Analytical solutions for plate buckling from static analysis approach

In this chapter, analytical solutions for the buckling loads of thin rectangular plates with different boundary conditions are derived. The plate materials considered include isotropic, orthotropic, and symmetrically laminated composites. 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 all possible combinations of boundary conditions is lacking. The analytical method presented herein 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 a series form, and the coefficients are solved to match the edge conditions. The solution presented for this plate will fit different boundary conditions, of the deflection, slope, shear force, and bending moment along the common edges of neighboring plates. By using this new method, exact buckling loads and buckling modes of many new cases of classical boundary conditions are found (cases involving clamped, simply supported, guided, and free boundaries). Results are given for several stiffness ratios in both directions of the plate, and for unidirectional and several cases of bidirectional loading.