Free-edge stress fields in cylindrically curved cross-ply laminated shells

Abstract

This paper discusses a semi-analytical approach to the determination of three-dimensional stress fields in cylindrically curved orthotropic symmetrically or unsymmetrically laminated composite shells under bending load under consideration of free-edge effects. The analysis method incorporates a plane-strain analysis in the innermost regions of the shell (the so-called inner solution) in conjunction with a free-edge solution which enables the accurate determination of the interlaminar stress field at the free shell edges. The free-edge solution employs a discretization of the laminated shell into a number of mathematical layers with respect to the thickness direction wherein in each layer interface approximate and a priori unknown displacement functions are introduced. Lagrangian shape functions are used to interpolate between the displacement functions in the interfaces, and various orders of shape functions are investigated in this paper. The differential equations and boundary conditions that describe the current stress problem are derived from the principle of minimum elastic potential of the laminated shell. The resultant differential equations allow for an exact solution for the displacement functions whereas the boundary conditions at the free shell edges are satisfied in an integral sense. The results of the developed analysis method are verified by comparison with detailed finite element computations, and it is found that the semi-analytical approach works with comparable accuracy, however only at a fraction of the required computational effort.