Abstract
The main purpose of this paper is the investigation of the nonlinear torsional buckling and postbuckling of sandwich functionally graded cylindrical shells with the von Karman large deflection nonlinearities under thermal effect by an analytical method. The shell skin is reinforced by stringer, circular ring and spiral stiffeners, the material properties of shell skin and stiffeners are assumed to vary continuously through the thickness. The very large effect of spiral stiffeners on the buckling load-carrying capacity of a cylindrical shell in comparison with orthogonal stiffeners is clearly proved in numerical investigations. Based on the Donnell shell theory and the improved smeared stiffener technique for both thermal and mechanical terms of spiral stiffeners, the equilibrium equations of the shell are established in this paper. By using the Galerkin method, the postbuckling curves and critical buckling loads are obtained. The effects of temperature change, stiffeners, material and dimensional parameters on the nonlinear torsional buckling and postbuckling of shell are numerically analyzed.
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Appendices
Appendix I
in which
Case A:
If \(\Delta T=\mathrm{const.}\), then
If \(\Delta T = \mathrm{const.}\), then
Case B: The expressions are similar to case A by replacing \(E_c\) with \(E_m\) and \(\alpha _c\) with \(\alpha _m\).
In the above, \(d_s ,d_r\) and \(d_l\) are the distances between two stringers, rings and spiral, respectively. Also, \(b_s\), \(b_r\) and \(b_l\) denote widths of stiffeners, respectively. The \(h_s\), \(h_r\) and \(b_l\) represent the height of the stiffeners (Fig. 1).
Appendix II
Appendix III
in which
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Nam, V.H., Phuong, N.T. & Trung, N.T. Nonlinear buckling and postbuckling of sandwich FGM cylindrical shells reinforced by spiral stiffeners under torsion loads in thermal environment. Acta Mech 230, 3183–3204 (2019). https://doi.org/10.1007/s00707-019-02452-5
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DOI: https://doi.org/10.1007/s00707-019-02452-5