A rather thorough and novel buckling analysis of an axially-loaded orthotropic circular cylindrical shell is formulated. The analysis assumes prebuckling rotations are negligible and uses a unique re-defining of the orthotropic material properties in terms of a so-called geometric mean isotropic (GMI) material. Closed-form expressions for the buckling stress in terms of cylinder geometry and orthotropic material properties are presented, the particular closed form depending on the specific character of the orthotropic material relative to the GMI material. With the formulation, the specific character of the buckling deformations - e.g., axisymmetric or nonaxisymmetric, the number of axial and circumferential waves - can be established. By using the maximum radius of curvature of an elliptical cross section in this formulation, the analysis is used to demonstrate the detrimental effects of an elliptical cross section on axial buckling capacity when compared to a circular cross section with the same circumference. Using the circumferentially-varying radius of curvature of an elliptical cross section, the analysis is then further used as the basis for developing two methods for improving the axial buckling capacity of elliptical cylinders. The first approach involves varying the wall thickness of an isotropic elliptical cylinder with circumferential position. Uniformly stable elliptical cross sections which preserve the same critical stress, critical load, or volume of an axially loaded circular cylinder of the same circumference are designed with the formulation. The second approach involves maintaining a uniform wall thickness but varying the orthotropic material properties with circumferential position. This approach is applied to a cylindrical lattice structure where it is assumed that the ribs are dense enough to be able to describe the lattice structure by means of an equivalent homogenized material. The orthotropic properties of the homogenized material are varied by varying the lattice rib angle with circumferential position. Considerable recovery of the axial buckling capacity of the variable-rib-angle design elliptical cylinder compared to the same cylinder constructed in isogrid fashion is demonstrated. In fact, recovery relative to an isogrid circular cylinder of the same circumference is demonstrated. For both approaches confirming finite element models are used to verify the findings. The two different approaches are compared, and finally the two approaches are recognized as special cases of a more general design philosophy. / Ph. D.

This study focuses on the improvement of the axial buckling capacity of elliptical composite cylinders through the use of a circumferentially-varying lamination sequence. The concept of varying the lamination sequence around the circumference is considered as a viable approach for off-setting the disadvantages of having the cylinder radius of curvature vary with circumferential position, the source of the reduced buckling capacity when compared to a circular cylinder with the same circumference. Post-buckling collapse behavior and material failure characteristics are also of interest. Two approaches to implementing a circumferential variation of lamination are examined. For the first approach the lamination sequence is varied in a stepwise fashion around the circumference. Specifically, each quadrant of the cylinder circumference is divided into three equal-length regions denoted as the crown, middle, and side regions. Eight different cylinders designs, whereby each region is constructed of either a quasi-isotropic or an axially-stiff laminate of equal thickness, are studied. Results are compared to the baseline case of an elliptical cylinder constructed entirely of a quasi-isotropic laminate. Since the thickness of the quasi-isotropic and axially-stiff laminates are the same, all cylinders weight the same and thus comparisons are meaningful. Improvements upwards of 18% in axial buckling capacity can be achieved with one particular stepwise design. The second approach considers laminations that vary circumferentially in a continuous fashion to mitigate the effects of the continuously-varying radius of curvature. The methodology for determining how to tailor the lamination sequence circumferentially is based on the analytical predictions of a simple buckling analysis for simply-supported circular cylinders. With this approach, axial buckling load improvements upwards of 30% are realized. Of all the cylinders considered, very few do not exhibit material failure upon collapse in the post-buckled state. Of those that do not, there is little, if any, improvement in bucking capacity. Results for the pre-buckling, buckling, post-buckling, and material failure are obtained from the finite-element code ABAQUS using both static and dynamic analyses. Studies with the code demonstrate that the results obtained are converged. / Ph. D.