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

Presented here is a total-Lagrangian displacement-based ®nite-element formulation for general anisotropic beams undergoing large displacements and rotations. The theory fully accounts for geometric nonlinearities (large rotations), general initial curvatures, and extensionality by using Jaumann stress and strain measures, an exact coordinate transformation, and a new concept of orthogonal virtual rotations. Moreover, transverse shear deformations are accounted for by using a ®rst-order shear-deformation theory. To verify the accuracy of the ®nite- element model, two test ®xtures have been built for bending and twisting experiments. Large static deformation tests of beams with di€erent loading conditions have been performed. The ®nite-element results agree closely with the experimental results and numerically exact solutions obtained by using a multiple shooting method to solve for post-buckling deformations of highly ¯exible beams undergoing large static rotations and displacements in three- dimensional space.