New nonlinear thermomechanical buckling solutions of spherical caps and annular spherical shells

New thermomechanical buckling solutions of spherical caps and annular spherical shells accounting for the pre-buckling nonlinearity, which is important but was generally neglected in previous studies, are presented in this study. The nonlinearity in the buckling equation of a spherical shell is separated into the pre-buckling equations using the parameter perturbation. Subsequently, the quasilinearization method and the partitioned solution scheme is employed, wherein a series of variable-coefficient matrix equations are solved to rapidly obtain the nonlinear solution. The matrix exponential computation involved is tackled using the precise integration method, leading to the derivation of the state transition equation. A global matrix equation is then formulated incorporating the boundary conditions, from which the buckling eigenvalues are determined. The convergence study and benchmark buckling solutions are presented. In addition, the impacts of temperature change, pre-buckling nonlinearity, shell thickness, and BCs on the buckling behavior are quantitatively investigated through comprehensive numerical and graphic results.