Heterogeneous structure of functionally graded materials and gradual continuous variation of these materials made them to find growing applications in different areas, such as heat shield, gas turbine cover in order to reduce slate, heat cover in gas motors, components of heat exchangers, plasma cover in nuclear components, artificial bone, electro-magnetic fields, etc. In this thesis, elastic-plastic buckling of a FGM Rectangular plate under uniaxial and biaxial compression has been investigated. To this end, a MAPLE and MATLAB computer code has been developed. A metal-metal type has been assumed for the FG plate. Commercial aluminum and ST1403 steel were chosen as the special case study. The mechanical properties of the plate, including elasticity modulus and Ramberg-Osgood parameters were assumed to vary according to a power-law and exponential functions through the thickness. Derivations of equations are based on the classical plate theory (CPT). To minimize the integral criterion of stability, based on Rayleigh-Ritz method, In this method, the displacement functions of the plate are approximately represented by the product of mathematically complete two-dimensional polynomial functions and boundary equations raised to appropriate powers that ensure the satisfaction of the geometric boundary conditions. Substituting the trial function in the stability criterion and minimizing with respect to the unknown coefficients results in a homogeneous algebraic set of equations in terms of unknown coefficients. For non-trivial solution, the determinant of coefficient matrix should be equated to zero. Using this equation, critical buckling load is determined. The results of present study were compared with existing analytical solutions for homogenous rectangular plate and a good agreement was observed. The plastic buckling behaviour of the plate is captured by using the incremental and deformation theories of plasticity. The effect of boundary condition type, FGM power index, plate thickness ratio, loading ratio and aspect ratio on the critical elastic-plastic buckling load has been investigated. Results show that increasing the thickness ratio and decreasing FGM power index in volume fraction lead to increasing elastic-plastic critical buckling load.
