## Theses and Dissertations

#### Issuing Body

Mississippi State University

#### Committee Member

Sullivan, Rani W.

Myers, Oliver

Hammi, Youssef

12-9-2011

#### Document Type

Dissertation - Open Access

#### Major

Mechanical Engineering

#### Degree Name

Doctor of Philosophy

#### College

James Worth Bagley College of Engineering

#### Department

Department of Mechanical Engineering

#### Abstract

Equations of motion with required boundary conditions for doubly curved deep and thick composite shells are shown using two formulations. The first is based upon the formulation that was presented initially by Rath and Das (1973, J. Sound and Vib.) and followed by Reddy (1984, J. Engng. Mech. ASCE). In this formulation, plate stiffness parameters are used for thick shells, which reduced the equations to those applicable for shallow shells. This formulation is widely used but its accuracy has not been completely tested. The second formulation is based upon that of Qatu (1995, Compos. Press. Vessl. Indust.; 1999, Int. J. Solids Struct.). In this formulation, the stiffness parameters are calculated by using exact integration of the stress resultant equations. In addition, Qatu considered the radius of twist in his formulation. In both formulations, first order polynomials for in-plane displacements in the z-direction are utilized allowing for the inclusion of shear deformation and rotary inertia effects (first order shear deformation theory or FSDT). Also, FSDTQ has been modified in this dissertation using the radii of each laminate instead of using the radii of mid-plane in the moment of inertias and stress resultants equations. Exact static and free vibration solutions for isotropic and symmetric and anti-symmetric cross-ply cylindrical shells for different length-to-thickness and length-to-radius ratios are obtained using the above theories. Finally, the equations of motion are put together with the equations of stress resultants to arrive at a system of seventeen first-order differential equations. These equations are solved numerically with the aid of General Differential Quadrature (GDQ) method for isotropic, cross-ply, angle-ply and general lay-up cylindrical shells with different boundary conditions using the above mentioned theories. Results obtained using all three theories (FSDT, FSDTQ and modified FSDTQ) are compared with the results available in literature and those obtained using a three-dimensional (3D) analysis. The latter (3D) is used here mainly to test the accuracy of the shell theories presented here.

#### URI

https://hdl.handle.net/11668/19012