Research On Thermal Buckling Of Functionally Graded Spherical Shells

In recent years,with the rapid development of high-tech fields,the demand for materials is getting higher and higher.Functional gradient materials is especially suitable for the material on both sides of the large temperature difference environment,its heat resistance,reusability and reliability are the use of ceramic matrix composites can not be compared.Functionally graded materials are the new kind of composite material with gradient variation along the thickness direction,which is made up of materials such as metal,ceramic,plastic and so on.Because of its excellent mechanical properties and novel design ideas are widely used in aerospace,medical,electromagnetic,nuclear engineering,optics and other fields.Plate and shell structures are widely used in many fields,and the stability of structures is one of the problems to be solved in practical engineering applications.How to accurately predict the critical point of the buckling of plate and shell structure has been one of the difficult problems for researchers.Especially the thermal buckling problems,the critical pressure and critical temperature should be obtained accurately at the same time.Because most of the functionally graded materials are used in the fields of the high and new technology,and therefore the accuracy of the thermal stability of the structure is higher.So it is very important to study the thermal buckling of functionally graded materials.In this paper,the thermal buckling of functionally graded material thin spheres under linear and nonlinear conditions is studied.1,Based on the nonlinear thermal isotropic complete constitutive equation,through the Christoffel symbol based on derivative vector coordinates,the constitutive equations of FGM thin spherical shell is derived in the spherical coordinate system of heat.2,The stability equation of axisymmetric spherical shell is derived by using tensor method.The thermal constitutive equation is applied to the stability equation of the spherical shell,and the thermal buckling equations of the shell are obtained.3,In the linear case,considering the external pressure and temperature by using the Galerkin method and Ritz method of simply supported the shell thermal buckling problems.The change tendency of the critical pressure and the change tendency of the critical temperature caused by the change of the thickness and the physical property parameters of the thin spherical shell are analyzed.4,In the nonlinear case,using Ritz method analysis of thermal buckling of simply supported hemisphere.(1)under the action of the pressure at different temperature(the critical temperature not reached),the relation between critical pressure and thickness;(2)in different thickness,the relation between critical pressure and temperature;(3)under the action of different external pressure(the critical pressure not reached),the relation between the critical temperature and the thickness.