Abstract
The classical shell theory (CST) without considering the shear deformation has been commonly used in the calculation of shells structures recently. However, the impact of theory of plates and shells subjected to the shear deformation on the calculation is increasingly pronounced along with the wide use of composite laminated structures. In this paper, based on first-order shear deformation theory (FSDT) of cylindrical shells, the displacement control differential equation of moderately thick cylindrical shells has been obtained, so has been the edge force at longitudinal of the shells. Meanwhile, a group of unit force is introduced to deduce the displacement of edge beam under the action of edge force. A join condition of moderately thick cylindrical ribbed shells is established according to the continuity of displacement as well. Most notably, the displacement analytical solution of bending problems of moderately thick cylindrical ribbed shells is obtained, which has profound theoretical significance for further improving the analytical solution of moderately thick cylindrical shells.
Highlights
With the advent of new materials, various shell structures have experienced unprecedented development
A join condition of moderately thick cylindrical ribbed shells is established according to the continuity of displacement as well
The join condition of moderately thick cylindrical ribbed shells is established according to the continuity of displacement, and the displacement analytical solution of bending problems of moderately thick cylindrical ribbed shells has been obtained as well
Summary
With the advent of new materials, various shell structures have experienced unprecedented development. Based on Kirchhoff-Love’s classical theory of thin shells [4], the comparatively perfect result of dynamic excitation was obtained within the low radio-wave band when R/h ≫ 1 It may cause 30% or even more error by putting this theory into the deformation, stress, and frequency analysis of composite shells, because the ratio of their elastic modulus and shear modulus usually reach 25–40. The FSDT cannot always satisfy the unstressed boundary conditions of upper and lower surface of shells, it can get a simpler equation and readily establish the boundary conditions, with clear physical significance of component internal forces. Whether the new equation can be solved in transverse shear deformation is another tough problem during the research of bending problem of moderately thick shells [9, 10]. The join condition of moderately thick cylindrical ribbed shells is established according to the continuity of displacement, and the displacement analytical solution of bending problems of moderately thick cylindrical ribbed shells has been obtained as well
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