The application of an exact finite strip to the buckling of symmetrically laminated composite rectangular plates and prismatic plate structures

This paper presents theoretical developments of an exact finite strip for the buckling analysis of symmetrically laminated composite plates and plate structures. The so-called exact finite strip is developed based on the concept that it is effectively a plate and the von-Kármán’s equilibrium equation is solved exactly to obtain the general form of out-of-plane buckling deflection mode for the corresponding strip. This shape function is used to obtain a transcendental stiffness matrix for the strip through the minimization of the potential energy technique. The overall stiffness matrix for the whole section is obtained by assembling the individual strip stiffness matrices. Within the overall stiffness matrix, due to the special characteristics of the developed exact strip, it is not possible to identify a separate geometric stiffness matrix, which is independent of the buckling load parameter in the case of conventional FEM or FSM methods. In this paper, two secure methods (i.e. bisection method and recursive Newton’s method) for finding the buckling load and the corresponding buckling mode of the plate structures are used. The calculated buckling loads and the corresponding modes are exact in the sense that in their calculation, the usual approximations which are made in the conventional finite element or finite strip methods are avoided.