Local buckling of profiled skin sheets resting on tensionless elastic foundations under in-plane shear loading

• Local buckling of profiled skin sheets on tensionless elastic foundations under in-plane shear has been studied.
• Fitted formulas for contact shearing buckling coefficient have been developed.
• Analytical study and numerical simulation are conducted.
• Effect of relative foundation stiffness and skin profile parameters has been investigated.

In this paper, the local buckling behaviour of profiled skin sheets resting on tensionless elastic Winkler foundations under in-plane shear loadings is studied. The profiled sheets are modelled as thin orthotropic plates with the buckling behaviour being expressed through a group of nonlinear partial differential equations. For very long plates with both ends clamped, the buckling mode is composed of a series of periodically repeating buckling waves and hence an infinite plate model with only one buckle wave is effective to predict the buckling behaviour. The infinite orthotropic plate is further simplified to a one-dimensional mechanical model by assuming a lateral buckling mode function. After solving the governing equations of the one-dimensional model in both contact and non-contact regions, shear buckling coefficients of the system and the related buckling modes are obtained. Fitted formulae for the contact shear buckling coefficients in terms of relative foundation stiffness and skin profile parameters are developed. The analytical solutions are verified through examining extreme cases from previous studies and a series of finite element (FE) models in ABAQUS. Finally, a practical example is given to show the efficiency of the developed method.