Elastoplastic Deformations Of Functionally Graded Material Cylindrical Shells

With the development of science and technology,functionally graded materials(FGM)have been widely used in products such as aero-engines and AFM to achieve high sensitivity and obtain desired performance.At the same time,the mechanical characteristics of functionally graded material plates and shells have also been comprehensively studied by scholars.However,most of the existing studies have only focused on the mechanical properties of elastic deformation,and relatively few studies dedicated to the elastoplastic deformations.In this study,the elastoplastic bending deformations of FGM cylindrical shells under thermal loading and mechanical loading are examined,respectively.The main contents are as follows:Based on the classical shell theory,the elastoplastic deformations of the functionally graded material cylindrical shell with two fixed boundaries subjected to thermal loadings are studied by the symplectic method.Considering axial and radial stresses,temperature dependent constitutive equations are derived based on the TTO model of elastoplastic stress-strain relations of functionally graded materials.In the symplectic space,the dual equations under the Hamilton system is solved,and the analytical expression of the elastoplastic bending deflections of the FGM cylindrical shell is obtained by combining the bifurcation conditions.Based on the Mises yield criterion,the elastoplastic interface of the FGM cylindrical shell was solved and substituted into the expression of the thermal membrane force.And then the corresponding temperatures are obtained by using the inverse solution.In this studied,the solution processes of the symplectic method for solving the elastoplastic thermal bending problems of the FGM structure in the Hamiltonian system is established.The influences of the ratio of diameter to thickness,the temperature ratio of the ceramic side to the metal side and the constituent of the materials on the elastoplastic bending deflections,the elastoplastic deformation interfaces and elastoplastic stresses of the functionally graded material cylindrical shell are obtained.It is found that the ceramic weakens the deformation of the functionally graded material cylindrical shell.Based on the classical shell theory,the elastoplastic bending problem of FGM cylindrical shell subjected to mechanical loading was studied by using the symplectic method under the Hamilton system.The linear hybrid enhanced elastoplastic model was used to simulate the elastoplastic properties of FGMcylindrical shell.Based on the TTO model,the elastoplastic constitutive relations of functionally graded materials are established,and the canonical equation is deduced based on Hamilton principle.The solutions of the bending deflections of FGM cylindrical shell are converted into the symptectic eigen solution problem in symplectic space.The inverse solutions give the elastoplastic interface of bending stress and structural deformations.A detailed analysis of the effect of the geometric parameters on the bending deformation of the functionally graded material cylindrical shell is carried out under different loading conditions.During the loading process,the cylindrical shell first plastically deforms on the metal side.As the loads increases,the area where the plastic deformation occurs shifts toward the ceramic side.The results show that the constituent parameter of the FGM cylindrical shell has a great influence on the elastoplastic bending.With the increase of the constituent parameter,the strength of the FGM cylindrical shell decreases,and the elastoplastic bending deflection increasesThis research has theoretical contributions for the study of elastoplastic deformation of functionally graded material structures under external loads and thermal loads and positive significance for the use of FGM structural plastic properties.