New total-Lagrangian FEA and experiments on highly flexible structures

摘要

Presented here is a new total-Lagrangian displacement-based finite-element formulation for 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 first-order shear deformation theory with shear correction factors obtained by matching the shear strain energy and stress resultants with those of a layerwise higher-order shear deformation theory. ^Two test fixtures have been built for bending and twisting tests with different loading conditions. ^Large static deformation tests on several beams have been performed. ^Difficulties in measuring large deformations involving large rotations and influence of initial imperfections will be discussed. ^Experimental results are compared with finite-element results, showing that the finite-element model is accurate in predicting large deformations of flexible beams. ^(Author)