On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory
暂无分享,去创建一个
Dinar Camotim | Manuel Ritto-Corrêa | D. Camotim | M. Ritto-Corrêa | M. Ritto‐Corrêa | Manuel Ritto‐Corrêa
[1] K. C. Gupta,et al. An historical note on finite rotations , 1989 .
[2] J. C. Simo,et al. A finite strain beam formulation. The three-dimensional dynamic problem. Part I , 1985 .
[3] M. Géradin,et al. A beam finite element non‐linear theory with finite rotations , 1988 .
[4] E. Reissner,et al. On One‐Dimensional Large‐Displacement Finite‐Strain Beam Theory , 1973 .
[5] K. Bathe,et al. Large displacement analysis of three‐dimensional beam structures , 1979 .
[6] F. Gruttmann,et al. A geometrical nonlinear eccentric 3D-beam element with arbitrary cross-sections , 1998 .
[7] E. Dvorkin,et al. On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments , 1988 .
[8] D. Camotim,et al. Integration algorithm forJ2 elastoplasticity under arbitrary mixed stress-strain control , 2001 .
[9] Filip C. Filippou,et al. Non-linear spatial Timoshenko beam element with curvature interpolation , 2001 .
[10] A. Ibrahimbegovic,et al. Finite rotations in dynamics of beams and implicit time-stepping schemes , 1998 .
[11] Dinar Camotim,et al. Work-conjugacy between rotation-dependent moments and finite rotations , 2003 .
[12] D. W. Scharpf,et al. Finite element method — the natural approach , 1979 .
[13] John Argyris,et al. Nonlinear finite element analysis of elastic systems under nonconservative loading—natural formulation part II. Dynamic problems , 1981 .
[14] J. C. Simo,et al. A three-dimensional finite-strain rod model. Part II: Computational aspects , 1986 .
[15] A. Ibrahimbegovic. On finite element implementation of geometrically nonlinear Reissner's beam theory: three-dimensional curved beam elements , 1995 .
[16] J. C. Simo,et al. A Geometrically-exact rod model incorporating shear and torsion-warping deformation , 1991 .
[17] J. C. Simo,et al. Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms , 1995 .
[18] J. C. Simo,et al. The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: intrinsic definition and geometric interpretation , 1992 .
[19] Stuart S. Antman,et al. Kirchhoff’s problem for nonlinearly elastic rods , 1974 .
[20] M. Crisfield,et al. Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[21] E. Reissner. On finite deformations of space-curved beams , 1981 .
[22] Byung Chai Lee,et al. GEOMETRICALLY NON-LINEAR AND ELASTOPLASTIC THREE-DIMENSIONAL SHEAR FLEXIBLE BEAM ELEMENT OF VON-MISES-TYPE HARDENING MATERIAL , 1996 .
[23] Gordan Jelenić,et al. Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics , 1999 .
[24] E. Reissner. On one-dimensional finite-strain beam theory: The plane problem , 1972 .
[25] Satya N. Atluri,et al. Variational approaches for dynamics and time-finite-elements: numerical studies , 1990 .
[26] Werner Wagner,et al. THEORY AND NUMERICS OF THREE-DIMENSIONAL BEAMS WITH ELASTOPLASTIC MATERIAL BEHAVIOUR ∗ , 2000 .
[27] E. Stein,et al. On the parametrization of finite rotations in computational mechanics: A classification of concepts with application to smooth shells , 1998 .
[28] E. Ramm,et al. Shell theory versus degeneration—a comparison in large rotation finite element analysis , 1992 .
[29] M. Géradin,et al. Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra , 1988 .
[30] J. Argyris. An excursion into large rotations , 1982 .
[31] A. Ibrahimbegovic,et al. Computational aspects of vector-like parametrization of three-dimensional finite rotations , 1995 .