Mixed models and reduction techniques for large-rotation nonlinear problems

Abstract

Mixed models and reduction techniques are presented for the large-rotation nonlinear analysis of curved beams. A total Lagrangian description of the beam deformation is used, and the analytical formulation is based on a form of Reissner's large-deformation theory with the effects of transverse shear deformation and extensibility of the centerline included. Only planar deformations are considered, and the fundamental unknowns consist of the three internal forces and the three generalized displacements of the beam. The element characteristic arrays are obtained by using the Hellinger-Reissner mixed variational principle. The polynomial interpolation (or shape) functions used in approximating the internal forces are, in general, of different degree than those used for approximating the generalized displacements, and the forces are discontinuous at interelement boundaries. The use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated. Numerical results are presented to demonstrate the high accuracy and effectiveness of both the mixed models and the reduction techniques.