Steady Thermal Stress Analysis Of Infinite Long FGM Hollow Circular Cylinder By Finite Element Method

Functionally graded material(functionally graded material is called FGM for short) is a special nonhomogeneous material with superiority that is far higher than traditional material.Because it is used widely in the aviation,nuclear reactor,internal combustion engine,and so on,it is seen as one of composite materials with the most prospects during the high temperature application.It is important to analyze the size and distribution of thermal stress.Among the methods of FGM thermal stress analyses that exist,the finite element method is one of the most effective calculation method,and it can solve composite material problems easily,such as multi-type,large deformation and geometrically nonlinear problems and so on.This paper selects ceramics/metal FGM infinite long hollow circular cylinder as research object,according to thermal elastic mechanic's theory and the finite element theory.The article did some researches as follows:1.Starting from the governing equation for heat conduction of FGM hollow circular cylinder,this paper proves that the functional for problem of FGM hollow circular cylinder heat conduction exists when the material properties are described by a function of the coordinates.As a result,the functional from the equation is derived, and the associated variation principles are established,and derive finite element basic equation of the FGM hollow circular cylinder heat conduction problem by functional variation principle.The calculation program about the finite element method of heat conduction is compiled by Fortran.2.Starting from the governing equation for the thermoelastic field of FGM hollow circular cylinder,this paper presents the functional from the equation of FGM hollow circular cylinder thermoelastic problem when the material properties are described by a function of the coordinates.This paper derives the finite element basic equation of FGM hollow circular cylinder thermoelastic problem by functional variation principle.The calculation program about the finite element method of thermoelastic problem is compiled by Fortran.3.This paper programs the finite element software to analyze the value.When M=1,A=0,this paper inspects the accuracy of numerical simulation model. 4.Through numerical calculation,the paper presents the thermal stress distribution of infinite long FGM hollow circular cylinder in the steady temperature field.The results indicate:(1) The control failure stress in the inner wall of FGM infinite long hollow circular cylinder and the nearby part is circumferential thermal stressσ_θθ,but the control failure stress in the axial and the nearby part is axial thermal compressive stressσ_zz.(2) The distribution shape coefficient of material composition M and porosity have a significant effect on the distribution of the radial thermal stressσ_rr,the circumferential thermal stressσ_θθ and the axial thermal stressσ_zz in the FGM infinite long hollow circular cylinder;The graded layer thickness affects on the distribution of the radial thermal stressσ_rr greatly,and it also has a significant effect on the circumferential thermal stressσ_θθ in the vicinity of axial thermal stress,but it has little effect onσ_θθ that near the part in the middle of cylinder,and it has little effect on the axial thermal stressσ_zz.