-similar method to create a theoretical infinite number of layers of elements around the crack tip, do not include any theoretical or numerical representation of the crack tip singularity. These approaches seem to rely solely on the use of infinitely small elements to represent the singularity.…”

Section: Super Singular Element Methodsmentioning

confidence: 99%

Super singular element method for two-dimensional crack analysis

Tsang

Oyadiji²

2008

Proc. R. Soc. A.

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Super singular element method (SSEM) is an accurate method devoted to stress singularity analysis accomplished by stress analysts who have little or no experience of fracture mechanics. The basic idea of SSEM is to transform nodal displacements inside a superelement to global variables, which are the coefficients of the Williams eigenfunction series (ES) that accurately represents crack tip singularity. The stress singularity is modelled by the superelement and the Williams' ES, hence refining the finite-element meshes near the singular point and creation of crack faces can be avoided. The stress intensity factor, T-stress, and the higher order coefficients can be obtained directly from the global variables without any post-processing. The implementation of the SSEM is rather easy; since only matrix multiplication and transformation are required. The SSEM has been incorporated into standard finite-element program ABAQUS. Several two-dimensional crack problems have been performed to compare the SSEM with published results.

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Section: Super Singular Element Methodsmentioning

confidence: 99%

Super singular element method for two-dimensional crack analysis

Tsang

Oyadiji²

2008

Proc. R. Soc. A.

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“…Liu and Chiou [21][22][23] utilized IEM formulations to solve a variety of elasticity and singularity problems. In addition, the authors proposed a convergence criterion for the IEM formulation which extended the imaginary "infinity layer" concept to practical applications and ensured the convergence of the overall IE stiffness matrix.…”

Section: Introductionmentioning

confidence: 99%

Development of Plate Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities

2013

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A Plate Infinite Element Method (PIEM) formulation based on Reissner-Mindlin theory is proposed for the stress analysis of cracked plates under bending and tension. The validity of the proposed formulation is demonstrated by comparing the results obtained for the normalized Stress Intensity Factor (SIF) under various loading conditions with the solutions presented in the literature. Importantly, the proposed formulation enables the effects of different crack lengths to be analyzed without the need to re-mesh the computational domain for each simulation/analysis. Overall, the PIEM formulation provides an accurate and computationally-efficient means of analyzing a wide variety of plate bending problems.

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“…Also Zakeri & Xia [9] have examined the railway track by applying 2D-infinite beam element model. Several 2D infinite element models of a beam have been presented [10]. In this paper details related to mapping of an infinite element to a finite element ( Fig.…”

Section: Introductionmentioning

confidence: 99%

Application of 2D-infinite beam elements in dynamic analysis of train-track interaction

Zakeri

Xia

2009

J Mech Sci Technol

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Railway structure is a structure with an infinite length for which its modeling is usually carried out by accepting some assumptions for boundary conditions. In practice, there are various methods of modeling by forming equations of motions and dynamic analysis. One of these methods is modeling the railway track by finite element method. Generally in such modeling, a limited length of a track is modeled and executed by implementing some boundary conditions. Assortment of boundary conditions has an effect on dynamic responses. To reduce such effects, usually the length of the track is chosen to such a measure to minimize the dynamic responses of the end points of the track elements to zero. Doing so would cause an increase in the length of the track and hence add to an equation's degrees of freedom, volume of output and prolongation of analysis time. For this reason, a combination of finite elements and infinite beam elements (two end elements) has been proposed for railway track modeling. Also, matrices of mass, damping and stiffness of one infinite element which has been laid on a visco-elastic bed, have been calculated by implementing selected shape functions. Therefore, by applying two infinite beam elements on either side of the model, a railway track is formed like a beam on an elastic bed which creates the possibility of eliminating the boundary condition effects.

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2-D infinite element modeling for elastostatic problems with geometric singularity and unbounded domain

Cited by 9 publications

References 18 publications

Super singular element method for two-dimensional crack analysis

Super singular element method for two-dimensional crack analysis

Development of Plate Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities

Application of 2D-infinite beam elements in dynamic analysis of train-track interaction

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