Aerospace Engineering

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A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations

1992-09-01 , Guiggiani, Massimo , Krishnasamy, Geeta , Rudolphi, Thomas , Rudolphi, Thomas , Rizzo, F. , Aerospace Engineering

The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems.

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Review of: Finite Elements, Theory and Applications

1989-08-01 , Rudolphi, Thomas , Rudolphi, Thomas , Aerospace Engineering

This volume covers the proceedings of the workshop sponsored by the Institute for Computer Applications in Science and Engineering ((CASE) held 28-30 July 1988 in Hampton, Virginia, at the NASA Langley Research Center. It consists of 13 articles by finite element researchers and practitioners and 13 intended to assess the impact of the theory on practice and to suggest areas of future research. About one-half of the articles review the theoretical aspects of the finite element method while the remaining are devoted to advanced applications where research is still required.

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Review of: Boundary Elements IX, Vols. 1–3

1988-07-01 , Rudolphi, Thomas , Takle, Eugene , Rudolphi, Thomas , Aerospace Engineering , Geological and Atmospheric Sciences

This three-volume edition contains edited versions of 128 papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany, from 31 August to 4 September 1987. The conference series is devoted to a review of the latest developments in the technique and theory of the boundary element methods (BEM) with emphasis on new advances and trends. This particular meeting was to be devoted to ''the engineering aspects versus mathematical formulations, in an effort to consolidate the basis of many new applications.'' Whether this goal was achieved is necessarily going to be determined by whether the reader has the mathematical ability to digest and interpret the several papers that address the mathematical bases of some of the newer applications. Each volume is divided into six to eight sections of related papers. One or two invited papers lead off most of the sections, followed by three to five contributed papers touching on both mathematical theory and applications of boundary elements. The references at the end of each contribution, when summed together, represent a substantial compilation of related literature representing a diversity of languages.

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Boundary Element Solutions to Wave Scattering by Surface Irregularities on a Fluid-solid Interface

1995 , Shenoy, S. , Rudolphi, Thomas , Rudolphi, Thomas , Rizzo, F. , Aerospace Engineering

The boundary element method is used to solve fluid-solid half-space problems with fluid-filled dimples and air bubbles on the solid surface. The problems, formulated in the Fourier (frequency) domain, are described by the fullspace three-dimensional acoustic and elastodynamic boundary integral equations (BIE), with pressure and displacement serving as primary variables. The techniques developed are general and may be with any kind of incident wave, however, plane waves are used in all numerical experiments. The equations governing the acoustic region are first converted mathematically to equations like those of an elastic region. The two regions are coupled and solved for the displacements using the interface conditions. On obtaining the displacements, the tractions, pressures and pressure gradients are computed using the same interface conditions. The numerical results obtained are verified using reciprocity relations and by comparison with solutions available for the halfspace elastodynamic problem

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Nonhomogeneous potential and elasticity problems by combined boundary and finite elements

1985 , Rudolphi, Thomas , Rudolphi, Thomas , Aerospace Engineering

The usage of the boundary integral equation method for nonhomogeneous problems and the combination of this method with the finite element method is discussed. A formulation of the finite element method and the conversion of the direct boundary integral equations into a stiffness type of equation is reviewed for potential problems. The problems associated with corner flux discontinuities, infinite elements, and symmetrization of the stiffness matrix are discussed. An algorithm for the construction of the stiffness matrices for the more general multi-degree of freedom problem is given along with some examples.