Vijaya Kumar

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


This thesis presents a generalized numerical method for the geometrically nonlinear analysis of thin laminated composite shells. Exact expansion of the Green's strain components are used for the inplane strains and linear strain-displacement relations are used for the transverse shear strains. These relations are then obtained for a general laminated shell geometry described by orthogonal curvilinear coordinates. Parabolic variation of the transverse shear stresses along the thickness and the effects of rotary inertia are included in the formulation. The developed equations of motion are based on a total Lagrangian frame of reference.;A Ritz-type solution scheme which involves a new concept of using Bezier surface patches to represent the displacement fields is presented in this thesis. The shape and size of these patches are controlled by certain arbitrary points called Control Points. Owing to the special characteristics of these Control Points, the treatment of displacements, slopes, curvatures, etc. at a particular edge becomes very simple. Hence the enforcement of boundary conditions along the edges is straightforward.;Initially, the linear free vibration study of laminated shells is performed by simplifying the nonlinear equations of motion. Numerical examples involving laminated spherical, conical and circular and noncircular cylindrical shells with open and closed geometries are investigated in detail. Good convergence of the natural frequencies is observed by using only eighth order Bezier surface patches. The validity and accuracy of the present analysis are demonstrated by comparing the calculated results with those available in the literature. The influences of material strength, number of layers, fiber orientation and boundary conditions on the natural frequencies are also examined for various shell geometries.;The geometrically nonlinear equations of motion are cast in a matrix form in terms of the Bezier control points. These equations are then solved using Beta-m time integration method and Newton-Raphson iterations. The numerical results obtained are initially compared with those available in the literature. The linear and nonlinear dynamic responses of laminated circular and noncircular cylindrical panels under point load are investigated and the effect of noncircularity on the response is also examined.



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