Large-deformation tests and total-Lagrangian finite-element analyses of flexible beams

Presented here is a total-Lagrangian displacement-based finite-element form ulation for general anisotropic beams undergoing large displacements and ro tations. The theory fully accounts for geometric nonlinearities (large rota tions), general initial curvatures, and extensionality by using Jaumann str ess and strain measures, an exact coordinate transformation, and a new conc ept of orthogonal virtual rotations. Moreover, transverse shear deformation s are accounted for by using a first-order shear-deformation theory. To ver ify the accuracy of the finite-element model, two test fixtures have been b uilt for bending and twisting experiments. Large static deformation tests o f beams with different loading conditions have been performed. The finite-e lement results agree closely with the experimental results and numerically exact solutions obtained by using a multiple shooting method to solve for p ost-buckling deformations of highly flexible beams undergoing large static rotations and displacements in three-dimensional space. (C) 2000 Elsevier S cience Ltd. All rights reserved.