Consistent higher-order beam theory for thin-walled box beams using recursive analysis: Membrane deformation under doubly symmetric loads

We propose a consistent higher-order beam theory in which cross-sectional deformations defining degrees of freedom are derived in the framework consistent with the mechanics of the proposed one-dimensional beam theory. This approach contrasts with earlier methods in which the procedure used to derive sectional deformations and the final beam theory are based on models of different levels. An advantage of the proposed consistent approach is that the generalized force-stress relation even for self-equilibrated forces such as bimoments can now be explicitly written. Also, sectional deformations can be systematically derived in closed form by the recursive and hierarchical approach. Accordingly, the accuracy in both displacement and stress can be adjusted so that obtained results are fully comparable with plate/shell results. We mainly conduct analysis of membrane deformations occurring in thin-walled box beams subjected to doubly symmetric loads such as axially-loaded forces. This case is elaborately chosen to better explain the fundamental concepts of our newly proposed approach. A brief description is also provided to show that these concepts are applicable to other types of loads such as bending and torsion. We confirm the accuracy of the theory proposed here by calculating stress and displacement in several examples.