Critical behavior of flat and stiffened shell structures through different kinematical models: A comparative investigation

In the present work buckling stresses of prismatic flat and stiffened shell structures are derived within the framework of the Kantorovich approach, making reference to both Von Karman and Koiter–Sanders theories, the latter exploiting the Green–Lagrange strain tensor which is needed if the expected buckling modes involve comparable in-plane and out-of-plane displacements. Additionally, in order to highlight the contribution of each nonlinear term of the Koiter–Sanders model, two further intermediate choices are also considered, namely an enhanced Von Karman model and a spurious model which collects selected terms from different theoretical approaches, generally adopted in literature with the aim of simplifying the numerical analyses. The obtained results show how in buckling problems where the weight of in-plane displacements cannot be neglected the Von Karman model tends to overestimate the critical load, while the three considered alternative models result substantially equivalent, at least from the practical standpoint.

► Plate and shell buckling is described in both Von Karman and Koiter–Sanders theory.
► Two additional intermediate strain–displacement models are considered.
► Importance of each nonlinear term is assessed.
► Closed form solution of the equilibrium equations is adopted as shape function.
► Results obtained show that the Von Karman model can overestimate the critical load.