Locking-free isogeometric collocation formulation for three-dimensional geometrically exact shear-deformable beams with arbitrary initial curvature
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[1] E. Stein,et al. On the parametrization of finite rotations in computational mechanics: A classification of concepts with application to smooth shells , 1998 .
[2] Ignacio Romero,et al. A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations , 2008 .
[3] Leopoldo Greco,et al. B-Spline interpolation of Kirchhoff-Love space rods , 2013 .
[4] F. Auricchio,et al. On the geometrically exact beam model: A consistent, effective and simple derivation from three-dimensional finite-elasticity , 2008 .
[5] Giancarlo Sangalli,et al. Optimal-order isogeometric collocation at Galerkin superconvergent points , 2016, 1609.01971.
[6] Hector Gomez,et al. Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models , 2014, J. Comput. Phys..
[7] J. Argyris. An excursion into large rotations , 1982 .
[8] Z. Li,et al. A co-rotational formulation for 3D beam element using vectorial rotational variables , 2006 .
[9] P. Wriggers,et al. Isogeometric large deformation frictionless contact using T-splines , 2014 .
[10] Nicholas Fantuzzi,et al. A new doubly-curved shell element for the free vibrations of arbitrarily shaped laminated structures based on Weak Formulation IsoGeometric Analysis , 2017 .
[11] T. Hughes,et al. ISOGEOMETRIC COLLOCATION METHODS , 2010 .
[12] T. R. Hughes,et al. Mathematical foundations of elasticity , 1982 .
[13] Alessandro Reali,et al. An isogeometric collocation approach for Bernoulli–Euler beams and Kirchhoff plates , 2015 .
[14] Robert L. Taylor,et al. On the role of frame-invariance in structural mechanics models at finite rotations , 2002 .
[15] F. Auricchio,et al. Single-variable formulations and isogeometric discretizations for shear deformable beams , 2015 .
[16] Claudio Borri,et al. Two shape parametrizations for structural optimization of triangular shells , 2016 .
[17] Timon Rabczuk,et al. An isogeometric collocation method using superconvergent points , 2015 .
[18] A. Ibrahimbegovic,et al. Computational aspects of vector-like parametrization of three-dimensional finite rotations , 1995 .
[19] Debasish Roy,et al. Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam , 2008 .
[20] Habibou Maitournam,et al. Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams , 2014 .
[21] T. Hughes,et al. A Simple Algorithm for Obtaining Nearly Optimal Quadrature Rules for NURBS-based Isogeometric Analysis , 2012 .
[22] Gordan Jelenić,et al. INTERPOLATION OF ROTATIONAL VARIABLES IN NONLINEAR DYNAMICS OF 3D BEAMS , 1998 .
[23] Alain Combescure,et al. Locking free isogeometric formulations of curved thick beams , 2012 .
[24] Jari Mäkinen,et al. Critical study of Newmark-scheme on manifold of finite rotations , 2001 .
[25] Josef Kiendl,et al. An isogeometric collocation method for frictionless contact of Cosserat rods , 2017 .
[26] H. Nguyen-Xuan,et al. An extended isogeometric thin shell analysis based on Kirchhoff-Love theory , 2015 .
[27] T. Hughes,et al. Efficient quadrature for NURBS-based isogeometric analysis , 2010 .
[28] Ignacio Romero,et al. The interpolation of rotations and its application to finite element models of geometrically exact rods , 2004 .
[29] Thomas J. R. Hughes,et al. Consistent linearization in mechanics of solids and structures , 1978 .
[30] K. C. Gupta,et al. An historical note on finite rotations , 1989 .
[31] Habibou Maitournam,et al. Selective and reduced numerical integrations for NURBS-based isogeometric analysis , 2015 .
[32] J. Mäkinen. Total Lagrangian Reissner's geometrically exact beam element without singularities , 2007 .
[33] Marcelo Epstein,et al. The Geometrical Language of Continuum Mechanics , 2010 .
[34] Alessandro Reali,et al. Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods , 2012 .
[35] Rakesh K. Kapania,et al. On a geometrically exact curved/twisted beam theory under rigid cross-section assumption , 2003 .
[36] Alessandro Reali,et al. Isogeometric collocation methods for the Reissner–Mindlin plate problem , 2015 .
[37] Alessandro Reali,et al. Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint) , 2007 .
[38] L. Heltai,et al. A natural framework for isogeometric fluid–structure interaction based on BEM–shell coupling , 2017, 1702.04502.
