Development of Orthotropic Beam Element Using a Consistent Higher Order Deformation Theory

Abstract

In order to analyze beam structures more accurately and effectively, a two-node orthotropic beam element is proposed. This beam element is formulated using a consistent higher order deformation theory of orthotropic beams of which the transverse normal deformation can be effectively estimated. The stiffness matrix and the vector of equivalent nodal forces of the beam element are derived explicitly by the Galerkin method. In order to examine the reliability and the characteristics of the beam element, the analytical and the finite element solutions of a simple cantilevered beam are compared with each other. As a result, the following conclusions are obtained; (1) the accuracy of the suggested orthotropic beam element is very excellent and so the transverse normal deformation and shear stress of an orthotropic beam can be effectively estimated. (2) It can be used for accurately analyzing the general beam structures regardless of the Euler's or the Timoshenko's beam.