Static analysis of FGM cylindrical shells and the effect of stress concentration using quasi-3D type higher-order shear deformation theory

Abstract

This paper explores the stress concentration effect and the static responses of FGM cylindrical shells with various boundary conditions using the quasi-3D type higher-order shear deformation theory and the analytical approach. The displacement field is expressed by polynomials of the coordinate along the thickness direction. Compared to the polynomial used to analyze the transverse displacement, the order of the in-plane displacement polynomial is increased by one. The equations of equilibrium and their corresponding boundary conditions are derived based on the principle of virtual work. Using simple trigonometric series and the Laplace transform, the solutions of boundary problems with different conditions are derived. The results from the present theoretical models are compared with previously published data using several other models, including the 3D exact model. The paper also exhibits the effects of the boundary condition, the relative thickness, the relative length and the power-law index on the displacements and the stresses of shells. The stress concentration phenomenon is studied, and then the effects of several structural and material parameters on the concentrated stress are shown and assessed.