A simple finite element for the geometrically exact analysis of Bernoulli–Euler rods

[1]  Paulo M. Pimenta,et al.  A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy , 2017 .

[2]  Wolfgang A. Wall,et al.  Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures , 2016, International Journal of Solids and Structures.

[3]  Alexander Popp,et al.  Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff–Love Theory Versus Simo–Reissner Theory , 2016, 1609.00119.

[4]  J. Korelc,et al.  On path-following methods for structural failure problems , 2016 .

[5]  Peter Wriggers,et al.  Automation of Finite Element Methods , 2016 .

[6]  Roland Wüchner,et al.  Nonlinear isogeometric spatial Bernoulli Beam , 2016 .

[7]  S. Krylov,et al.  Extension of non-linear beam models with deformable cross sections , 2015 .

[8]  Wolfgang A. Wall,et al.  An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods , 2014 .

[9]  E. Campello,et al.  Effect of higher order constitutive terms on the elastic buckling of thin-walled rods , 2014 .

[10]  Leopoldo Greco,et al.  B-Spline interpolation of Kirchhoff-Love space rods , 2013 .

[11]  Jose Manuel Valverde,et al.  Invariant Hermitian finite elements for thin Kirchhoff rods. I: The linear plane case ☆ , 2012 .

[12]  Frédéric Boyer,et al.  Geometrically exact Kirchhoff beam theory : application to cable dynamics , 2011 .

[13]  P. Wriggers,et al.  An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells , 2011 .

[14]  F. Gruttmann,et al.  A nonlinear Hu–Washizu variational formulation and related finite-element implementation for spatial beams with arbitrary moderate thick cross-sections , 2011 .

[15]  E. Campello,et al.  Shell curvature as an initial deformation: A geometrically exact finite element approach , 2009 .

[16]  F. Gruttmann,et al.  A mixed hybrid finite beam element with an interface to arbitrary three-dimensional material models , 2009 .

[17]  Ignacio Romero,et al.  The interpolation of rotations and its application to finite element models of geometrically exact rods , 2004 .

[18]  Frédéric Boyer,et al.  Finite element of slender beams in finite transformations: a geometrically exact approach , 2004 .

[19]  Eduardo M. B. Campello,et al.  A FULLY NONLINEAR MULTI-PARAMETER ROD MODEL INCORPORATING GENERAL CROSS-SECTIONAL IN-PLANE CHANGES AND OUT-OF-PLANE WARPING , 2003 .

[20]  Werner Wagner,et al.  THEORY AND NUMERICS OF THREE-DIMENSIONAL BEAMS WITH ELASTOPLASTIC MATERIAL BEHAVIOUR ∗ , 2000 .

[21]  Werner Wagner,et al.  Shear stresses in prismatic beams with arbitrary cross‐sections , 1999 .

[22]  W. Smoleński Statically and kinematically exact nonlinear theory of rods and its numerical verification , 1999 .

[23]  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.

[24]  F. Gruttmann,et al.  A geometrical nonlinear eccentric 3D-beam element with arbitrary cross-sections , 1998 .

[25]  Paulo M. Pimenta,et al.  Geometrically Exact Analysis of Spatial Frames , 1993 .

[26]  J. C. Simo,et al.  The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: intrinsic definition and geometric interpretation , 1992 .

[27]  Thomas J. R. Hughes,et al.  Formulations of finite elasticity with independent rotations , 1992 .

[28]  J. C. Simo,et al.  A three-dimensional finite-strain rod model. Part II: Computational aspects , 1986 .

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

[30]  A. B. Whitman,et al.  An exact solution in a nonlinear theory of rods , 1974 .

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

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

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

[34]  Leopoldo Greco,et al.  An isogeometric implicit G1 mixed finite element for Kirchhoff space rods , 2016 .

[35]  E. Campello,et al.  A Fully Nonlinear Thin Shell Model of Kirchhoff-Love Type , 2010 .

[36]  Peter Wriggers,et al.  New trends in thin structures : formulation, optimization and coupled problems , 2010 .

[37]  P. Wriggers,et al.  An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods , 2008 .

[38]  P. Pimenta Geometrically exact analysis of initially curved rods , 1996 .

[39]  Goto Yoshiaki,et al.  Elastic buckling phenomenon applicable to deployable rings , 1992 .

[40]  J. C. Simo,et al.  A Geometrically-exact rod model incorporating shear and torsion-warping deformation , 1991 .

[41]  Stephen P. Timoshenko,et al.  History of strength of materials : with a brief account of the history of theory of elasticity and theory of structures , 1983 .