Type of Document Dissertation Author Paschero, Maurizio Author's Email Address mpascher@vt.edu URN etd-04032008-173035 Title Improvement of the axial buckling capability of elliptical cylindrical shells Degree PhD Department Engineering Science and Mechanics Advisory Committee

Advisor Name Title Hyer, Michael W. Committee Chair Batra, Romesh C. Committee Member Beex, A. A. Louis Committee Member Patil, Mayuresh J. Committee Member Thangjitham, Surot Committee Member Keywords

- Stability
- Material tailoring
- Variable thickness cylinders
- Elliptical cylinders
- Anisogrid cylinders
Date of Defense 2008-03-25 Availability unrestricted AbstractA rather thorough and novel buckling analysis of an axially-loaded orthotropic circular cylindricalshell 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.

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