A semi-analytical solution for critical buckling loads of orthotropic stiffened rectangular thin plates

Abstract

Stiffened plates are widely used in various engineering fields as main load-carrying components. Semi-analytical methods are effective for studying the eigenbuckling problems of stiffened rectangular plates, but there are no semi-analytical solutions available for stiffened plates with arbitrary homogeneous boundary conditions. This work aims to develop a semi-analytical method for solving the eigenbuckling problems of orthotropic stiffened thin plates. In this method, base functions for constructing the mode functions of stiffened plate are the mode functions of a simple plate (a plate without stiffener), and the base functions are obtained with the extended separation-of-variable method, which is a closed-form solution method for the eigenvalue problems of plates. The critical buckling load is achieved by substituting the mode functions into the Rayleigh's principle. The present method can deal with arbitrary homogeneous boundary conditions without anticipating the forms of the base functions for different boundary conditions. The accuracy can be improved by using more superposition terms. Besides, an exact closed-form solution of simply supported stiffened plates is achieved, serving as benchmark solutions. Numerical experiments validate the accuracy of the present solutions, and the study on the minimum stiffener stiffness is conducted for different boundary conditions.