Elastoplastic Buckling Of Functionally Graded Circular Plate

Functionally graded materials(FGM)is a new type of composite material.Its material properties show continuous gradient changes along one or more directions,thus avoiding the stress concentration phenomenon in classical laminated composites.Functionally graded materials(FGM)have been widely used in various engineering structures in recent years due to the continuous change of their properties in the form of gradients,which reduces the thermal stress and stress concentration factor.In this paper,based on the classical plate theory,the elastoplastic buckling behavior of functionally graded material(FGM)circular plate under peripheral compression load is studied.Firstly,based on the TTO model and the linear mixed reinforced elastoplastic model of bi-directional stress,the elastoplastic physical parameters and the elastoplastic eigenequations of functionally graded materials are given.Then,the Hamilton principle is introduced to transform the elastoplastic buckling problem of FGM circular plate into the eigenvalue problem in symplectic space.The canonical equation is established and solved analytically.The elastoplastic buckling mode of FGM circular plate is obtained.Finally,the numerical results of elastoplastic interface and critical buckling load are obtained by considering various boundary constraints and solving based on Mises yield condition,At the same time,the numerical results are analyzed and discussed,and the effects of gradient index,boundary conditions and thickness to radius ratio on the critical buckling load and elastoplastic interface are obtained.It is found that the critical buckling load decreases with the increase of volume fraction or diameter to radius ratio,and the critical buckling load of fixed boundary is larger than that of simply supported boundary.In this paper,the symplectic geometry method for solving the elastoplastic buckling of functionally graded structures in Hamiltonian system is established,and the main factors affecting the elastoplastic buckling of the structures are obtained.The results can provide a theoretical and technical reference for the engineering application of FGM Structure,and the research methods can be applied to the elastoplastic stability of other similar composite structures.