Static Response Of Functionally Graded Curved Beams With Varying Curvature And Cylindrical Shells Subjected To Mechanical And Thermal Loads

The researches on the static and dynamic responses of functionally graded material(FGM)beams,plates and shells have become an important direction in solid mechanics of inhomogenenous materials.This thesis focuses on the static responses of FGM curved beams with varying curvatures and circular cylindrical shells,subjected to thermomechanical loads by employing analytical approach combined with numerical computation.The main content consists of the following two parts.1.Based on an exact geometrically nonlinear theory of planar elastic curved beams and first order shear deformation theory,taking the axial extension and the transverse shear deformation into account in the strain-displacement relationships,governing equations for both FGM Euler and Timoshenko curved beams with varying curvatures subjected to thermomechanical loads and with large elastic deformations are formulated,respectively.Because of the curvature change,the stiffness coefficients related to the curvature become the functions of the arc length coordinate,so the coefficients of governing equations are variable.In the governing equations,the basic unknown quantities are shown as the functions of axial coordinate before the deformation,and the independent variables are expressed in terms of the parameter of the parametric equations of the curved beam axis.The shooting method is employed to numerically solve the above mentioned strong nonlinear two-point boundary value problem of ordinary differential equations with multiple unknowns.The nonlinear bending of FGM Euler elliptical curved beams with various boundary conditions is analyzed.The influence of material gradient index,thermal loading and structural geometric parameters on the internal forces and deformation of the curved beams is discussed in detail.Then,by using the same mathematical model and numerical method,the stability of the Euler elliptical curved beams with fixed-fixed ends subjected to different kinds of mechanical loads are evaluated.The configurations and equilibrium paths of the buckling curved beams are plotted.Finially,the thermoelasticity deformation of uniformly or transversely non-uniformly heated FGM Timoshenko cycloidal and elliptical curved beams is investigated.The results of Timoshenko curved beams are compared with Euler curved beams to examine the effect of the shear deformation.2.In the second part,thermal buckling behavior of cylindrical shells made of functionally graded materials is studied.It is assumed that material properties and non-uniform temperature rise change only through the thickness direction.Based on the classical linear thin shell theory,the dimensionless governing equations of thermal buckling in terms of the displacement components are derived.Method of separation of variables is employed to transform the governing partial differential equations into ordinary differential equations with three coupled unknown functions.Then by using shooting method to search for the numerical solution to the above mentioned differential equations with simply supported edge conditions and fixed ends.The critical buckling temperatures are obtained.Then,the buckling analysis of functionally graded material circular cylindrical shell under homogeneous and inhomogeneous thermal loads is carried out.In this part,the effects of functionally graded index n,the dimensionless geometrical parameters h/R and l/R,and the temperature-rise parameter fTon the critical buckling are examined.It is found that the dimensionless critical buckling temperatures for the two types of temperature fields decrease with the increase of h/R,and are not sensitive to the change of l/R.The increase in buckling temperature with an increase in the values of n,accounts for the fact that a great value of the power index implies the shell has a large amount of the ceramic components which leads to the stiffness of the shell to be strengthened.The value of the ratio of the outer and inner surface temperature rises of the shell,fT,has reflected the inhomogeneous degree of the temperature fields.The non-dimensional critical buckling temperatures decrease with the increase of fT.For the fixed-fixed shell,the critical buckling temperatures are greater than those of pinned-pinned shell.