טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTenenbaum Israelsky Joseph
SubjectAnalytic Solution for Uni-Axial and Bi-Axial Buckling
Loads for Thin Rectangular Orthotropic and
Isotropic Plates
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Emeritus Moshe Eisenberger


Abstract

In this research a new analytical solution for finding the buckling loads of thin isotropic, orthotropic and composite rectangular plates with different boundary conditions is derived. The methods currently known in the literature for finding the buckling loads of plates are mainly numerical. Although some plates with specific boundary conditions have analytical solutions, a comprehensive analytical method providing analytical solutions that fit many possible combinations of boundary conditions is lacking. The solution method in this study is based on the development of a static solution for a plate. The physical meaning of buckling is the loss of stiffness, and it is found as the value of the in-plane loading intensity at which a zero force on the plate surface will generate infinite displacement. The solution is obtained in series form, and the coefficients are solved to match the edge boundary conditions.  Using this new method, analytical buckling loads and buckling modes of many new cases of classical boundary conditions are found (cases involving clamped, simply supported, guided, free and vertically and rotationally flexible boundaries). Results are given for several stiffness ratios in both directions of the plate, and for uni-directional and several combinations of bi-directional load intensities.


Thin plates are structural elements used in various fields including, but not limited to, civil, aeronautical, and mechanical engineering. In all these fields, plates can be found in a state in which a force is applied parallel to its plane. For example, in civil engineering a floor slab with an applied lateral force due to wind, and in aeronautical engineering the panels of the fuselage under compression forces. These in-plane loads can lead to buckling, in other words the loss of stability of the plate.

For decades, the interest in elastic stability has been growing since the beginning of the nineteenth century when iron structures were starting to emerge. The first solution was obtained by  Navier (1819), and his solution was for a simply supported plate along all four edges. For the cases where two opposite edges are simply supported  Levy (1899) developed exact solution.