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Two singular points finite elements in the analysis of kinked cracks

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Abstract

A formulation for incorporating two singular points (TSP) of variable orders in a single finite element is presented. Though the element does not satisfy any of the convergence criterion, its performance is found to be good, which has been demonstrated by considering number of examples on kinked cracks. In each case only one such element is incorporated in the whole discretization. These examples illustrate the usefulness of the element to analyse kinked cracks of various sizes and shapes and subjected to different loading and boundary conditions. Computed J-integrals are compared with analytical solutions, wherever possible, and the accuracy appears quite good. Effect of size of the element on, and the path independence of, J are also examined.

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Abbreviations

ξ, η:

conventional natural coordinate system

ρ1, ρ2 :

another elemental natural coordinate system

L ij :

equation of side ij of an element

A ij , B ij :

constants

N i :

shape function associated node i

λ1, λ2 :

constants associated with the order of singularities

α, β:

an elemental natural coordinate system

u i , v i :

displacement components in the Cartesian directions

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Authors and Affiliations

  1. Reactor Engineering Division, Bhabha Atomic Research Centre, 400 085, Bombay, India

    B. K. Dutta & A. Kakodkar

  2. Department of Mechanical Engineering, Indian Institute of Technology, 400 076, Bombay, India

    S. K. Maiti

Authors
  1. B. K. Dutta
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  2. A. Kakodkar
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  3. S. K. Maiti
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Communicated by S. N. Atluri, December 8, 1989

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Dutta, B.K., Kakodkar, A. & Maiti, S.K. Two singular points finite elements in the analysis of kinked cracks. Computational Mechanics 7, 329–339 (1991). https://doi.org/10.1007/BF00350162

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  • DOI: https://doi.org/10.1007/BF00350162

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