A Cantilever Subjected to Axial Force, Bending Moment, and Shear Force

We present an exact analysis of the displacement and stress fields in an elastic 2-D cantilever subjected to axial force, shear force and moment, in which the end conditions are exactly satisfied. The problem is formulated on the basis of the state space formalism for 2-D deformation of an orthotropic body. Upon delineating the Hamiltonian characteristics of the formulation and by using eigenfunction expansion, a rigorous solution which satisfies the end conditions is determined. The results show that the end condition alters the stress significantly only near the end, and elementary solutions in the form of polynomials can give sufficiently accurate results except near the ends. Such a system would give rise to localized stresses and displacements in the immediate neighborhood of the ends, and the effect may be expected to diminish with distance on account of geometrical divergence.

A New Model of Orthotropic Bodies

The solution of linearly elastic and orthotropic solid bodies is very complicated, thus a new element model for solving linearly elastic and orthotropic bodies is presented by using the generalized Hooke's law and the superposition principle. This new model is a simple truss consisting of some bars, and then the solution of orthotropic body becomes simple. Furthermore, this new model reveals the physical mechanism of a solid body under the action of applied forces.