Buckling and postbuckling analysis of rectangular plates resting on elastic foundations with the use of the spectral method

Buckling and contact effects for a von Kármán’s plate, unilaterally connected with a nonlinear elastic tensionless foundation are investigated. The foundation is modeled as nonlinear elastic (Winkler-type) and shear deformable (Pasternak-type) medium. Compressive and tensile loading forces along the edges of the plate are considered. The spectral method is developed for the discretization of the boundary value problems. A parametric analysis of compressive and tensile loadings is given. Bifurcation phenomena of the solution of the equations are explored. The iterative scheme with the path-following algorithm is employed to solve the resulting system of nonlinear algebraic equations. Numerical results are presented.