Multi-Scale Overlapping Domain Decomposition to Consider Local Deformations in the Analysis of Thin-Walled Members

Abstract:

Thin-walled members that have one dimension relatively large in comparison to the cross-sectional dimensions are usually modelled by using beam-column type finite element formulations. Beam-column elements however, are based on the assumption of rigid cross-section, thus they cannot consider the cross-sectional deformations such as local buckling and only allows considerations of the beam axis behaviour such as flexural or lateral-torsional buckling. Shell-type finite elements can be used to model the structure in order to consider these local deformation effects. Based on the Bridging multi-scale approach, this study proposes a numerical technique that is able to split the global analysis, which is performed by using simple beam-type elements, from the local analysis which is based on more sophisticated shell-type elements. As a result, the proposed multi-scale method allows the usage of shell elements in a local region to incorporate the local deformation effects on the overall behaviour of thin-walled members without necessitating a shell-type model for the whole member.

• Periodical: Applied Mechanics and Materials (Volume 553)
• Pages: 667-672
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.553.667
• Online since: May 2014
• Authors: R. Emre Erkmen
• Keywords: Local Deformation, Multi-Scale Analysis, Thin-Walled Member

References

[1] T. Belytschko, Y. Korungauz, D. Organ, M. Fleming, P. Krysl, Meshless methods: An overview and recent developments. Comp. Meth. Appl. Mech. Engrg. 139 (1996) 3-47.

DOI: 10.1016/s0045-7825(96)01078-x

[2] T. Strouboulis, K. Copps, I. Babuska, The generalized finite element method. Comp. Meth. Appl. Mech. Engrg. 190 (2001) 4081-4193.

DOI: 10.1016/s0045-7825(01)00188-8

[3] W.K. Liu, S. Hao, T. Belytschko, S. Li, C.T. Chang, Multi-scale methods. Int. Jour. Num. Meth. Engrg. 50 (2000) 993-1013.

[4] K. Haidar, J.F. Dube, P.C. Gilles, Modelling crack propagation in concrete structures with a two scale approach. Int. Jour. Num. Anal. Meth Geomech. 45 (2003) 601-620.

DOI: 10.1002/nag.318

[5] W.K. Liu, R.A. Uras, Y. Chen, Enrichment of the finite element method with the reproducing kernel particle method. Jour. Appl. Mech., ASME 64 (1997) 861-870.

DOI: 10.1115/1.2788993

[6] M.A. Bradford, G. Hancock, Elastic interaction of local and lateral buckling in beams. Thin-walled Struc. 2 (1984) 1-25.

DOI: 10.1016/0263-8231(84)90013-2

[7] F. Fafard, D. Beaulieu, G. Dhatt, A rational model for distortional buckling of tapered members. Comp. Struc. 25 (1987) 183-190.

[8] R.E. Erkmen, Bridging multi-scale approach to consider the effects of local deformations in the analysis of Thin-walled members. Comput. Mech. 52 (2013) 65-79.

DOI: 10.1007/s00466-012-0798-3

[9] J-L Batoz, M.B. Tahar, Evaluation of a new quadrilateral thin plate bending element. Int. Jour. Num. Meth. Engrg. 18 (1982) 1655-1677.

DOI: 10.1002/nme.1620181106

[10] A. Ibrahimbegovic, R.L. Taylor, E.L. Wilson, A robust quadrilateral membrane finite element with drilling degrees of freedom. Int. Jour. Num. Meth. Engrg. 30 (1990) 445-457.

DOI: 10.1002/nme.1620300305

[11] D. Qian, G.J. Wagner, W.K. Liu. A Multi-scale projection method for the analysis of carbon nanotubes. Comp. Meth. Appl. Mech. Engrg. 193 (2004) 1603-1632.