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- W2056552723 abstract "Numerous investigators, notably Mindlin, have developed higher-order theories for beams, plates, and shells in which the variation of displacement through the thickness is represented in terms of series expansions. A major difficulty one encounters in those formulations is the derivation of hierarchal partial differential equations of motion accounting for the coupling between different orders of thickness dependence. The present work develops an alternative scheme that avoids the derivation of such equations by applying the assumed modes method in conjunction with Hamilton’s principle. An infinitely long cylinder provides the framework for the development. The basis functions representing the dependence on radial position consist of Legendre polynomials, which have been used in the past to analyze static deflections of thick cylindrical shells, while sinusoidal functions represent the variation along the circumference. The assumed mode representation leads to ordinary differential equations of motion governing the amplitudes of the basis functions. Because of the axisymmetric geometry, the modal equations decouple in the circumferential direction. When the shell is geometrically thin, h/a≪1, each radial mode couples to two adjacent modes above and below. The extent of this coupling increases with increasing h/a, but the mass and stiffness matrices for the modal amplitudes are banded in any case. [Work supported by ONR.]" @default.
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- W2056552723 date "1991-10-01" @default.
- W2056552723 modified "2023-09-26" @default.
- W2056552723 title "An assumed modes approach for higher‐order effects in circular cylindrical shells." @default.
- W2056552723 doi "https://doi.org/10.1121/1.402221" @default.
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