Multi-scale nonlinear modelling of sandwich structures using the Arlequin method

作者: Heng Hu , Salim Belouettar , Michel Potier-Ferry , El Mostafa Daya , Ahmed Makradi

DOI: 10.1016/J.COMPSTRUCT.2009.08.051

关键词:

摘要: Abstract The paper presents a combination of the Arlequin Method (AM) and Asymptotic Numerical (ANM) for studying nonlinear problems related to mechanical behavior sandwich composite structures. is multi-scale method in which different models are crossed glued each other. ANM an alternative falls into category numerical perturbation techniques. By introducing power series expansions equilibrium equation, problem transformed sequence linear solved by standard finite element method. Compared other classical solvers (Newton–Raphson Method, Modified Newton–Raphson Method), offers considerable interest computation time reliability. To validate this method, AM combined with simulate local damage 2D–2D 2D–2D-coupled beams. simulation results compared reference solution calculated from 2D beam without any coupling. In case beam, shows good agreement both deformation at loaded point. However, 2D–1D-coupled deviate due constant thickness 1D zig-zag used model zone beam.

参考文章(18)
D.J. Mead, S. Markus, The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions Journal of Sound and Vibration. ,vol. 10, pp. 163- 175 ,(1969) , 10.1016/0022-460X(69)90193-X
Norbert Büchter, Ekkehard Ramm, Deane Roehl, Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept International Journal for Numerical Methods in Engineering. ,vol. 37, pp. 2551- 2568 ,(1994) , 10.1002/NME.1620371504
Jacob Fish, Stilianos Markolefas, Adaptive s-method for linear elastostatics Computer Methods in Applied Mechanics and Engineering. ,vol. 104, pp. 363- 396 ,(1993) , 10.1016/0045-7825(93)90032-S
Hashmi Ben Dhia, Guillaume Rateau, The Arlequin method as a flexible engineering design tool International Journal for Numerical Methods in Engineering. ,vol. 62, pp. 1442- 1462 ,(2005) , 10.1002/NME.1229
H. Zahrouni, B. Cochelin, M. Potier-Ferry, Computing finite rotations of shells by an asymptotic-numerical method Computer Methods in Applied Mechanics and Engineering. ,vol. 175, pp. 71- 85 ,(1999) , 10.1016/S0045-7825(98)00320-X
Heng Hu, Salim Belouettar, Michel Potier-Ferry, El Mostafa Daya, Multi-scale modelling of sandwich structures using the Arlequin method Part I: Linear modelling Finite Elements in Analysis and Design. ,vol. 45, pp. 37- 51 ,(2008) , 10.1016/J.FINEL.2008.07.003
B. Cochelin, N. Damil, M. Potier-Ferry, Asymptotic-numerical methods and Pade approximants for non-linear elastic structures International Journal for Numerical Methods in Engineering. ,vol. 37, pp. 1187- 1213 ,(1994) , 10.1002/NME.1620370706
J. M. Cadou, M. Potier-Ferry, B. Cochelin, N. Damil, ANM for stationary Navier-Stokes equations and with Petrov-Galerkin formulation International Journal for Numerical Methods in Engineering. ,vol. 50, pp. 825- 845 ,(2001) , 10.1002/1097-0207(20010210)50:4<825::AID-NME53>3.0.CO;2-0