Multi-scale modelling of sandwich structures using the Arlequin method Part I: Linear modelling

The paper presents an Arlequin based multi-scale method for studying problems related to the mechanical behaviour of sandwich composite structures. Towards this end, different models are mixed and glued to each other. Several coupling operators are tested in order to assess the usefulness of the proposed approach. A new coupling operator is proposed and tested on the different glued Arlequin zones. A free-clamped sandwich beam with soft core undergoing a concentrated effort on the free edge is used as a typical example (benchmark) in the validation procedure. Numerical simulations were conducted as the preliminary evaluation of the various coupling operators and the discrepancies between local and global models in the gluing zone have been addressed with sufficient care.

[1]  Jacob Fish,et al.  Adaptive s-method for linear elastostatics , 1993 .

[2]  I. Babuska,et al.  The design and analysis of the Generalized Finite Element Method , 2000 .

[3]  J. Fish.  The s-version of the finite element method , 1992 .

[4]  J. Reddy,et al.  THEORIES AND COMPUTATIONAL MODELS FOR COMPOSITE LAMINATES , 1994 .

[5]  Hachmi Ben Dhia,et al.  Multiscale mechanical problems: the Arlequin method , 1998 .

[6]  Michel Potier-Ferry,et al.  An amplitude equation for the non-linear vibration of viscoelastically damped sandwich beams , 2004 .

[7]  Jacob Fish,et al.  UNSTRUCTURED MULTIGRID METHOD FOR SHELLS , 1996 .

[8]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[9]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[10]  G. Rateau.  Méthode Arlequin pour les problèmes mécaniques multi-échelles : applications à des problèmes de jonction et de fissuration de structures élancées , 2003 .

[11]  G. Dhatt,et al.  Modélisation des structures par éléments finis , 1990 .

[12]  Jacob Fish,et al.  THE S-VERSION OF FINITE ELEMENT METHOD FOR LAMINATED COMPOSITES , 1996 .

[13]  Jacob Fish,et al.  Adaptive global-local refinement strategy based on the interior error estimates of the h-method , 1994 .

[14]  D. J. Mead,et al.  The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions , 1969 .

[15]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[16]  G. Rateau,et al.  Analyse mathématique de la méthode Arlequin mixte , 2001 .

[17]  D. K. Rao,et al.  Frequency and Loss Factors of Sandwich Beams under Various Boundary Conditions , 1978 .

[18]  Guillaume Rateau,et al.  The Arlequin method as a flexible engineering design tool , 2005 .

[19]  Salim Belouettar,et al.  Review and assessment of various theories for modeling sandwich composites , 2008 .