Non-linear spatial Timoshenko beam element with curvature interpolation

The paper presents a spatial Timoshenko beam element with a total Lagrangia n formulation. The element is based an curvature interpolation that is inde pendent of the rigid-body motion of the beam element and simplifies the for mulation. The section response is derived from plane section kinematics. A two-node beam element with constant curvature is relatively simple to formu late and exhibits excellent numerical convergence. The formulation is exten ded to N-node elements with polynomial curvature interpolation. Models with moderate discretization yield results of sufficient accuracy with a small number of iterations at each load step. Generalized second-order stress res ultants are identified and the section response takes into account non-line ar material behaviour. Green-Lagrange strains are expressed in terms of sec tion curvature and shear distortion, whose first and second variations are functions of node displacements and rotations. A symmetric tangent stiffnes s matrix is derived by consistent linearization and an iterative accelerati on method is used to improve numerical convergence for hyperelastic materia ls. The comparison of analytical results with numerical simulations in the literature demonstrates the consistency, accuracy and superior numerical pe rformance of the proposed element. Copyright (C) 2001 John Wiley & Sons, Lt d.