## Dissertations

Dissertation

Summer 8-31-2001

#### Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)

#### Department

Mechanical Engineering

A. C. Ugural

Bernard Koplik

Rong-Yaw Chen

Benedict C. Sun

C.T. Thomas Hsu

#### Abstract

Conical shells are extensively used in space crafts, robots, shelters, domes, tanks, and in machinery or devices (e.g. as Belleville washers). Thus, the design of minimum weight, maximum strength, stiffened conical (and cylindrical) shells under combined loads has long been of interest to designers. The objective of this study is to improve the strength of conical shells and reduce the weight of the structure. Buckling of composite conical shells subjected to combined axial loading, external pressure, and bending is investigated using energy and finite element methods. The conical shells have single and multiple layers, different cone angle, length, and radius. These parameters are considered to determine optimal condition against loads. It shall be demonstrated that these layers will improve buckling values of compression, external pressure, and bending of the composite shell. The applied loading is resisted primarily by in-plane stresses of the conical shell.

Donnell-type shell theory and Minimum Potential Energy Methods are presented for linear bending analysis of composite laminated conical shells with isotropic and orthotropic stretching-bending coupling under combined loading. The buckling equations for the shells are expressed in terms of displacements. The solution is developed in the form of a power series in terms of a particularly convenient coordinate system. The energy method is used to develop the recurrence relations to calculate coefficients of the series. A set of typical boundary conditions, thicknesses, the direction of layers axes of orthotropy, number of them, the circumferential wave number, and different materials are considered to analyze the buckling.

The energy solution is extended to include the buckling of composite cones subjected to combined loads. This step shows clearly what type of load contributes more than other loads for buckling. The parameters for the cones are also investigated to find the interesting values for strong structures. Finite Element Analysis is extensively used to verify the results. The numerical solutions obtained are also compared with those of cylinders.

COinS