Investigation On Elastoplastic Buckling Behaviors Of Functionally Graded Rectangle

The stability of the composite material structures has been of concern to practical engineering. This article present the elastic-plastic buckling problem of FGM rectangular plates through theoretical research and building the theoretical model of elastic-plastic buckling and elastic buckling of FGM rectangular plate. Among them, the elastic-plastic buckling of FGM rectangular plates constitute important innovation point of this article, the research of this theory further reveal mechanics nature of FGM structural buckling performance,which not only perfecte the composite plate and shell of the development of the theory of elastic-plastic stability, but also lay a reliable foundation for the potential engineering applications of the structure of the new materials.In terms of elastic buckling, the paper uses the classical plate and shell theory to study the elastic buckling performance of FGM rectangular plates under biaxial in-plane load, through Galerkin principle to obtain the buckling critical condition and the analytic expressions of the theore of the buckling critical load of the stucture, finally the paper discusses the material composition and size parameters on the influence of the structural buckling behavior, the research has shown that with the increase of ceramic component content of FGM rectangular plate, the stability of the structure will improve; Thickness parameters had a great influence on the stability of the structure, the decrease of width-to-thickness ratio will lead to the sharply increase of buckling stable performance of the structures, those two basic conclusion is suitable for the elastic-plastic buckling problem of FGM rectangular plates.Elastic-plastic buckling study of FGM rectangular plate is important content in the main body of this paper. According to the different forms of the load, the load that the structure bear include uniaxial load and biaxial load. The condition of FGM rectangular plates under biaxial in-plane load has considered the complex stress state, which is different from the condition of the structure under uniaxial in-plane load. Based on the assumption of uniform strain distribution before buckling and connecting with the von Mises yield criterion, the analytical expression of the elastic-plastic interface position of the materials of FGM rectangular plates under in-plane load was deduced. With the change of external load, the position of this interface will be changed. Finally, through the semi-analytical method to determine the elastic-plastic buckling condition of the structure, including structural buckling critical load,buckling mode, materials elastic-plastic buckling interface position, the material flow area size, and so on. This method is essentially iterative convergence between structure internal force and the buckling critical internal force of structure, for the theoretical predicts of elastic-plastic buckling critical load of the structure. In addition, ABAQUS numerical simulation results verify the theoretical results of the paper. At the same time we get elastic-plastic post-buckling behavior of FGM rectangular plate.In theory and the results of numerical simulation analysis, we discusse how the component parameters and the structure size parameters, influence the elastic-plastic buckling critical load, the stability region and post-buckling behavior. And we approximately divide the elastic buckling,the elastic-plastic buckling and the plastic buckling limit of the structure. For the in-plane uniaxial load cases, we compares the deformation theory and flow theory, numerical simulation of ABAQUS and discusse the difference between the three results. The study showed that the difference between the theoretical predictions of the elastic-plastic buckling critical load and the theoretical predictions of the elastic buckling critical load is very big. In the case of thick plate size, the ratio is even lower than 0.4; Flow theory and deformation theory exist certain differences on the results of the elastic-plastic buckling analysis of the structure, through the comparison, we think the latter result more accurate; Elastic FGM rectangular plate have stable post-buckling equilibrium path, namely, the structural post-buckling bearing capacity increases with the compression displacement decreases, when the structure has elastic-plastic material, FGM rectangular plate belong to the structure that have unstable post-buckling equilibrium path, with compression displacement decreases, the post-buckling bearing capacity of the structure will increase sharply.In in-plane biaxial load cases, the research shows that: along with the increase of structural ceramics component content, the stability area of the structure increases gradually, the stable performance improved; The stability region of the structure is affected by the size parameters of the structure obviously, with the increase in width-to-thickness ratio, the stability area of the structure increases sharply, the stable performance decrease.