An analytical and experimental investigation of the response of elliptical composite cylinders

An analytical and experimental investigation of the response of composite cylinders of elliptical cross-section to axial compression and internal pressure loadings is discussed. Nine eight-ply graphite-epoxy elliptical cylinders, three layups for each of three cross sectional aspect ratios, are specifically examined. The lay-ups studied are a quasi-isotropic (±45/0/90)g, an axially-stiff (±45/0₂)g, and a circumferentially-stiff (±45/90₂)g. The elliptical cross sections studied are characterized by semi-minor axis (b) to semi-major axis (a) ratios of b/a = 0.70, 0.85, and 1.00 (circular). The cross sections are obtained by holding the semi-major axis constant for all cross sections, and only varying the semi-minor axis. The nominal semi-major axis for all specimens was 5.00 in. (127 mm), and all specimens were cut to the same length, which provided a length-to-radius ratio of 2.9 for the circular cylinders. For the elliptical cross section cylinders, the length to- radius ratios, L/R(s), ranged from two to slightly greater than six, where R(s) is the function describing the circumferential variation of the radius. A geometrically nonlinear special-purpose analysis, based on Donnell’s nonlinear shell equations, is developed to study the prebuckling responses of geometrically perfect cylinders. In this analysis the circumferentially-varying radius of curvature of the cylinder is expanded in a cosine series. While elliptical sections are studied here, it should be noted that such an expansion will accommodate any cross section with at least two axes of symmetry. The displacements are likewise expanded in a harmonic series using the Kantorovich method. The total potential energy, written in terms of the displacements, is then integrated over the circumferential coordinate. The variational process then yields the governing Euler-Lagrange equations and boundary conditions. This process has been automated using the symbolic manipulation package Mathematica ©. The resulting nonlinear ordinary differential equations are then integrated via the finite difference method. A geometrically nonlinear finite element analysis is also utilized to compare with the prebuckling solutions of the special-purpose analysis and to study the prebuckling and buckling responses of geometrically imperfect cylinders. The imperfect cylinder geometries are represented by an analytical approximation of the measured shape imperfections. An accompanying experimental program is carried out to provide a means for comparison between the real and theoretical systems using a test fixture specifically designed for the present investigation to allow for both axial compression and internal pressurization. A description of the test fixture is included. Three types of tests were run on each specimen: (1) low internal pressure with no axial end displacement, (2) low internal pressure with a low level compressive axial displacement and, (3) compressive axial displacement to failure, with no internal pressure. The experimental data from these tests are compared to predictions for both perfect and imperfect cylinder geometries. Prebuckling results are presented in the form of displacement and strain profiles for each of the three sets of load conditions. Buckling loads are also compared to predicted values based upon classical estimates as well as linear and nonlinear finite element results which include initial shape imperfections. Lastly, the postbuckling and failure characteristics observed during the tests are described.