On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach

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

[2]  J. Argyris An excursion into large rotations , 1982 .

[3]  C. DeWitt-Morette,et al.  Analysis, manifolds, and physics , 1977 .

[4]  S. Antman,et al.  5.—Qualitative Aspects of the Spatial Deformation of Non-linearly Elastic Rods. , 1975, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[5]  Albert I. King,et al.  Computation of Rigid-Body Rotation in Three-Dimensional Space From Body-Fixed Linear Acceleration Measurements , 1979 .

[6]  T. Belytschko,et al.  Computational Methods for Transient Analysis , 1985 .

[7]  J. C. Simo,et al.  A finite strain beam formulation. The three-dimensional dynamic problem. Part I , 1985 .

[8]  T. Hughes,et al.  Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis , 1980 .

[9]  R. P. Nordgren,et al.  On Computation of the Motion of Elastic Rods , 1974 .

[10]  E. Reissner On finite deformations of space-curved beams , 1981 .

[11]  Thomas J. R. Hughes,et al.  Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics , 1976 .

[12]  The Role of Saint Venant’s Solutions in Rod and Beam Theories , 1979 .

[13]  Stuart S. Antman,et al.  The Theory of Rods , 1973 .

[14]  D. W. Scharpf,et al.  Finite element method — the natural approach , 1979 .

[15]  J. C. Simo,et al.  On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part II , 1986 .

[16]  A. Love,et al.  The Mathematical Theory of Elasticity. , 1928 .

[17]  Charles S. Kenney,et al.  Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity , 1981 .

[18]  John Argyris,et al.  Nonlinear finite element analysis of elastic systems under nonconservative loading—natural formulation part II. Dynamic problems , 1981 .

[19]  P. Likins,et al.  Floating reference frames for flexible spacecraft , 1977 .

[20]  E. Reissner,et al.  On One‐Dimensional Large‐Displacement Finite‐Strain Beam Theory , 1973 .

[21]  Stuart S. Antman,et al.  Kirchhoff’s problem for nonlinearly elastic rods , 1974 .

[22]  S. Antman,et al.  Travelling waves in hyperelastic rods , 1979 .

[23]  The Hamiltonian Structure of Nonlinear Elasticity: The Convective Representation of Solids, Rods, and Plates, , 1987 .

[24]  T. Hughes Numerical Implementation of Constitutive Models: Rate-Independent Deviatoric Plasticity , 1984 .

[25]  Robert L. Taylor,et al.  Numerical formulations of elasto-viscoplastic response of beams accounting for the effect of shear , 1984 .

[26]  E. Reissner Some remarks on the problem of column buckling , 1982 .