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Some elasticity problems of a general anisotropic solid subjected to anti-plane loadings

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Abstract

Plane elasticity problems of a general anisotropic material subjected to both in-plane and anti-plane loadings are formulated based on Lekhnitskii’s complex variable approach. Some useful solutions to half-plane problems and elliptical cavity problems are derived for cases involving anti-plane loadings. Asymptotical crack-tip elastic fields are reviewed and comparisons are made for crack problems and slender elliptical cavity problems. Specifically, it is shown that the stress state at a rounded crack tip can be characterized by a stress rounding factor and the stress intensity factor of the associated slit crack. An important conclusion is that, for a fixed loading condition and a fixed shape of the cavity, the influence of the shape of the cavity on the stress concentration factor can be separated from the influence of the material properties.

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  1. Department of Power Mechanical Engineering, National Tsing Hua University, Hsin Chu, 30013, Taiwan

    Chun-Ron Chiang

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  1. Chun-Ron Chiang
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Correspondence to Chun-Ron Chiang.

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Chiang, CR. Some elasticity problems of a general anisotropic solid subjected to anti-plane loadings. Acta Mech 203, 49–61 (2009). https://doi.org/10.1007/s00707-008-0030-x

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  • DOI: https://doi.org/10.1007/s00707-008-0030-x

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