Nonlinear dynamic analysis of creased shells

Recent studies analyze the behavior of advanced shell structures, like foldable, multistable or morphing shell structures. Simulating a thin foldable curved structure is not a trivial task: the structure may go through many snapping transitions from a stable configuration to another. Then, one could claim arc-length methods or use a dynamic approach to perform such simulations. This work presents a geometrically exact shell model for nonlinear dynamic analysis of shells. An updated Lagrangian framework is used for describing kinematics. Several numerical examples of folding a thin dome are presented, including creased shells. The triangular shell finite element used offers great flexibility for the generation of the unstructured curved meshes, as well as great results.

[1]  Sung Bo Kim,et al.  Geometrically Nonlinear Analysis of Thin-Walled Space Frames , 1999 .

[2]  P. M. Naghdi,et al.  ON THE THEORY OF THIN ELASTIC SHELLS , 1957 .

[3]  Adnan Ibrahimbegovic,et al.  Study of geometric non-linear instability of 2D frame structures , 2015 .

[4]  Boštjan Brank,et al.  Dynamics and time-stepping schemes for elastic shells undergoing finite rotations , 2003 .

[5]  Martin Trautz,et al.  The application of folded plate principles on spatial structures with regular, irregular and free-form geometries , 2009 .

[6]  Paul M. Weaver,et al.  The application of residual stress tailoring of snap-through composites for variable sweep wings , 2006 .

[7]  Peter Wriggers,et al.  A master-surface to master-surface formulation for beam to beam contact. Part I: frictionless interaction , 2016 .

[8]  Boštjan Brank,et al.  ON NON-LINEAR DYNAMICS OF SHELLS: IMPLEMENTATION OF ENERGY-MOMENTUM CONSERVING ALGORITHM FOR A FINITE ROTATION SHELL MODEL , 1998 .

[9]  D. A. Danielson,et al.  Nonlinear Shell Theory With Finite Rotation and Stress-Function Vectors , 1972 .

[10]  Boštjan Brank,et al.  Stress resultant geometrically exact form of classical shell model and vector‐like parameterization of constrained finite rotations , 2001 .

[11]  Ekkehard Ramm,et al.  Constraint Energy Momentum Algorithm and its application to non-linear dynamics of shells , 1996 .

[12]  Joze Korelc,et al.  Multi-language and Multi-environment Generation of Nonlinear Finite Element Codes , 2002, Engineering with Computers.

[13]  Sergio Pellegrino,et al.  Bistable prestressed shell structures , 2004 .

[14]  Paulo M. Pimenta,et al.  Static analysis of offshore risers with a geometrically-exact 3D beam model subjected to unilateral contact , 2014 .

[15]  Joze Korelc,et al.  Automatic Generation of Finite-Element Code by Simultaneous Optimization of Expressions , 1997, Theor. Comput. Sci..

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

[17]  Tomohiro Tachi,et al.  Freeform Rigid-Foldable Structure using Bidirectionally Flat-Foldable Planar Quadrilateral Mesh , 2010, AAG.

[18]  P. Wriggers.  Nonlinear Finite Element Methods , 2008 .

[19]  E. Reissner,et al.  Stress Strain Relations in the Theory of Thin Elastic Shells , 1952 .

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

[21]  Paul M. Weaver,et al.  Morphing shell structures: A generalised modelling approach , 2015 .

[22]  Adnan Ibrahimbegovic,et al.  Performance of time‐stepping schemes for discrete models in fracture dynamic analysis , 2006 .

[23]  G. Kirchhoff,et al.  Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. , 1850 .

[24]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part VI: Conserving algorithms for non‐linear dynamics , 1992 .

[25]  Joachim Block,et al.  Ultralight Deployable Booms for Solar Sails and Other Large Gossamer Structures in Space , 2011 .

[26]  I. Cohen,et al.  Geometrically controlled snapping transitions in shells with curved creases , 2014, Proceedings of the National Academy of Sciences.

[27]  Thomas C. Hull,et al.  Using origami design principles to fold reprogrammable mechanical metamaterials , 2014, Science.

[28]  P. M. Naghdi,et al.  On the nonlinear theory of elastic shells under the Kirchhoff hypothesis , 1963 .

[29]  J. G. Simmonds,et al.  The Nonlinear Theory of Elastic Shells , 1998 .

[30]  Clóvis de Arruda Martins,et al.  Structural stability of flexible lines in catenary configuration under torsion , 2013 .

[31]  Paul M. Weaver,et al.  Bistable plates for morphing structures: A refined analytical approach with high-order polynomials , 2010 .

[32]  Rigoberto Burgueño,et al.  Buckling-induced smart applications: recent advances and trends , 2015 .

[33]  A. E. H. Love,et al.  The Small Free Vibrations and Deformation of a Thin Elastic Shell , 1887 .

[34]  Peter Wriggers,et al.  A triangular finite shell element based on a fully nonlinear shell formulation , 2003 .

[35]  Christopher Jenkins,et al.  Analysis of crease-wrinkle interaction for thin sheets , 2012 .

[36]  M. van Hecke,et al.  Programmable mechanical metamaterials. , 2014, Physical review letters.

[37]  Sergio Pellegrino,et al.  Systematically Creased Thin-Film Membrane Structures , 2008 .

[38]  Alfred J. Crosby,et al.  Snapping Surfaces , 2007 .

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

[40]  A. Ibrahimbegovic.  Stress Resultant Geometrically Exact Shell Theory for Finite Rotations and Its Finite Element Implementation , 1997 .

[41]  L. Donnell,et al.  Stability of Thin-Walled Tubes Under Torsion , 1934, Journal of Fluids Engineering.