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Structural Engineering and Mechanics   Volume 30, Number 3, October20 2008, pages 279-296
DOI: https://doi.org/10.12989/sem.2008.30.3.279
 
Exact integration for the hypersingular boundary integral equation of two-dimensional elastostatics
Xiaosong Zhang and Xiaoxian Zhang

 
Abstract     [Buy Article]
    This paper presents an exact integration for the hypersingular boundary integral equation of two-dimensional elastostatics. The boundary is discretized by straight segments and the physical variables are approximated by discontinuous quadratic elements. The integral for the hypersingular boundary integral equation analysis is given in a closed form. It is proven that using the exact integration for
discontinuous boundary element, the singular integral in the Cauchy Principal Value and the hypersingular integral in the Hadamard Finite Part can be obtained straightforward without special treatment. Two
numerical examples are implemented to verify the correctness of the derived exact integration.
 
Key Words
    hypersingular boundary integral equation; exact integration; singular integral in CPV; hypersingular integral in HFP.
 
Address
Xiaosong Zhang: Dept. of Engineering Mechanics, Shijiazhuang Railway Institute, Shijiazhuang, 050043, Hebei Province, P. R. China
Xiaoxian Zhang: Dept. of Engineering, The University of Liverpool, Brodie Tower, Brownlow Street, Liverpool, L69 3GQ, U.K.
 

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