Application of the absolute nodal coordinate formulation to large rotation and large deformation problems, J. Mech. Des, vol.120, issue.2, pp.188-195, 1998. ,
A nonlinear dynamical theory for heterogeneous, anisotropic, elastic rods, AIAA J, vol.15, issue.1, pp.8-15, 1977. ,
A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams, Int. J. Solids Struct, vol.26, issue.11, pp.1253-1273, 1990. ,
On one-dimensional finite-strain beam theory: the plane problem, Z. für Angew. Math. Phys. ZAMP, vol.23, issue.5, pp.795-804, 1972. ,
On finite deformations of space-curved beams, Z. für Angew. Math. Phys. ZAMP, vol.32, issue.6, pp.734-744, 1981. ,
A finite strain beam formulation. the three-dimensional dynamic problem. part i, Comput. Methods Appl. Mech. Eng, vol.49, issue.1, pp.55-70, 1985. ,
Geometrically exact 3d beam theory: implementation of a strain-invariant finite element for statics and dynamics, Comput. Methods Appl. Mech. Eng, vol.171, issue.1, pp.141-171, 1999. ,
A beam finite element non-linear theory with finite rotations, Int. J. Numer. Methods Eng, vol.26, issue.11, pp.2403-2438, 1988. ,
Computational aspects of vector-like parametrization of three-dimensional finite rotations, Int. J. Numer. Methods Eng, vol.38, issue.21, pp.3653-3673, 1995. ,
A three-dimensional finite-strain rod model. part ii: computational aspects, Comput. Methods Appl. Mech. Eng, vol.58, issue.1, pp.79-116, 1986. ,
On the differentiation of the Rodrigues formula and its significance for the vector-like parameterization of Reissner-Simo beam theory, Int. J. Numer. Methods Eng, vol.55, issue.9, pp.1005-1032, 2002. ,
The quaternion-based three-dimensional beam theory, Comput. Methods Appl. Mech. Eng, vol.198, issue.49, pp.3944-3956, 2009. ,
Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam, Comput. Methods Appl. Mech. Eng, vol.198, issue.3, pp.555-571, 2008. ,
On the parametrization of the three-dimensional rotation group, SIAM Rev, vol.6, issue.4, pp.422-430, 1964. ,
On a virtual work consistent three-dimensional Reissner-Simo beam formulation using the quaternion algebra, Acta Mech, vol.224, issue.8, pp.1709-1729, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01518592
Non Linear Finite Element Analysis of Solids and Structures, vol.1, 1991. ,
An incremental approach to the solution of snapping and buckling problems, Int. J. Solids Struct, vol.15, issue.7, pp.529-551, 1979. ,
A new method to compute perturbed bifurcations: application to the buckling of imperfect elastic structures, Int. J. Eng. Sci, vol.28, issue.9, pp.943-957, 1990. ,
A path-following technique via an asymptotic-numerical method, Comput. Struct, vol.53, issue.5, pp.1181-1192, 1994. ,
Power series analysis as a major breakthrough to improve the efficiency of asymptotic numerical method in the vicinity of bifurcations, J. Comput. Phys, vol.236, pp.594-607, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00707513
Continuation of equilibria and stability of slender elastic rods using an asymptotic numerical method, J. Mech. Phys. Solids, vol.61, issue.8, pp.1712-1736, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01447361
Flexible Multibody Dynamics: a Finite Element Approach, 2001. ,
Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.455, pp.1125-1147, 1999. ,
Application of Quaternions to Computation with Rotations, 1979. ,
Quaternions for Computer Graphics, 2011. ,
A non-linear beam space-time finite element formulation using quaternion algebra: interpolation of the Lagrange multipliers and the appearance of spurious modes, Comput. Mech, vol.10, issue.5, pp.359-368, 1992. ,
The Finite Element Method: Solid Mechanics, vol.2, 2000. ,
Reduced minimization theory in beam elements, Int. J. Numer. Methods Eng, vol.37, issue.12, pp.2125-2145, 1994. ,
, Dynamics of Multibody Systems, 2013.
On the role of frame-invariance in structural mechanics models at finite rotations, Comput. Methods Appl. Mech. Eng, vol.191, issue.45, pp.5159-5176, 2002. ,
The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech, vol.34, issue.2, pp.121-133, 2004. ,
Interpolation of finite rotations in flexible multi-body dynamics simulations, Proc. Inst. Mech. Eng. Part K: J. Multi-body Dyn, vol.222, issue.4, pp.353-366, 2008. ,
On higher order integration of angular velocities using quaternions, Mech. Res. Commun, vol.55, pp.77-85, 2014. ,
Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures, Comput. Methods Appl. Mech. Eng, vol.192, issue.49, pp.5209-5248, 2003. ,
Non-linear spatial Timoshenko beam element with curvature interpolation, Int. J. Numer. Methods Eng, vol.50, issue.4, pp.761-785, 2001. ,
, Méthode Asymptotique Numérique, 2007.
A comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems, J. Sound Vib, vol.333, issue.12, pp.2554-2567, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01065672
, Méthodes numériques pour les systèmes dynamiques non linéaires: application aux instruments de musique auto-oscillants, 2012.
, Manlab -an Interactive Path-following and Bifurcation Analysis Software, 2011.
Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra, Comput. Mech, vol.4, issue.2, pp.115-135, 1988. ,
Large displacement analysis of three-dimensional beam structures, Int. J. Numer. Methods Eng, vol.14, issue.7, pp.961-986, 1979. ,
Kinematically exact curved and twisted strain-based beam, Int. J. Solids Struct, vol.49, issue.13, pp.1802-1817, 2012. ,
Instability of clamped-hinged circular arches subjected to a point load, J. Appl. Mech, vol.42, issue.4, pp.894-896, 1975. ,
Nonlinear finite element analysis of elastic systems under nonconservative loading-natural formulation. part i. quasistatic problems, Comput. Methods Appl. Mech. Eng, vol.26, issue.1, pp.75-123, 1981. ,