Elasticity Stability And Natural Frequency Of Circular Cylindrical Shells With FGMs Layers

Elasticity stability and vibration of thin circular cylindrical shells are important problems in theoretical study of structural mechanics and in engineering applications. In this paper,based on the Fliigge thin shell theory,elastic stability and free vibration of sandwich circular cylindrical shells with FGM middle layer under end circumferential shear load and uniformly normal compression load were studied and by using a semi-analytical method.In the first part,we used semi-analytical method to study elasticity stability of a simply supported sandwich circular cylindrical shell with a FGMs middle layer under end circumferential shear load.The inner and outer layers of the shell are comprised of the same homogeneous material but the middle layer is made of a functionally graded material whose Young's modulus varies continuously in the thickness direction,which keeps a consecution in the material properties at the interface.Firstly,based on the Flugge thin shell theory,the governing equations in terms of the displacements for static buckling of the structure were formulated.Secondly,the solution is expressed in terms of Fourier series functions that identically satisfy the boundary conditions and an eigenvalue problem for linear algebraic equations was obtained.Finally,critical buckling loads which show the characteristic of buckling of the structure were attained by numerical method.For the numerical results it can be found that the buckling load decreases with an increases in the radius to thickness ratio and that it increases with the increment in the average value of Young's modulus of the FGM middle layer.In the second part,based on the Fl(?)gge thin shell theory,we studied the responses of elastic stability and free vibration of a simply supported circular sandwich cylindrical shell with FGM layer under uniformly distributed normal compressive load. By using numerical method natural frequencies of the shell corresponding to different changes in the values of the graded material properties are computed.Characteristic curves of the buckling load and the natural frequency versus the length to radius ratio and the radius to thickness ratio for different values of the power index of variation of the material properties were presented.Effects of the geometric and the physical parameters on the buckling load and the natural frequency are examined in detail. Especially,influences of the normal compressive load on the natural frequency were also analyzed.The numerical results show that natural frequency decreases with the increase in the value of the compressive load when it is less then critical load. The research result of this dissertation has theoretical meaning for further understanding to the buckling and vibration behavior of the FGM cylindrical shells and has reference value for the engineering design of new material structures.