Abstract:
Presented in this thesis is the linear buckling and nonlinear free vibration analyses of higher orderthick plates resting on 2-parameter elastic foundations via the finite element method. In this study,the shear deformation of thick plates is taken into account - complied with Reddys plate theory.Also, the Filonenko-Borodichs model of elastic foundation is applied to the analysis. Formulatingtotal work-energy functional consists of couple functional terms from the plate and its elasticfoundation. The higher-order equations of motion is derived through the Hamiltons principle andLagranges equation. The four nodes plate-bending element is used to approximate the displacementand slopes at node and the surface rotations. Establishing total mass and stiffness matrices, linearand cubic polynomial interpolation functions are employed in order to solve the buckling loads andinvestigate the nonlinear free vibration problem. To delineate the nonlinear free vibrationcharacteristics of the higher order plates, the finite element procedure and modified direct iterationtechnique are utilized to govern the problem. Numerical solutions obtained demonstrate theinfluences of the plates physical parameters, foundations parameters, and non-dimensional in-plane load ratios.