Exact 3-D Stress and Stiffness Analysis of Functionally Graded Cylindrical Shells

Abstract

The deflection and stress distributions of metal-ceramic functionally graded cylindrical shells are determined in the present work based on the Sampling Surfaces method (SaS). The material properties are assumed to vary continuously along the radial direction according to a power law distribution of the volume fraction of the constituents. In the three-dimensional formulation developed, the displacement field of not-equally-spaced surfaces parallel to the middle surface of the functionally graded shell is expressed as fundamental shell unknowns. The straindisplacement relationships, which are invariant rigid-body shell motions in the convected curvilinear coordinate system are then determined. By using sufficient number of sampling surfaces located at Chebyshev polynomial nodes, the exact 3-D elasticity solution for the functionally graded cylindrical shell is obtained. The effects of material properties and shell geometry on both the deflection and 3-D stress field are determined. The results of the present analysis are compared with the existing solutions available in the literature. The results reveal that by considering large number of sampling surfaces inside the thickness of the cylindrical shell, the accuracy of the solution can be improved significantly wherein the error will approach zero. A practical value for the number of sampling surfaces is determined and presented.