A composite beam finite element for multibody dynamics: Application to large wind turbine modeling

This work presents a beam finite element with multibody capabilities for modeling high aspect ratio composite wind turbine components, particularly the tower and the blades. The proposed formulation is based on an Updated Lagrangian approach, in which the virtual work equations are written as a function the director field and its derivatives. The cross-sectional modeling of the wind turbine components is based on the constitutive relations obtained from the analysis of the mechanics of composite laminates. The formulation of the equations of motion and the derivation of a hinge joint is presented. Several results for a large wind turbine model are shown.

[1]  Carlo L. Bottasso,et al.  Aero-servo-elastic modeling and control of wind turbines using finite-element multibody procedures , 2006 .

[2]  Xin Long,et al.  Aerodynamic loads calculation and analysis for large scale wind turbine based on combining BEM modified theory with dynamic stall model , 2011 .

[3]  J. Mäkinen Total Lagrangian Reissner's geometrically exact beam element without singularities , 2007 .

[4]  Olivier A. Bauchau,et al.  Modeling rotorcraft dynamics with finite element multibody procedures , 2001 .

[5]  Søren Nielsen,et al.  A component mode synthesis algorithm for multibody dynamics of wind turbines , 2009 .

[6]  Jianhong Wang,et al.  Dynamic analysis of horizontal axis wind turbine by thin-walled beam theory , 2010 .

[7]  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 .

[8]  E. Stein,et al.  On the parametrization of finite rotations in computational mechanics: A classification of concepts with application to smooth shells , 1998 .

[9]  Dewey H. Hodges,et al.  A rigorous, engineer‐friendly approach for modelling realistic, composite rotor blades , 2007 .

[10]  M. L. Buhl,et al.  Comparison of Wind-Turbine Aeroelastic Codes Used for Certification: Preprint , 2006 .

[11]  Dewey H. Hodges,et al.  Nonlinear Composite Beam Theory , 2006 .

[12]  Jingyan Wu,et al.  A new multibody modelling methodology for wind turbine structures using a cardanic joint beam element , 2007 .

[13]  M. Géradin,et al.  Flexible Multibody Dynamics: A Finite Element Approach , 2001 .

[14]  P. Betsch,et al.  Frame‐indifferent beam finite elements based upon the geometrically exact beam theory , 2002 .

[15]  A. Ibrahimbegovic,et al.  Computational aspects of vector-like parametrization of three-dimensional finite rotations , 1995 .

[16]  Carlos E. S. Cesnik,et al.  VABS: A New Concept for Composite Rotor Blade Cross-Sectional Modeling , 1995 .

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

[18]  M. Géradin,et al.  A beam finite element non‐linear theory with finite rotations , 1988 .

[19]  K. Washizu Variational Methods in Elasticity and Plasticity , 1982 .

[20]  C. L. Bottasso - Aeroelastic simulation of tilt-rotors using non-linear finite element multibody procedures , 2003 .

[21]  Lin Liao,et al.  Theory of initially twisted, composite, thin-walled beams , 2003 .

[22]  Gordan Jelenić,et al.  Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics , 1999 .

[23]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[24]  Alberto Cardona,et al.  Rigid and flexible joint modelling in multibody dynamics using finite elements , 1991 .

[25]  Søren Nielsen,et al.  Non-linear dynamics of wind turbine wings , 2006 .

[26]  Robert L. Taylor,et al.  Non-linear dynamics of flexible multibody systems , 2003 .

[27]  S. Report,et al.  The Sandia 100-meter All-glass Baseline Wind Turbine Blade: SNL100-00 , 2011 .

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

[29]  Søren Nielsen,et al.  Nonlinear parametric instability of wind turbine wings , 2007 .

[30]  A. Ibrahimbegovic,et al.  On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3D geometrically exact beam model , 2000 .

[31]  S. P. Machado,et al.  A consistent total Lagrangian finite element for composite closed section thin walled beams , 2012 .

[32]  Martin Otto Laver Hansen,et al.  Aerodynamics of Wind Turbines , 2001 .

[33]  Torben J. Larsen,et al.  Aeroelastic effects of large blade deflections for wind turbines , 2004 .

[34]  A. Ibrahimbegovic,et al.  Finite rotations in dynamics of beams and implicit time-stepping schemes , 1998 .

[35]  D. Hodges A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams , 1990 .

[36]  A. Ibrahimbegovic On finite element implementation of geometrically nonlinear Reissner's beam theory: three-dimensional curved beam elements , 1995 .

[37]  Spyros G. Voutsinas,et al.  STATE OF THE ART IN WIND TURBINE AERODYNAMICS AND AEROELASTICITY , 2006 .

[38]  J. Z. Zhu,et al.  The finite element method , 1977 .

[39]  M. A. Crisfield,et al.  Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics , 1997 .

[40]  Marshall L. Buhl,et al.  A Comparison of Wind Turbine Aeroelastic Codes Used for Certification , 2006 .

[41]  J. C. Simo,et al.  On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach , 1988 .

[42]  S. P. Machado,et al.  A geometrically exact nonlinear finite element for composite closed section thin-walled beams , 2011 .