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Contact analysis using Trefftz and interface finite elements

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Wang K. Y. , Dhanasekar M. , Qin Q. H. , Kang Y. L.

Computer Assisted Mechanics and Engineering Sciences

2006

tom Vol. 13, No. 3

457-471

Hybrid-Trefftz (HT) finite element (FE) analysis of two-dimensional elastic contact problems is addressed with the aid of interface elements and an interfacial constitutive relation. This paper presents the formulation of a four-noded HT finite element for discretizing the contacting bodies and a four-noded interface element that could be embedded in the prospective contact zone for simulating the interaction behaviour. Due to the superior performance, the Simpson-type Newton--Cotes integration scheme is utilized to compute interface element formulation numerically. In order to evaluate the applicability of the present approach two benchmark examples are investigated in detail. Comparisons have been made between the results by the present approach and analytical as well as traditional FE solutions using ABAQUS software.

Interaction of surface and internal cracks in railhead

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Dhanasekar M. , Han J. , Qin Q. H.

Computer Assisted Mechanics and Engineering Sciences

2007

tom Vol. 14, No. 1

79-89

This paper presents a two-dimensional model for the analysis of interaction between surface and internal cracks in the railheads subjected to wheel loading. The shape of the railhead, the surface crack and the internal crack are modelled as curved cracks defined by the theory of continuous distribution of dislocation in an infinite body. From the boundary conditions along these cracks, a system of singular integral equations is deduced. Influence functions in these singular integral equations are first expanded into the Cauchy kernel multiplying normal functions and later are reduced to a system of linear equations and solved numerically. Stress intensity factors (SIFs) of the surface crack tip are calculated from the numerical solution of distribution function along these cracks directly, eliminating need for any indirect integral method. The method does not require meshing and hence idealisation of the shapes of the cracks, thereby improving accuracy and reducing pre- and post processing efforts. Interaction between the internal crack and the surface crack is examined in detail through several examples.