LAUSR

The nonlinear governing equations of three shell theories (Donnell, Love, and Sanders) with first-order approximation and von Kármán’s geometric nonlinearity for laminated sandwich cylindrical shells with isotropic, functionally graded (FG) or isogrid lattice layers are decoupled. This uncoupling makes it possible to present a semi-analytical solution for the nonlinear bending and post-buckling behavior of short and long doubly simply supported, doubly clamped, and cantilever laminated sandwich cylindrical shells subjected to various types of thermo-mechanical loadings. The results for deflection, stress, critical axial traction, and mode shapes in FG shells are verified with those obtained from ABAQUS code. Finally, the case studies are presented for FG shells and laminated sandwich shells with different layups such as $$[\hbox {Al; ZrO}_2]$$[Al;ZrO2], $$[\hbox {Al; FG core; ZrO}_2]$$[Al; FG core;ZrO2], $$[\hbox {Al; Gr; ZrO}_2]$$[Al; Gr;ZrO2], $$[\hbox {Al; Gr; FG core; ZrO}_2]$$[Al; Gr; FG core;ZrO2], $$[\hbox {Al; isogrid lattice core; Al}]$$[Al; isogrid lattice core; Al]. The closed-form solutions presented here for the kinetic parameters and critical axial loading in a nonlinear analysis can be used in the conceptual design of laminated sandwich cylindrical shells with arbitrary layups and boundary conditions. Furthermore, introducing an equivalent Young’s modulus through the shell thickness, a simple formula is presented for the calculation of critical load in long shells with simple and clamped ends under axial loading with a maximum error of 10%. Moreover, findings show that the boundary-layer type behavior is seen only in long cylindrical shells in the pre-buckling region. Under thermal loading, snap-through buckling is observed in clamped shells. However, in simply supported shells by increasing the temperature, the transverse deflection increases, and while $$\Delta T-w/h$$ΔT-w/h curves do not show any buckling phenomenon, the $$N^{0}/N_{\mathrm{cr}}^{*} -\Delta T$$N0/Ncr∗-ΔT curves show such a behavior.