A robust algorithm for calculating the spatial deformations of rods without tensile strength

A globally convergent iterative algorithm for computing the spatial deformations of elastic beams without tensile strength is presented. The core of the algorithm is an iterative scheme (consistent with the classical Kirchhoff rod theo ry) for locating the neutral axis and thus for determining the curvature. We prove uniqueness and local stability for the general case and global stability for symmetric cross sections. The scheme is embedded in an iteration-free global boundary value problem solver (the so-called Parallel Hybr id Algorithm) to determine spatial equilibrium configurations. The obvious applications are steel reinforced concrete beams and columns, with or without pre-stressing.