Automatic analysis of multicell thin-walled sections

An automatic procedure is outlined for the determination of the shear centre and the evaluation of the overall state of stress in multicell thin-walled sections subject to axial force, bending moment, shearing force and torque. Graph theory is shown to be the rationale to establish a topological model of the section which is preliminary to a computer implementation of the shear stress analysis. Specifically, we exploit the main features of the Depth-First-Search graph algorithm in order to automatically determine a number of independent circuits equal to the degree of connection m of the section. The algorithm also localize the m slits which make the section open, a preliminary step for the analysis of multicell sections subject to a shearing force. Further, the evaluation of the first elastic area moment at any point of the open section is addressed by means of the Open-Section-Cut algorithm elaborated in this paper. The outlined procedure entails a considerable simplification of the analysis, since the geometrical data which need to be assigned are only the strictly necessary ones, namely the coordinates of the vertices, the branches connecting them and their thickness. A numerical example, carried out for a ship's hull by means of a computer program written in Mathematica, shows the effectiveness of the proposed approach.