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Evaluation of strongly singular domain integrals for internal stresses in functionally graded materials analyses using RIBEM

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Abstract

An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method. To solve this problem, a singularity separation technique is presented in the paper to split the singular integral into regular and singular parts by subtracting and adding a singular term. The singular domain integral is transformed into a boundary integral using the radial integration method. Analytical expressions of the radial integrals are obtained for two commonly used shear moduli varying with spatial coordinates. The regular domain integral, after expressing the displacements in terms of the radial basis functions, is also transformed to the boundary using the radial integration method. Finally, a boundary element method without internal cells is established for computing the stresses at internal nodes of the functionally graded materials with varying shear modulus.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, 116024, Dalian, China

    Hai-Feng Peng, Jian Liu & Qiang-Hua Zhu

  2. Department of Civil Engineering, University of Siegen, D-57068, Siegen, Germany

    Ch. Zhang

Authors
  1. Hai-Feng Peng
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  2. Jian Liu
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  3. Qiang-Hua Zhu
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  4. Ch. Zhang
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Corresponding author

Correspondence to Qiang-Hua Zhu.

Additional information

The project was supported by the National Natural Science Foundation of China (11172055 and 11202045).

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Peng, HF., Liu, J., Zhu, QH. et al. Evaluation of strongly singular domain integrals for internal stresses in functionally graded materials analyses using RIBEM. Acta Mech Sin 30, 917–926 (2014). https://doi.org/10.1007/s10409-014-0077-y

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  • DOI: https://doi.org/10.1007/s10409-014-0077-y

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