[39] A. Ibrahimbegovic. On finite element implementation of geometrically nonlinear Reissner's beam theory: three-dimensional curved beam elements , 1995 .
[40] Alessandro Reali,et al. Isogeometric Analysis of Structural Vibrations , 2006 .
[41] Alessandro Reali,et al. An Introduction to Isogeometric Collocation Methods , 2015 .
[42] Leopoldo Greco,et al. Consistent tangent operator for an exact Kirchhoff rod model , 2015 .
[43] J. C. Simo,et al. On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach , 1988 .
[44] Debasish Roy,et al. A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization , 2009 .
[45] Thomas J. R. Hughes,et al. Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .
[46] A. Ibrahimbegovic. On the choice of finite rotation parameters , 1997 .
[47] Alessandro Reali,et al. AN ISO GEOMETRIC ANALYSIS APPROACH FOR THE STUDY OF STRUCTURAL VIBRATIONS , 2006 .
[48] Les A. Piegl,et al. The NURBS Book , 1995, Monographs in Visual Communication.
[49] Enzo Marino,et al. Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams , 2016 .
[50] Roland Wüchner,et al. Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .
[51] M. Crisfield. A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements , 1990 .
[52] Peter Wriggers,et al. Isogeometric contact: a review , 2014 .
[53] Leopoldo Greco,et al. An isogeometric implicit G1 mixed finite element for Kirchhoff space rods , 2016 .
[54] Alessandro Reali,et al. Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations , 2013 .
[55] Adnan Ibrahimbegovic,et al. Quadratically convergent direct calculation of critical points for 3d structures undergoing finite rotations , 2000 .
[56] Ping Hu,et al. Order reduction method for locking free isogeometric analysis of Timoshenko beams , 2016 .
[57] 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.
[58] Laura De Lorenzis,et al. The variational collocation method , 2016 .
[59] J. C. Simo,et al. A finite strain beam formulation. The three-dimensional dynamic problem. Part I , 1985 .
[60] M. Géradin,et al. A beam finite element non‐linear theory with finite rotations , 1988 .
[61] T. Hughes,et al. Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .
[62] Alessandro Reali,et al. Assumed Natural Strain NURBS-based solid-shell element for the analysis of large deformation elasto-plastic thin-shell structures , 2015 .
[63] K. Bathe,et al. Large displacement analysis of three‐dimensional beam structures , 1979 .
[64] Jari Mäkinen,et al. Rotation manifold SO(3) and its tangential vectors , 2008 .
[65] Dinar Camotim,et al. On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory , 2002 .
[66] E. Dvorkin,et al. On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments , 1988 .
[67] J. F. Caseiro,et al. On the Assumed Natural Strain method to alleviate locking in solid-shell NURBS-based finite elements , 2014 .
[68] Alessandro Reali,et al. Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates , 2017 .
[69] T. Hughes,et al. Isogeometric collocation for elastostatics and explicit dynamics , 2012 .
[70] Thomas J. R. Hughes,et al. Isogeometric collocation for large deformation elasticity and frictional contact problems , 2015 .
[71] Gordan Jelenić,et al. Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics , 1999 .
[72] Ignacio Romero,et al. An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy–momentum conserving scheme in dynamics , 2002 .
[73] Thomas J. R. Hughes,et al. A large deformation, rotation-free, isogeometric shell , 2011 .
[74] Jean-Louis Batoz,et al. On the role of geometrically exact and second-order theories in buckling and post-buckling analysis of three-dimensional beam structures , 1996 .
[75] Roland Wüchner,et al. Nonlinear isogeometric spatial Bernoulli Beam , 2016 .
[76] Manfred Bischoff,et al. Numerical efficiency, locking and unlocking of NURBS finite elements , 2010 .
[77] John A. Evans,et al. Isogeometric collocation: Neumann boundary conditions and contact , 2015 .
[78] José Paulo Moitinho de Almeida,et al. A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures , 2011 .
[79] Sai-Kit Yeung,et al. Isogeometric collocation methods for Cosserat rods and rod structures , 2017 .
[80] Les A. Piegl,et al. A menagerie of rational B-spline circles , 1989, IEEE Computer Graphics and Applications.
[81] J. C. Simo,et al. A three-dimensional finite-strain rod model. Part II: Computational aspects , 1986 .
[82] Alessandro Reali,et al. Locking-free isogeometric collocation methods for spatial Timoshenko rods , 2013 .