Displacement potential solution of a deep stiffened cantilever beam of orthotropic composite material

Abstract

An analytical solution of the elastic field of a deep stiffened cantilever beam of orthotropic composite material is presented in the paper. The cantilever beam is subjected to a parabolic shear loading at its free lateral end and the two opposing longitudinal edges are stiffened. Unidirectional fibre-reinforced composite is considered for the present analysis where the fibres are assumed to be directed along the beam length. Following a new development, the present mixed-boundary-value elastic problem is formulated in terms of a single potential function defined in terms of the associated displacement components. This formulation reduces the problem to the solution of a single fourth-order partial differential equation of equilibrium and is capable of dealing with mixed modes of boundary conditions appropriately. The solution is obtained in the form of an infinite series. Results of different stress and displacement components at different sections of the composite beam are presented numerically in the form of graphs. Finally, in an attempt to check the reliability as well as the accuracy of the present solution, the problem is solved by using two standard numerical methods of solution. A comparison of the results shows that the analytical and numerical solutions of the present problem are in good agreement and thus establishes the soundness as well as the reliability of the present displacement potential approach to solution of the elastic field of orthotropic composite structures.