New buckling solutions of truncated conical shells incorporating pre-buckling nonlinearity.

• New buckling solutions of truncated conical shells are obtained. • Pre-buckling nonlinearity is incorporated for accurate buckling analysis. • A quasilinearization-precise integral method is developed for nonlinear PDEs. • The effects of size parameters and boundary conditions are quantitatively revealed. The pre-buckling nonlinearity is found to have a remarkable effect on both the buckling loads and modes of shells according to the previous studies. In this study, we present a novel accurate buckling analysis of the truncated conical shells under broad boundary constraints incorporating the pre-buckling nonlinearity by a quasilinearization-precise integral method (Q-PIM). Specifically, the nonlinear buckling equations of the shells are transformed into several linear ones by the perturbation and quasilinearization, and they are then solved by the PIM. The produced state transition equations by the PIM are assembled into a global matrix equation, involving the boundary conditions (BCs), to yield the buckling solutions of the shells with or without incorporating the pre-buckling nonlinearity. The convergence study and benchmark buckling solutions verified by the refined finite element method are presented. The quantitative effects of the size parameters and BCs on the nonlinear critical buckling loads as well as the pre-buckling nonlinearity are investigated. [ABSTRACT FROM AUTHOR]