On the analysis of thin-walled beams based on Hamiltonian formalism. (1st July 2016) - Han, Shilei; Bauchau, Olivier A.
Highlights: The Hamiltonian approach is generalized to beams consisting of thin-walled panels. The proposed approach can handle curved sectional geometries. Closed-form central and extremity solutions are found. Correct boundary conditions based on the weak form formulation are derived. The beam's 6 × 6 sectional stiffness matrix is a by-product of the analysis. Abstract: In this paper, the Hamiltonian approach developed for beam with solid cross-section is generalized to deal with beams consisting of thin-walled panels. The governing equations of plates and cylindrical shells for the panels are cast into Hamiltonian canonical equations and closed-form central and extremity solutions are found. Typically, the end-effect zones for thin-walled beams are much larger than those for beams with solid cross-sections. Consequently, extremity solutions affect the solution significantly. Correct boundary conditions based on the weak form formulation are derived. Numerical examples are presented to demonstrate the capabilities of the analysis. Predictions are found to be in good agreement with those of plate and shell FEM analysis.