Steel and Composite Structures

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Stochastic finite element analysis of composite plates considering spatial randomness of material properties and their correlations

  • Noh, Hyuk-Chun (Department of Civil and Environmental Engineering, Sejong University)
  • Received : 2010.01.27
  • Accepted : 2011.02.14
  • Published : 2011.03.25
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Abstract

Considering the randomness of material parameters in the laminated composite plate, a scheme of stochastic finite element method to analyze the displacement response variability is suggested. In the formulation we adopted the concept of the weighted integral where the random variable is defined as integration of stochastic field function multiplied by a deterministic function over a finite element. In general the elastic modulus of composite materials has distinct value along an individual axis. Accordingly, we need to assume 5 material parameters as random. The correlations between these random parameters are modeled by means of correlation functions, and the degree of correlation is defined in terms of correlation coefficients. For the verification of the proposed scheme, we employ an independent analysis of Monte Carlo simulation with which statistical results can be obtained. Comparison is made between the proposed scheme and Monte Carlo simulation.

Keywords

Acknowledgement

Supported by : Korea Institute of Energy Technology Evaluation and Planning(KETEP)

References

  1. Antonio C.C., Hoffbauer L.N. (2007), "Uncertainty analysis based on sensitivity applied to angle-ply composite structures", Reliability Eng. Sys. Safety, 92(10), 1353-1362. https://doi.org/10.1016/j.ress.2006.09.006
  2. Cavdar O., Bayraktar A., Cavdar A. and Adanur S. (2008), "Perturbation Based Stochastic Finite Element Analysis of the Structural Systems with Composite Sections under Earthquake Forces", Steel. Comp. Struct., An Int'l Journal, 8(2), 129-144. https://doi.org/10.12989/scs.2008.8.2.129
  3. Deodatis, G. (1991), "Weighted integral method I: Stochastic stiffness matrix", J. Eng. Mech., ASCE, 117(8), 1851-1864. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:8(1851)
  4. Graham, L. and Deodatis, G. (1998), "Variability response functions for stochastic plate bending problems", Struct. Safety., 20, 167-188. https://doi.org/10.1016/S0167-4730(98)00006-X
  5. Lal A., Singh B.N., Kumar R. (2007), "Natural frequency of laminated composite plate resting on an elastic foundation with uncertain system properties", Struct. Eng. Mech., 27(2), 199-222 . https://doi.org/10.12989/sem.2007.27.2.199
  6. Ngah, M.F. and Young, A. (2007), "Application of the spectral stochastic finite element method for performance prediction of composite structures", Comp. Struct., 78, 447-456. https://doi.org/10.1016/j.compstruct.2005.11.009
  7. Nigam, N.C. and Narayanan S. (1994), Applications of random vibrations, New Delhi: Narosa.
  8. Noh, H.C. (2004), "A formulation for stochastic finite element analysis of plate structures with uncertain Poisson's ratio", Comp. Meth. Appl. Mech. Eng., 193(45-47), 4857-4873. https://doi.org/10.1016/j.cma.2004.05.007
  9. Noh, H.C. and Park, T. (2006), "Monte Carlo simulation-compatible stochastic field for application to expansionbased stochastic finite element method", Comp. Struct., 84(31-32), 2363-2372. https://doi.org/10.1016/j.compstruc.2006.07.001
  10. Papadopoulos, V., Papadrakakis, M. and Deodatis, G. (2006), "Analysis of mean and mean square response of general linear stochastic finite element systems", Comp. Meth. Appl. Mech. Eng., 195(41-43), 5454-5471. https://doi.org/10.1016/j.cma.2005.11.008
  11. Schuëller, G.I. (2001), "Computational Stochastic Mechanics - Recent Advances", Comp. Struct., 79, 2225-2234. https://doi.org/10.1016/S0045-7949(01)00078-5
  12. Singh, B.N., Yadav, D. and Iyengar, N.G.R. (2002), "Free vibration of composite cylindrical panels with random material properties", Comp. Struct., 58, 435-442. https://doi.org/10.1016/S0263-8223(02)00133-2
  13. Stefanou, G. (2009), "The stochastic finite element method: Past, present and future", Comp. Meth. Appl. Mech. Eng., 198, 1031-1051. https://doi.org/10.1016/j.cma.2008.11.007

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