Blended isogeometric shells

Abstract We propose a new isogeometric shell formulation that blends Kirchhoff–Love theory with Reissner–Mindlin theory. This enables us to reduce the size of equation systems by eliminating rotational degrees of freedom while simultaneously providing a general and effective treatment of kinematic constraints engendered by shell intersections, folds, boundary conditions, the merging of NURBS patches, etc. We illustrate the blended theory’s performance on a series of test problems.

[1]  T. Hughes,et al.  Nonlinear finite element shell formulation accounting for large membrane strains , 1983 .

[2]  David J. Benson,et al.  A simple rigid body algorithm for structural dynamics programs , 1986 .

[3]  T. Hughes,et al.  ISOGEOMETRIC COLLOCATION METHODS , 2010 .

[4]  E. Ramm,et al.  Shear deformable shell elements for large strains and rotations , 1997 .

[5]  M. Ortiz,et al.  Subdivision surfaces: a new paradigm for thin‐shell finite‐element analysis , 2000 .

[6]  Thomas J. R. Hughes,et al.  Nonlinear finite element analysis of shells: Part I. three-dimensional shells , 1981 .

[7]  Jerry I. Lin,et al.  Explicit algorithms for the nonlinear dynamics of shells , 1984 .

[8]  D. F. Rogers,et al.  An Introduction to NURBS: With Historical Perspective , 2011 .

[9]  Long Chen.  FINITE ELEMENT METHOD , 2013 .

[10]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[11]  Yuri Bazilevs,et al.  3D simulation of wind turbine rotors at full scale. Part II: Fluid–structure interaction modeling with composite blades , 2011 .

[12]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[13]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[14]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[15]  T. Hughes,et al.  Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis , 1980 .

[16]  Hongwei Lin,et al.  Watertight trimmed NURBS , 2008, ACM Trans. Graph..

[17]  David J. Benson,et al.  A single surface contact algorithm for the post-buckling analysis of shell structures , 1990 .

[18]  Thomas J. R. Hughes,et al.  A large deformation, rotation-free, isogeometric shell , 2011 .

[19]  Fehmi Cirak,et al.  Shear‐flexible subdivision shells , 2012 .

[20]  G. S. Sekhon,et al.  Large Deformation -I , 2003 .

[21]  T. Belytschko,et al.  X‐FEM in isogeometric analysis for linear fracture mechanics , 2011 .

[22]  Yuri Bazilevs,et al.  The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches , 2010 .

[23]  David W. Murray,et al.  Nonlinear Finite Element Analysis of Steel Frames , 1983 .

[24]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

[25]  Yuri Bazilevs,et al.  A computational procedure for prebending of wind turbine blades , 2012 .

[26]  T. Belytschko,et al.  A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM , 2010 .

[27]  J. Yoon,et al.  One point quadrature shell element with through-thickness stretch , 2005 .

[28]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

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

[30]  Arend L. Schwab,et al.  Dynamics of Multibody Systems , 2007 .

[31]  D. Schillinger,et al.  An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry , 2011 .

[32]  Eugenio Oñate,et al.  Advances in the formulation of the rotation-free basic shell triangle , 2005 .

[33]  Fehmi Cirak,et al.  Subdivision shells with exact boundary control and non‐manifold geometry , 2011 .

[34]  Scott E. Schoenfeld,et al.  Quickly convergent integration methods for plane stress plasticity , 1993 .

[35]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .