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Singular stress analysis of an anisotropic elastic medium containing polygonal holes using a novel hybrid finite element method

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Abstract

A novel hybrid finite element method based on a numerical procedure is proposed to compute singular field near V-shaped notch corners in an anisotropic material containing polygonal holes. The finite element method is established by the following three steps: (1) an ad hoc one-dimensional finite element formulation is employed to determined numerical eigensolutions of the singular field near an V-shaped notch corner; (2) a super corner tip element is constructed to determine the strength of the singular field, in which the independent assumed stress fields are extracted from the eigensolutions; (3) a novel hybrid finite element equation is obtained by coupling the super corner tip element with the conventional hybrid stress elements. In numerical examples, generalized stress intensity factors for interactions between two polygonal holes with various geometry, space position and material property are mainly discussed. All the numerical results show that present method yields satisfactory singular stress field solutions with fewer elements. Compared with the conventional finite element methods and integral equation methods, the present method is more suitable for dealing with micromechanics of anisotropic materials.

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Acknowledgments

The authors acknowledge the support of National Natural Science Foundation of China through Grant Nos. 10362002, 10662004 and 51065008, the Jiangxi Provincial Natural Science Foundation of China through Grant Nos. 2007GZW0862 and 2010GZW0013, and the Jinggang-Star training Plan for Young Scientists of Jiangxi Province through Grant No. 20112BCB23013.

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Authors and Affiliations

  1. School of Mechatronics Engineering, East China Jiaotong University, Nanchang, 330013, Jiangxi, People’s Republic of China

    Xue-Cheng Ping, Lin Leng & Si-Hai Wu

  2. School of Civil Engineering, East China Jiaotong University, Nanchang, 330013, Jiangxi, People’s Republic of China

    Meng-Cheng Chen

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  1. Xue-Cheng Ping
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Correspondence to Meng-Cheng Chen.

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Ping, XC., Chen, MC., Leng, L. et al. Singular stress analysis of an anisotropic elastic medium containing polygonal holes using a novel hybrid finite element method. Int J Mech Mater Des 8, 219–236 (2012). https://doi.org/10.1007/s10999-012-9187-5

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  • DOI: https://doi.org/10.1007/s10999-012-9187-5

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