Local buckling of profiled skin sheets resting on tensionless elastic foundations under uniaxial compression

Abstract

This paper details an analytical study on the contact buckling problem of infinite profiled skin sheets in unilateral contact with Winkler foundations. The profiled sheets are modelled as thin orthotropic plates resting on tensionless Winkler foundations. The buckling behaviour of the plates can be expressed through a group of nonlinear partial differential equations for both the contact and non-contact parts of the plate. The governing equations are further modified to a group of ordinary differential equations after representing the lateral plate buckling mode through an appropriate displacement function. Thus the system is simplified as a one-dimensional mathematical model. After solving the governing equations of the one-dimensional model, contact buckling coefficients of the system and the related buckling modes are obtained. Fitted formulae for the contact buckling coefficients in terms of relative foundation stiffness and skin profile parameters are also developed. The analytical solutions are verified through a series of finite element (FE) models set up in ABAQUS software. Finally, a practical design example is given to show the efficiency of the developed analytical method.