Rapid Stress Analytical Solutions of Steel Strips Subjected to Non-uniform Tensile Loads Based on New Symplectic Method

This paper deals with the stress distribution problem of steel strips subjected to non-uniform tensile loads at both ends, which induce the transverse in-plane compressive stress and is important for researching the transverse buckling of the steel strip. For stress distribution problem, the traditional finite element method (FEM) has acceptable accuracy while it takes too long computing time to be applied to on-site production and the semi-inverse analytical method needs to preset the form of stress solution and gets the solution with a certain error. Thence, a rapid symplectic analytical method for solving stress distribution problem of steel strips is presented, which is based on the Hamiltonian system unlike other traditional method based on the Lagrangian system. Furthermore, the rational and rigorous derivation without any forecast about the form of solution makes the stress result have high precision with short computing time. Finally, the symplectic method is demonstrated be more efficient and suitable in the on-line calculation by comparing with FEM.