Higher order composite beam theory built on Saint-Venant’s solution. Part-I: Theoretical developments

This two-part-paper proposes a higher order composite beam theory that can be viewed as an extension of Saint-Venant’s theory. Saint-Venant’s solution, is known to represent the exact 3D solution in the interior part of a beam, far from the end-sections where the boundary conditions are applied. The difference between these solutions contains the end-effects. The objective of the proposed theory is to capture a significant part of these end-effects in order to predict the 3D-stresses in a larger interior-part of the beam, and therefore better describe its structural behavior. Based on a kinematics built from the exact form of Saint-Venant displacement, the present theory is rigorously derived for the case of symmetric cross section made of orthotropic materials. Closed-form expressions are obtained for the stiffness matrix of the structural behavior and for the 3D-stresses. Easy to compare to those of Saint-Venant, these results highlight the contribution of this approach. Part-I is devoted to the theoretical developments and part-II illustrates the predictive capability of this theory through the analysis of tip loaded cantilever beams, focusing the built-in effects influence on the structural behavior of the beam.