Wave Propagation Modelling in Composite Plates

Article Preview

Abstract:

The paper presents results of numerical simulation for transverse elastic waves corresponding to A0 mode of Lamb waves propagating in a composite plate. This problem is solved by using the Spectral Finite Element Method. Spectral plate elements with 36 nodes defined at Gauss-Lobatto-Legendre points are used. As a consequence of selecting Lagrange polynomials discrete orthogonality guaranteed leading to a diagonal mass matrix. This results in a crucial reduction of numerical operations required for a chosen time integration scheme. Numerical calculations have been carried out for various orientations of reinforcing fibres within the plate as well as for various fibre volumes fractions. The paper shows that the velocities of transverse elastic waves in composite materials are functions of the fibre orientation and the fibre volume fraction.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

89-104

Citation:

Online since:

October 2007

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2008 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] J.R. Vinson and R.L. Sierakowski: Behavior of structures composed of composite materials. (Martinus-Nijhoff, Inc., 1989).

Google Scholar

[2] O.O. Ochoa and J.N. Reddy: Finite element analysis of composite laminates (Kluwer Academic Publishers, 1992).

Google Scholar

[3] J.M. Whitney: Structural analysis of laminated anisotropic plates (Technomic Publishing Co., 1987).

Google Scholar

[4] A.L. Kalamkarov: Composite and reinforced elements of construction (John Wiley & Sons Inc., 1992).

Google Scholar

[5] R.M. Jones: Mechanics of Composite Materials (Taylor & Francis Inc., 1999).

Google Scholar

[6] M. Krawczuk, W.M. Ostachowicz and A. Żak: Computational Mechanics Vol. 20 (1997), pp.79-83.

Google Scholar

[7] L.J. Bond, in: Elastic waves and ultrasonic non-destructive evaluation, edited by S.K. Datta, J. D Achenbach and Y.S. Rajapakse, North-Holland, Amsterdam (1990).

Google Scholar

[8] J.C. Strickwerda: Finite difference schemes and partial differential equations (WadsworthBrooks, Belmont, 1989).

Google Scholar

[9] H. Yamawaki and T. Saito: NDT&E International Vol. 8-9 (1992), pp.379-389.

Google Scholar

[10] O.C. Zienkiewicz: The finite element method (McGraw-Hill, 1989).

Google Scholar

[11] R.J. Talbot and J.S. Przemieniecki: International Journal of Solids and Structures Vol. 11 (1976), pp.115-138.

Google Scholar

[12] M. Koshiba, S. Karakida. and M. Suzuki: IEEE Transactions on Sonic and Ultrasonic Vol. 31 (1984), pp.18-25.

Google Scholar

[13] G.S. Verdict, P.H. Gien and C.P. Burger, in: Review of Progress in Quantitative Nondestructive Evaluation, edited by D.O. Thompson and D.E. Chimenti Vol. 11 (1992), pp.97-104.

Google Scholar

[14] D.N. Alleyne and P. Cawley: NDT&E International Vol. 25 (1992), pp.11-22.

Google Scholar

[15] C.A. Brebbia, J.C.F. Tells and L.C. Wrobel: Boundary elements techniques (Springer, Berlin, 1984).

Google Scholar

[16] Y. Cho and J.L. Rose: Journal of the Acoustical Society of America Vol. 99 (1996), pp.2079-2109.

Google Scholar

[17] Y.K. Cheung: Finite strip method in structural analysis (Pergamon Press, 1976).

Google Scholar

[18] G.R. Liu and Z.C. Xi: Elastic waves in anisotropic laminates (CRC Press, 2002).

Google Scholar

[19] G.R. Liu, J. Tani, K. Watanabe and T. Ohyoshi: Journal of Sound and Vibration Vol. 139 (1990), pp.313-330.

Google Scholar

[20] T. Liu, K. Liu and J. Zhang: Computer Methods in Applied Mechanics and Engineering Vol. 193 (2004), pp.2427-2452.

Google Scholar

[21] T. Liu, K. Liu and J. Zhang: Archive of Applied Mechanics Vol. 74 (2005), pp.477-488.

Google Scholar

[22] PP. Delsanto and R.B. Mignogna: Journal of Acoustical Society of America Vol. 104 (1998) pp.1-8.

Google Scholar

[23] H. Yim and Y. Sohn: IEEE Transactions on Ultrasonic, Ferroelectrics, and Frequency Control Vol. 47 (2000), pp.549-558.

Google Scholar

[24] P.P. Delsanto, T. Whitecomb, H.H. Chaskelis and R.B. Mignogna: Wave Motion Vol. 16 (1992), pp.65-80.

Google Scholar

[25] P.P. Delsanto, T. Whitecomb, H.H. Chaskelis, R.B. Mignogna and R.B. Kline: Wave Motion Vol. 20 (1994), pp.295-314.

DOI: 10.1016/0165-2125(94)90016-7

Google Scholar

[26] P.P. Delsanto, R.S. Schechter and R.B. Mignogna: Wave Motion Vol. 26 (1997), pp.329-339.

Google Scholar

[27] J.F. Doyle: Wave propagation in structures (Springer-Verlag, 1997).

Google Scholar

[28] A.T. Patera: Journal of Computational Physics Vol. 54 (1984), pp.468-488.

Google Scholar

[29] M. Krawczuk , M. Palacz and W. Ostachowicz: Journal of Sound and Vibration Vol. 264 (2003), pp.1139-1153.

DOI: 10.1016/s0022-460x(02)01387-1

Google Scholar

[30] D.R. Mahapatra and S. Golpalakrishnan: Computers and Structures Vol. 59 (2003) pp.67-88.

Google Scholar

[31] M. Palacz, M. Krawczuk: Computers and Structures Vol. 80 (2002), pp.1809-1816.

Google Scholar

[32] S.A. Rizzi and J.F. Doyle: Journal of Vibration and Acoustics Vol. 114 (1992), pp.569-577.

Google Scholar

[33] J.P. Boyd: Chebyshev and Fourier spectral methods (Springer, 1989).

Google Scholar

[34] C. Pozrikidis: Introduction to Finite and Spectral Element Methods using MATLAB® (Chapman & Hall/CRC, 2005).

Google Scholar

[35] C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang: Spectral methods in fluid dynamics (Springer, 1988).

DOI: 10.1007/978-3-642-84108-8

Google Scholar

[36] R. Spall: International Journal of Heat Mass Transfer Vol. 15 (1995), pp.2743-2748.

Google Scholar

[37] W. Dauksher and A.F. Emery, in: Review of Progress in Quantitative Non-destructive Evaluation, edited by D.O. Thompson and D.E. Chimenti Vol. 15 (1996), pp.97-104.

Google Scholar

[38] G. Seriani: Computational Methods Applied in Mechanical Engineering Vol. 164 (1998), pp.235-247.

Google Scholar

[39] http: /mathworld. wolfram. com.

Google Scholar

[40] M. Kleiber: Incremental finite element modelling in non-linear solid Mechanics (J. Wiley & Sons, New York, 1989).

Google Scholar