The stability of circular cylindrical shells under pure bending is investigated by means of Batdorf’s modified Donnell’s equation and the Galerkin method. The results of this investigation have shown that, contrary to the commonly accepted value, the maximum critical bending stress is for all practical purposes equal to the critical compressive stress.
SUMMARYThe development of a general curved triangular element based on an assumed displacement potential energy approach is presented for the analysis of arbitrarily laminated thick shells The associated laminated shell theory assumes transverse inextensibility and layerwise constant shear angle The present element is a quadratic triangle of C"-type in the curvilinear co-ordinate plane, which is then mapped onto a curved surface. Convergence of transverse displacement, moments, stresses and the effect of two Gauss quadrature schemes also form a part of the investigation. Examples of two laminated shell problems demonstrate the accuracy and efficiency of the present element. Comparison of the present LCST (layerwise constant shear-angle theory) based solutions, with those based on the CST (constant shear-angle theory) clearly demonstrates the superiority of the former over the latter. especially in the prediction of the distribution of the surface-parallel displacements and stresses through the laminate thickness.
IPcTRODUCTlONA reliable prediction of the response of thick laminated shell-type structures, made of highperformancc composite materials (e.g. graphite/epoxy) necessitates the incorporation of the transverse shear deformation or cross-scctional warping into the formulation.132 The vast majority of laminate analyses are restricted to flat plates, e.g. References 1-4. In comparison, investigations pertaining to laminated shells are sparse, the majority of which are, again, based on either classical lamination theory (CLT)"' based on the Love-Kirchhoff hypothesis or constant shear-angle theory (CLT)9-'s based on the Reissner-Mindlin hypothesis. However, since crosssectional warping in a laminated shell may often be very severe due to the combined effects of thickness, lamination and the possibility of a high degree of anisotropy, use of CLT or CST may lead to serious error. An improved theory known as the layerwise constant shear angle theory1q291b [LCST), which allows for a piece (layer)-wise constant approximation of the non-linear cross-sectional warping, leading to an elasticity solution in the limit, therefore, becomes an excellent practical alternative.The layerwise constant shear-angle assumption has been first utilized by Mau et al. '' for solution of multi-layer thick plates using a quadrilateral element shape and assumed stress hybrid finite element approach. Although this method has yielded results for certain simple multi-layer plate problems, it suffers from the following discrepancies: (1) compatibility of stresses must be satisfied at each interface, involving too many matrix inversions at the element level; (2)
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