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.

[1]  G. B. Sinclair.  The non-linear bending of a cantilever beam with shear and longitudinal deformations , 1979 .

[2]  John Argyris,et al.  Static and dynamic stability of nonlinear elastic systems under nonconservative forces—Natural approach , 1982 .

[3]  J. H. Argyris,et al.  A simple theory of geometrical stiffness with applications to beam and shell problems , 1976 .

[4]  R. D. Wood,et al.  GEOMETRICALLY NONLINEAR FINITE ELEMENT ANALYSIS OF BEAMS, FRAMES, ARCHES AND AXISYMMETRIC SHELLS , 1977 .

[5]  Robert Schmidt,et al.  Instability of Clamped-Hinged Circular Arches Subjected to a Point Load , 1975 .

[6]  Egor P. Popov,et al.  Incremental analysis of large deflections of shells of revolution , 1971 .

[7]  Ahmed K. Noor,et al.  Mixed models and reduced/selective integration displacement models for nonlinear shell analysis , 1982 .

[8]  Ahmed K. Noor,et al.  Tracing post-limit-point paths with reduced basis technique , 1981 .

[9]  C. Chon,et al.  On the tangent stiffness matrix in a convected coordinate system , 1980 .

[10]  Ahmed K. Noor,et al.  Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams , 1981 .

[11]  E. Reissner.  On one-dimensional finite-strain beam theory: The plane problem , 1972 .

[12]  Ahmed K. Noor,et al.  Recent advances in reduction methods for instability analysis of structures , 1983 .

[13]  Klaus-Jürgen Bathe,et al.  A geometric and material nonlinear plate and shell element , 1980 .

[14]  A. Noor.  Recent advances in reduction methods for nonlinear problems. [in structural mechanics , 1981 .

[15]  B. J. Hsieh,et al.  Non-Linear Transient Finite Element Analysis with Convected Co--ordinates , 1973 .

[16]  T. Y. Yang,et al.  Matrix displacement solution to elastica problems of beams and frames , 1973 .

[17]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[18]  Gerald Wempner,et al.  Finite elements, finite rotations and small strains of flexible shells , 1969 .

[19]  Ahmed K. Noor,et al.  Reduced Basis Technique for Nonlinear Analysis of Structures , 1980 .