Beam-like models for the analyses of curved, twisted and tapered HAWT blades in large displacements

Abstract. The continuous effort to better predict the mechanical behavior of wind turbine blades is related to lowering the cost of energy. But new design strategies and the continuous increase in the size and flexibility of modern blades make their aero-elastic modeling ever more challenging. For the structural part, the best compromise between computational efficiency and accuracy can be obtained by schematizing the blades as suitable beam-like elements. This paper addresses the modeling of the mechanical behavior of complex beam-like structures, which are curved, twisted and tapered in their reference state, undergo large displacements, 3D cross-sectional warping and small strains. A suitable model for the problem at hand is proposed. It can be used to analyze large deflections under prescribed loads and allows the 3D strain and stress fields in the structure to be determined. Analytical results obtained by applying the proposed modeling approach are illustrated.

[1]  P. Frank Pai,et al.  Problems in geometrically exact modeling of highly flexible beams , 2014 .

[2]  E. Reissner.  On finite deformations of space-curved beams , 1981 .

[3]  V. Berdichevskiĭ.  On the energy of an elastic rod , 1981 .

[4]  Lin Wang,et al.  State of the art in the aeroelasticity of wind turbine blades: aeroelastic modelling , 2016 .

[5]  Jimmy C. Ho,et al.  Variational asymptotic beam sectional analysis – An updated version , 2012 .

[6]  Dewey H. Hodges,et al.  Review of composite rotor blade modeling , 1990 .

[7]  Fred Nitzsche,et al.  Dynamics, vibration and control of rotating composite beams and blades: A critical review , 2017 .

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

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

[10]  Carlo L. Bottasso,et al.  Optimization‐based study of bend–twist coupled rotor blades for passive and integrated passive/active load alleviation , 2012 .

[11]  Giuseppe Ruta,et al.  A DIRECT ONE-DIMENSIONAL BEAM MODEL FOR THE FLEXURAL-TORSIONAL BUCKLING OF THIN-WALLED BEAMS , 2006 .

[12]  Donald L. Kunz,et al.  Survey and comparison of engineering beam theories for helicopter rotor blades , 1994 .

[13]  Tadashi Tanuma,et al.  Advances in Steam Turbines for Modern Power Plants , 2017 .

[14]  J. Gordon Leishman,et al.  Principles of Helicopter Aerodynamics , 2000 .

[15]  M. B. Rubin,et al.  An intrinsic formulation for nonlinear elastic rods , 1997 .

[16]  Aviv Rosen,et al.  Structural and Dynamic Behavior of Pretwisted Rods and Beams , 1991 .

[17]  M. Borri,et al.  Anisotropic beam theory and applications , 1983 .

[18]  Maureen Hand,et al.  Forecasting Wind Energy Costs and Cost Drivers: The Views of the World’s Leading Experts: , 2016 .

[19]  A. Peirce.  Computer Methods in Applied Mechanics and Engineering , 2010 .

[20]  David Rubin,et al.  Introduction to Continuum Mechanics , 2009 .

[21]  Jason Jonkman,et al.  Partitioned Nonlinear Structural Analysis of Wind Turbines using BeamDyn , 2016 .

[22]  G. M.,et al.  A Treatise on the Mathematical Theory of Elasticity , 1906, Nature.

[23]  Morten Hartvig Hansen,et al.  Modal properties and stability of bend–twist coupled wind turbine blades , 2016 .

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

[25]  P. Frank Pai,et al.  Three kinematic representations for modeling of highly flexible beams and their applications , 2011 .

[26]  Peretz P. Friedmann,et al.  Nonlinear equations of equilibrium for elastic helicopter or wind turbine blades undergoing moderate deformation , 1978 .

[27]  M. B. Rubin,et al.  Cosserat Theories: Shells, Rods and Points. Solid Mechanics and its Applications, Vol 79 , 2002 .