Mixed boundary-value approach to analysis of thick fiber-reinforced composite beams on simple supports

Abstract

This thesis addressess a new analytical scheme for determining the elastic field of thick fiber-reinforced composite beams on simple supports. More specifically, the stress and displacement fields of thick fiber-reinforced composite beams are investigated using an efficient analytical scheme based on displacement-potential elasticity approach.

In the present displacement-potential approach, the structural 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. The plane problem is reduced here, to the determination of the potential function from a single partial differential equation of equilibrium. All the parameters associated with the elastic field, namely stress, strain and displacements are expressed in terms of the same potential function. The solution of the equilibrium equation is obtained in the form of infinite series, the coefficients of which are determined by appropriately satisfying the given physical conditions at different bounding surfaces of the elastic body.

In the present analytical model, a long (slender) bar subjected to mixed mode of boundary conditions at the opposing lateral ends is considered as the limiting case of the beam of interest, that is, the short (thick/deep) beam. The lateral dimension of the short beam is assumed to be identical to that of the long beam. Assuming a suitable displacement-potential function for the long beam and adjusting the necessary loading and supports of the short beam with respect to the long beam, elastic field of the short beam is derived from the solution of the long beam. The application of the method is demonstrated for a number of beams of interest, namely, the conventional simply supported beam, symmetric and asymmetric overhanging beams, a guided overhanging beam. Two limiting cases of fiber-orientations for the fiber-reinforced composite beams are considered with a wide range of beam aspect ratio with a view to determine the limiting size of the beam for which fiber-orientation effect remains prominent particularly in terms of stresses. The fiber-orientation effect on the beam is also investigated in the perspective of the stiffness ratio of the composite material. In an attempt to verify the soundness and accuracy of the analytical scheme developed, the present potential function solutions are compared with the corresponding solutions of available theoreticalapproaches, namely classical beam theory and airy stress function as well as experimental results. The solutions are found to be in reasonable agreement with each other for beams of isotropic as well as fiber-reinforced composite materials with different fiber orientations, which eventually establishes the soundness and appropriateness of the displacement-potential based analytical scheme.