Singular solutions and an indirect boundary integral formulation for spherical shells.
Item
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Title
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Singular solutions and an indirect boundary integral formulation for spherical shells.
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Identifier
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AAI8821123
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identifier
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8821123
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Creator
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Simos, Nikolaos.
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Contributor
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Adviser: Ali M. Sadegh
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Date
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1988
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Mechanical
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Abstract
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Despite the various mathematical descriptions of the shell element, the analysis of practical engineering shell problems remains complex and rigorous. The development of numerical techniques has assisted such analyses to a great extent. However, the limits of applicability of the various computational techniques are not clearly delineated as yet and as a consequence new approaches and mathematical models continue to be introduced.;This investigation consists of three major parts. First, the singular solutions of a non-shallow spherical shell are derived in closed form. Such solutions correspond to the state of deformation and stress in a complete spherical domain under the action of surface point loads along the normal or tangential directions and concentrated surface moments. The singular loads involved apply in a self-equilibating fashion. The mathematical analysis is performed for both classical and improved theories.;Next, an Indirect Boundary Integral Method is formulated by utilizing the derived singular solutions. The method is built upon the superposition principle and it involves the embedding of a partial spherical shell of arbitrary boundary and surface traction onto a complete sphere of which the singular solutions are known. The introduction of a set of unknown fictitious line vectors along the boundary, equal in number to the prescribed boundary conditions, and their incorporation into the coupled integral equations will ensure the satisfaction of the specified constraints along the boundary. The advantage of such approach over other methods is the reduction of the problem dimension by one.;Finally, the performance of the introduced technique is evaluated through the solution of a number of spherical shell problems under various types of surface loading and different sets of boundary constraints such as fixed, simply supported, free to move in the normal direction and free. Further, problems associated with stress concentration as well as a case of a spherical shell with a through crack are solved with the Boundary Integral Method. The results obtained are compared with the available analytical solutions and also with the Finite Element solutions and they demonstrate excellent agreement while at the same time project computational efficiency over the Finite Element Method.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
