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- W2065928529 abstract "A major difficulty in implementing many of the more innovative acoustic formulations for the solution of submerged three-dimensional thin shells of arbitrary geometry in an unbounded fluid medium has been the difficulty of numerically approximating a hypersingular integral operator. A variational approach given by Hamdi reduces this hypersingularity/Cauchy singularity to a weak singularity allowing for its accurate numerical approximation. Recently, Mariem and Hamdi [A new boundary finite element method for fluid-structure interaction, Internat. J. Numer. Methods Engrg. 24 (1987) 1251–1267] presented an acoustic formulation for thin shells, where the pressure difference across the shell is related to the shell's normal velocity solely in terms of this integral operator. Despite its advantage of generating a symmetric fluid matrix, a double surface integration is required to form this matrix, some researchers have endeavoured to develop a collocation method of approximating this highly singular operator. In this paper, a novel solution to the numerical approximation of this operator is given. In the implementation of both the variational and collocation methodologies, quadratic quadrilateral elements are used to interpolate for the acoustic and geometric variables. Results are then presented for thin shell scattering and radiation problems for both closed and non-closed thin shells demonstrating the validity and accuracy of both methods." @default.
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- W2065928529 date "1992-12-01" @default.
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- W2065928529 title "A comparison of numerical collocation and variational procedures to the hypersingular acoustic integral operator" @default.
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- W2065928529 doi "https://doi.org/10.1016/0045-7825(92)90012-9" @default.
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