Abstract
A new analytical method is presented for the analysis of the stresses and displacements in a finitely long, thin-walled cylindrical shell structure of arbitrary cross-section whose median surface cross-section curvature is described approximately by a special coordinate transformation function that can map the non-circular cross-section curvature into a circular one. The cylindrical structure is acted upon by an external load and is allowed to have various boundary conditions at its edges. The displacement functions are first of all assumed for a circular cylindrical shell to be respectively a Fourier series in the circumferential direction and the characteristic beam functions which satisfy the various end conditions in the longitudinal direction and then mapped into the arbitrary cross-sectional cylindrical shell. The principle of minimum total potential energy is employed to obtain stresses and displacements for the non-circular cylindrical shell structures. Problems involving oval, square, and U-shaped cross-sectional cylindrical shell structures are studied.
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