Abstract:
This thesis deals with the analysis of stress and displacement fields of a mixed boundaryvalue
problem of fiber-reinforced composite materials. More specifically, the elastic field of
a thick stiffened simply-supported composite beam is investigated using an efficient
analytical scheme based on displacement-potential field formulation.
In the present displacement-potential approach, the elastic problem of composite materials
is formulated in terms of a single potential function of space variables, which is defined in
terms of the displacement components of plane elasticity. Accordingly, all the parameters
associated with the solution, namely stress, strain and displacements are expressed in terms
of the same potential function, which eventually reduces the plane problem to the
determination of the potential function from a single partial differential equation of
equilibrium. The solution of the equilibrium equation is obtained in the form of infinite
series, the coefficients of which are determined by appropriately satisfying the boundary
conditions at different edges of the beam.
Analytical expressions of the elastic field of the simply-supported beam are derived in terms
of the potential function using Fourier series. Solutions are obtained for two different types
of stiffeners (axial and lateral stiffeners) at the opposing lateral ends of the beam. Both the
isotropic as well as fiber-reinforced composite materials are considered for the present
analysis. Some of the practical issues of interest, like the effects of beam aspect ratio and
stiffeners are discussed in relation to the composite beam. The analytical scheme is then
extended to determine the fiber-orientation dependent stresses in stiffened simply-supported
beam. Two limiting cases of fiber orientation ( = 0o and 90o) are considered for a wide
range of beam aspect ratio.
In an attempt to verify the reliability and accuracy of the analytical scheme developed, the
present potential function solutions are compared with the corresponding solutions obtained
by classical beam theory and verified with two standard computational methods of
numerical techniques. The four solutions are found to be in excellent agreement with each
other for all the cases of stiffeners and fiber orientations considered, which eventually
establishes the soundness and appropriateness of the analytical scheme developed.
