Static Analysis Of Functionally Graded Laminated Cylindrical Thick Shells Under General Boundary Conditions

Functionally graded laminated cylindrical thick shells have become important components in engineering because of their good geometric configurations and excellent functional properties.However,the two-dimensional thin shell theory and medium thickness shell theory cannot meet the solving requirements because of the large geometric thickness,the anisotropy and non-uniformity of the materials,and the complicated load forms and boundary conditions.Based on the three-dimensional elastic equation,the state-space method can well analyze the(functionally graded)laminated cylindrical thick shells and obtain the exact solution of the related problems,and the precise distribution law of the relevant mechanical quantities along the radial direction can be show.It can also deal with the anisotropy,non-uniformity and interlayer continuity of materials.However,it is difficult to satisfy the boundary conditions strictly by analytical method when solving non-simply-supported boundary problems.It usually needs to be solved in combination with numerical methods.In this paper,an analytical method is proposed to overcome the limitation of the state space method for general boundary conditions.The method deals with the nonsimply supported boundary conditions of functionally graded laminated cylindrical thick shells,and obtains the exact analytical solutions of the related static problems under general boundary conditions.Firstly,for(functionally graded)laminated cylindrical thick shells with non-simply supported ends,based on the three-dimensional fundamental equations of elasticity,the state equation with partial differential operator is established by taking the thickness direction as the direction of state transition.Secondly,the variables are separated by Fourier series,and related boundary displacement functions are introduced according to the boundary conditions of nonsimply-supported ends,so that the displacement and stress boundary conditions are strictly satisfied along the thickness direction.Furthermore,the boundary displacement functions are substituted into the state equations as state variables,the nonhomogeneous state equations are transformed into homogeneous state equations by using the dimensional expanding method.Then,the variable coefficient matrixes in the state equations are transformed into constant coefficient matrixes by the approximate lamination method.The relationship between the internal and external mechanical quantities between sub-layers is obtained according to the state space theory.Finally,according to the stress conditions on the inner and outer surfaces of(functionally graded)cylindrical thick shells and the continuity conditions between layers,the global solutions of(functionally graded)cylindrical thick shells is obtained.In Chapter three to Chapter seven,the static problems of thick cylindrical shells with single and laminated(functionally graded)with clamped ends,one clamped end and one simply-supported end and cantilever are calculated and analyzed respectively.The accuracy and effectiveness of the method are verified,and the influence of related factors on the static response is further discussed.Firstly,the single-layer thick shell is calculated by selecting the number of different series terms and sub-layers,and the obtained solutions are compared with the numerical solutions,which verifies the high precision and good convergence of the present method.Secondly,for the single and laminated cylindrical thick shells with different span-radius ratios and thickness-radius ratios,their effects on the static responses are revealed by the exact distribution of the relevant mechanical quantities.Then,the new method is used to analyze the laminated cylindrical shells with different lay-up methods,and the influence of lay-up angle and lay-up number on the static response is discussed.Finally,for functionally graded single and laminated cylindrical thick shells,the effects of functionally gradient index,thickness-radius ratios and span-radius ratios on structural static response are discussed by the precise distribution of mechanical parameters.