A higher order deformation theory of orthotropic beams

If a beam is subjected to impact load or distributed load locally, the heig ht of the cross section in the beam directly under the load is deformed. In order to estimate accurately the deformation of the cross section height a nd the transversely normal and shear stress components, a consistent higher order deformation theory of orthotropic beams is proposed. In order to ver ify the validity and effectiveness of the proposed theory, the analytical s olution of a simple cantilevered beam problem is obtained and compared with the existed elastic solution. It is found that the displacement and stress components are identical to the corresponding solution of the Airy stress function in elasticity theory, and the deformation of the cross section hei ght and the transversely normal stress are also estimated reasonably.