Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior

Abstract This work mainly deals with the numerical study of inflatable fabric structures. As implicit integration schemes can lead to numerical difficulties such as singular stiffness matrices, explicit schemes are preferred. Since the final objective of this study is to obtain the final shape of a structure, a dynamic relaxation (DR) method is used. These methods allow us to obtain the final and stable shape of the inflatable fabric structures without doing so many time increments, which is the case when using a classical explicit integration method. Han and Lee [5] proposed an extension of the DR method stated by Barnes [13] suitable for triangular elements and elastic behavior. There are two main contributions in this paper. Firstly, we propose a modification of Han and Lee's method, allowing it to be used with any kind of membrane or solid finite elements and any reversible behavior. Secondly, we propose to rewrite the expression initially introduced by Barnes. Furthermore, these proposals are adapted for incremental loadings, allowing this way to obtain the pseudo-equilibriums of the intermediate phases. Numerical examples from academic problems (rectangular and circular membranes) show the efficiency and the reliability of proposed methods, with linear elasticity behavior, and also with a non-linear incremental behavior and finite deformation states.

[1]  M. Barnes,et al.  Form Finding and Analysis of Tension Structures by Dynamic Relaxation , 1999 .

[2]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[3]  Gérard Rio,et al.  Recherche de forme des gilets de sauvetage gonflables , 2007 .

[4]  H. Laurent,et al.  Formulation of a thin shell finite element with continuity C0 and convected material frame notion , 2001 .

[5]  W. J. Lewis,et al.  Tension Structures: Form and Behaviour , 2003 .

[6]  V. GIL.  JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: IASS , 2001 .

[7]  Jean-Christophe Thomas,et al.  Deflections of highly inflated fabric tubes , 2004 .

[8]  H. Laurent,et al.  A Hyperelasto-Visco-Hysteresis model for an elastomeric behaviour: Experimental and numerical investigations , 2010 .

[9]  Gunnar Tibert,et al.  Deployment Simulations of Inflatable Tensegrity Structures , 2008 .

[10]  手塚 明,et al.  Livermore Software Technology Corporation, 社長 , 2004 .

[11]  E. C. Ting,et al.  Large deflection analysis of 3D membrane structures by a 4-node quadrilateral intrinsic element , 2008 .

[12]  Olivier Baverel,et al.  Form-finding of a grid shell in composite materials , 2006 .

[13]  R. D. Wood.  A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes , 2002 .

[14]  Javad Alamatian,et al.  The dynamic relaxation method using new formulation for fictitious mass and damping , 2010 .

[15]  C. S. Krishnamoorthy,et al.  Geometrically non-linear analysis of plates and shallow shells by dynamic relaxation , 1995 .

[16]  Karol Miller,et al.  Computation of intra-operative brain shift using dynamic relaxation. , 2009, Computer methods in applied mechanics and engineering.

[17]  Ian F. C. Smith,et al.  Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm , 2011 .

[18]  Sang-Eul Han,et al.  A Study on the Stabilizing Process of Unstable Structures by Dynamic Relaxation Method , 2003 .

[19]  Mohamed A. Meguid,et al.  Evaluating the performance of an explicit dynamic relaxation technique in analyzing non-linear geotechnical engineering problems , 2010 .

[20]  T. Belytschko,et al.  Computational Methods for Transient Analysis , 1985 .

[21]  J. Remacle,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[22]  M. R. Barnes,et al.  Form-finding and analysis of prestressed nets and membranes , 1988 .