One of the ways of reinforcing the structures, using the foundations which are to attach to them and whereby buckling occurs only in one direction. In this thesis, analysis of unilateral buckling of point-restrained circular functionally graded material plates is studied. In this study, winkler foundation has been selected in order to become bilateral buckling to unilateral buckling. This foundation models by a series of discretized concentrated springs. In order to determine the number of springs per unit area, Convergence studies are conducted and the point restraints are used in order to model simply supported and clamped boundry condition. The material properties are assumed to vary continously through the thickness of plate based on power law functions, but poisson’s ratio is constant. The energy functional of a general circular plate with elastic foundation is calculated By using of ) is consideably greater than the values for nonhomogenous functionally graded plates(k?0). Also the unilateral buckling load doesn’t increase continously with increasing distance bolts from edge and maximum value allocated to. Convergence and comparison studies were undertaken to confirm the validity and accuracy of numerical results that can be provide benchmark data for further theorical and numerical studies. Keywords Unilateral buckle , Functionally Graded Material, Rayleigh-Ritz and lagrange multiplier method, Classical plate theory, Elastic foundation
