Stochastic elastic wave analysis of angled beams

- Journal title : Structural Engineering and Mechanics
- Volume 56, Issue 5, 2015, pp.767-785
- Publisher : Techno-Press
- DOI : 10.12989/sem.2015.56.5.767

Title & Authors

Stochastic elastic wave analysis of angled beams

Bai, Changqing; Ma, Hualin; Shim, Victor P.W.;

Bai, Changqing; Ma, Hualin; Shim, Victor P.W.;

Abstract

The stochastic finite element method is employed to obtain a stochastic dynamic model of angled beams subjected to impact loads when uncertain material properties are described by random fields. Using the perturbation technique in conjunction with a precise time integration method, a random analysis approach is developed for efficient analysis of random elastic waves. Formulas for the mean, variance and covariance of displacement, strain and stress are introduced. Statistics of displacement and stress waves is analyzed and effects of bend angle and material stochasticity on wave propagation are studied. It is found that the elastic wave correlation in the angled section is the most significant. The mean, variance and covariance of the stress wave amplitude decrease with an increase in bend angle. The standard deviation of the beam material density plays an important role in longitudinal displacement wave covariance.

Keywords

elastic wave;stochastic finite element;angled beam;impact;random parameter;uncertainty;

Language

English

References

1.

Abd-Alla, A.M., Abo-Dahab, S.M. and Bayones, F.S. (2015), "wave propagation in fibre-reinforced anisotropic thermo-elastic medium subjected to gravity field", Struct. Eng. Mech., 53(2), 277-296.

2.

Benaroya, H. and Rehak, M. (1988), "Finite element methods in probabilistic structural analysis: A selective review", Appl. Mech. Rev., 41, 201-213.

4.

Elishakoff, I., Ren, Y.J. and Shinozuka, M. (1997), "New formulation of FEM for deterministic and stochastic beams through generalization of Fuchs' approach", Comput. Meth. Appl. Mech. Eng., 144, 235-243.

5.

Ghanem, R.G. and Spanos, P.D. (1991), Stochastic finite elements: a spectral approach, Springer -verlag, New York, USA

6.

Gibson, L.J. and Ashby, M.F. (1997), Cellular solids: Structure and properties, Cambridge University Press, Cambridge, UK.

7.

Guo, Y.B., Shim, V.P.W. and Yeo, A.Y.L. (2010), "Elastic wave and energy propagation in angled beams", Acta Mech., 214, 79-94.

8.

Gupta, S. and Manohar, C.S. (2002), "Dynamic stiffness method for circular stochastic Timoshenko beams: response variability and reliability analysis", J. Sound Vib., 253, 1051-1085.

9.

Hosseini, S.A.A. and Khadem, S.E. (2005), "Free vibration analysis of rotating beams with random properties", Struct. Eng. Mech., 20, 293-312.

10.

Hosseini, S.A.A. and Khadem, S.E. (2007), "Vibration and reliability of a rotating beam with random properties under random excitation", Int. J. Mech. Sci., 49, 1377-1388.

11.

Hosseini, S.M. and Shahabian, F. (2014), "Stochastic analysis of elastic wave and second sound propagation in media with Gaussian uncertainty in mechanical properties using a stochastic hybrid mesh-free method", Struct. Eng. Mech., 49(1), 41-64.

12.

Hughes, T.J.R. (1987), The finite element method, Prentice-Hall, N.J.

13.

Ishida, R. (2001), "Stochastic finite element analysis of beam with stochastical uncertainties", AIAA J., 39, 2192-2197.

14.

Lee, J.P. and Kolsky, H. (1972), "The generation of stress pulses at the junction of two noncollinear rods", ASME J. Appl. Mech., 39, 809-813.

15.

Liu, M. and Gorman, D.G. (1995), "Formulation of Rayleigh damping and its extension", Comput. Struct., 57, 277-285.

16.

Nouy, A. and Clement, A. (2010), "Extended stochastic finite element method for the numerical simulation of heterogeneous materials with random material interfaces", Int. J. Numer. Meth. Eng., 83, 1312-1344.

17.

Papadopoulos, V., Papadrakakis, M. and Dodatis, G. (2006), "Analysis of mean and mean square response of general linear stochastic finite element systems", Comput. Meth. Appl. Mech. Eng., 195, 5454-5471.

18.

Sankaran, M. and Achintya, H. (1991), "Reliability-based optimization using SFEM", Lec. Note. Eng., 61, 241-250.

19.

Simha, K.R.Y. and Fourney, W.L. (1984), "Investigation of stress wave propagation through intersection bars", ASME J. Appl. Mech., 51, 345-353.

20.

Yamazaki, F., Shinozuka, M. and Dasgupta, G. (1985), "Neumann expansion for stochastic finite element analysis", ASCE J. Eng. Mech., 114, 1335-1354.

21.

Young, K.H. and Atkins, K.J. (1983), "Generation of elastic stress waves at a T-junction of square rods", J. Sound Vib., 88, 431-436.

22.

Zhong, W.X., Zhu, J.N. and Zhong, X.X. (1996), "On a new time integration method for solving time dependent partial differential equations", Comput. Meth. Appl. Mech. Eng., 130, 163-178.

23.

Zhong, W.X., Zhu, J.P. and Zhong, X.X. (1994), "A precise time integration algorithm for non-linear systems", Proc. 3rd World Congress on Computational Mechanics, Chiba, Japan.