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Elastic analysis of a circumferential crack in an isotropic curved beam using the modified mapping-collocation method
Date
2014-07-01
Author
Amireghbali, Aydin
Çöker, Demirkan
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The modified mapping-collocation (MMC) method was applied to the boundary value problem (BVP) of a circumferential crack in an isotropic elastic curved beam subjected to pure bending moment loading. The stress correlation technique is then used to determine opening and sliding mode stress intensity factor (SIF) values based on the computed stress field near the crack tip. The MMC method aims at solving two-dimensional BVP of linear elastic fracture mechanics (LEFM) circumventing the need for direct treatment of the biharmonic equation by combining the power of analytic tools of complex analysis (Muskhelishvili formulation, conformal mapping, and continuation arguments) with simplicity of applying the boundary collocation method as a numerical solution approach. A good qualitative agreement between the computed stress contours and the fringe shapes obtained from the photoelastic experiment on a plexiglass specimen is observed. A quantitative comparison with FEM results is also made using ANSYS. The effect of crack size, crack position and beam thickness variation on SIF values and mode-mixity is investigated.
Subject Keywords
Modified mapping-collocation (MMC) method
,
Linear elastic fracture mechanics (LEFM)
,
Stress intensity factor (SIF)
,
Circumferential crack
,
Curved beam
,
Complex analysis
URI
https://hdl.handle.net/11511/46852
Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
https://doi.org/10.1016/j.cam.2013.12.053
Collections
Department of Aerospace Engineering, Article
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Elastic analysis of a circumferential crack in an isotropic curved beam using modified mapping-collocation method
Amireghbali, Aydın; Çöker, Demirkan; Department of Aerospace Engineering (2013)
The modified mapping-collocation (MMC) method is applied to analyze a circumferential crack in an isotropic curved beam. Based on the method a MATLAB code was developed to obtain the stress field. Incorporating the stress correlation technique, the opening and sliding fracture mode stress intensity factors (SIF)s of the crack for the beam under pure bending moment load case are calculated. The MMC method aims to solve two-dimensional problems of linear elastic fracture mechanics (LEFM) by combining the powe...
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A. Amireghbali and D. Çöker, “Elastic analysis of a circumferential crack in an isotropic curved beam using the modified mapping-collocation method,”
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, pp. 131–138, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46852.