Dynamic Buckling Of Cylindrical Shells With Functionally Graded Materials

Functionally graded materials(FGM)are a new composite material which is composed of two or more materials component,which can realize continuous change of material properties along thickness direction by controlling the ratio of two components.Compared with the traditional laminated composite,there is no interfacial interface in FGM,so it can effectively avoid the stress concentration phenomenon.The greatest advantage of FGM is that it combines the heat resistance of ceramic materials with the crack resistance of metal materials,so that it is often used in environments where high temperature and large temperature gradients exist,such as applications to aerospace coating,nuclear reactor containers,and a series of important structures that require high thermal performance.At present,the research methods of the dynamic buckling of the FGM cylindrical shells are different,and their viewpoints vary,so the results are not the same.Based on this,several jobs are investigated in the following:1.This paper introduces the application of functionally graded materials and cylindrical shells,and the research status and results of FGM cylindrical shells.2.Based on Donnell shell theory and classical plate-shell theory,the buckling control equations of functionally graded cylindrical shells are obtained by using the Hamilton principle.The radial displacement expression is provided by the annular continuity of the cylindrical shell,and the dynamic buckling critical load expression is obtained by separating variable method.The numerical analysis of cylindrical shells of functionally graded material was performed using MATLAB.The influences of gradient index,the number of axial mode,the number of circumferential mode and diameter-thickness ratio,etc.on the critical load of dynamic buckling of functionally graded material cylindrical shell are discussed.3.Considering the first-order shear effect,the dynamic buckling of FGM cylindrical shells is discussed based on ritz method.Based on the hypothesis of Donnell shell theory,the dynamic buckling control equations of FGM cylindrical shells are deduced according to the Hamilton principle.By the property of the trigonometric function and the property of the solution of the equations,the expression of the buckling modal function with two boundary conditions is calculated.The critical load expression of dynamic buckling of cylindrical shells is obtained by simplifying the trigonometric functions in the control equation according to the Di Mo formula.The influence of gradient index and diameter thickness ratio,etc.of FGM on the critical load is discussed with MATLAB.