Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Response Variability of Laminated Composite Plates with Random Elastic Modulus

탄성계수의 불확실성에 의한 복합적층판 구조의 응답변화도

  • 노혁천 (세종대학교 토목환경공학과)
  • Published : 2008.08.30
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Abstract

In this study, we suggest a stochastic finite element scheme for the probabilistic analysis of the composite laminated plates, which have been applied to variety of mechanical structures due to their high strength to weight ratios. The applied concept in the formulation is the weighted integral method, which has been shown to give the most accurate results among others. We take into account the elastic modulus and in-plane shear modulus as random. For individual random parameters, independent stochastic field functions are assumed, and the effect of these random parameters on the response are estimated based on the exponentially varying auto- and cross-correlation functions. Based on example analyses, we suggest that composite plates show a less coefficient of variation than plates of isotropic and orthotropic materials. For the validation of the proposed scheme, Monte Carlo analysis is also performed, and the results are compared with each other.

본 연구에서는 역학적 특성이 우수하여 다양한 구조에 적용되고 있는 복합적층판에 대한 추계론적 유한요소해석 정식화를 제안한다. 정식화의 제시는 추계론적 수치해석기법 중 그 정확도가 매우 높은 것으로 알려져 있는 가중적분법에 기초하였다. 공간적 불확실성을 가지는 인수로는 두 재료축에 대한 탄성계수와 면내 전단탄성계수가 고려되었다. 이들 재료인수들은 독립적인 추계장함수로 모델링 되었으며, 이들 추계장이 구조거동에 미치는 영향은 지수함수형태의 자기 및 상호상관함수를 적용하여 산정하였다. 수치예제를 통하여 복합적층판이 등방성 및 이방성의 재료에 의한 판 구조에 비하여 거동의 변동계수가 낮음을 보여주었으며, 제안된 해석법의 검증을 위하여 몬테카를로 해석을 동시에 수행하고 그 결과를 상호 비교하였다.

Keywords

References

  1. 최창근, 노혁천 (1995) 평판구조의 추계론적 유한요소해석, 한국전산구조공학회논문집, 8(2), pp.127-136
  2. 최창근, 노혁천 (1999) 가중적분법을 이용한 반무한영역의 추 계론적 유한요소해석, 한국전산구조공학회논문집, 12(2), pp.129-140
  3. Antonio C.C., Hoffbauer L.N. (2007) Uncertainty analysis based on sensitivity applied to angle-ply composite structures, Reliability Engineering & System Safety, 92(10), pp.1353-1362 https://doi.org/10.1016/j.ress.2006.09.006
  4. Deodatis, G. (1991) Weighted integral method I: Stochastic stiffness matrix, Journal of Engineering Mechanics, ASCE, 117(8), pp.1851-1864 https://doi.org/10.1061/(ASCE)0733-9399(1991)117:8(1851)
  5. Deodatis, G., Wall, W., Shinozuka, M. (1991) Analysis of two-dimensional stochastic systems by the weighted integral method, In Spanos, P.D. and Brebbia, C.A. editors, Computational Stochastic Mechanics, pp.395-406
  6. Graham, L., Deodatis, G. (1998) Variability response functions for stochastic plate bending problems, Structural Safety, 20, pp.167-188 https://doi.org/10.1016/S0167-4730(98)00006-X
  7. Lal A., Singh B.N., Kumar R. (2007) Natural frequency of laminated composite plate resting on an elastic foundation with uncertain system properties, Structural Engineering and Mechanics, 27(2), pp.199-222 https://doi.org/10.12989/sem.2007.27.2.199
  8. Lawrence, M.A. (1987) Basis random variables in finite element analysis, International Journal for Numerical Methods in Engineering, 24, pp.1849-1863 https://doi.org/10.1002/nme.1620241004
  9. Ngah, M.F., Young, A. (2007) Application of the spectral stochastic finite element method for performance prediction of composite structures, Composite Structures, 78, pp.447-456 https://doi.org/10.1016/j.compstruct.2005.11.009
  10. Nigam, N.C., Narayanan S. (1994) Applications of random vibrations. New Delhi: Narosa
  11. Noh, H.C. (2004) A formulation for stochastic finite element analysis of plate structures with uncertain Poisson's ratio, Computer Methods in Applied Mechanics and Engineering, 193(45-47), pp.4857-4873 https://doi.org/10.1016/j.cma.2004.05.007
  12. Noh, H.C. (2006) Effect of Multiple Uncertain Material Properties on Statistical Behavior of Inplane and Plate Structures, Computer Methods in Applied Mechanics and Engineering, 195(19-22), pp.2697-2718 https://doi.org/10.1016/j.cma.2005.06.026
  13. Noh, H.C., Park, T. (2006) Monte Carlo simulationcompatible stochastic field for application to expansion- based stochastic finite element method, Computers and Structures, 84(31-32), pp.2363-2372 https://doi.org/10.1016/j.compstruc.2006.07.001
  14. Onkar, A.K., Upadhyay, C.S., Yadav, D. (2007) Probabilistic failure of laminated composite plates using the stochastic finite element method, Composite Structures, 77, pp.79-91 https://doi.org/10.1016/j.compstruct.2005.06.006
  15. Papadopoulos, V., Deodatis, G., Papadrakakis, M. (2005) Flexibility-based upper bounds on the response variability of simple beams, Computer Methods in Applied Mechanics and Engineering, 194(12-16), pp.1385-1404 https://doi.org/10.1016/j.cma.2004.06.040
  16. Papadopoulos, V., Papadrakakis, M., Deodatis, G. (2006) Analysis of mean and mean square response of general linear stochastic finite element systems, Computer Methods in Applied Mechanics and Engineering, 195(41-43), pp.5454-5471 https://doi.org/10.1016/j.cma.2005.11.008
  17. Reddy, J.N. (1997) Mechanics of Laminated Composite Plates, Theory and Analysis, CRC
  18. Schueuller, G.I. (2001) Computational Stochastic Mechanics-Recent Advances, Computers and Structures, 79, pp.2225-2234 https://doi.org/10.1016/S0045-7949(01)00078-5
  19. Singh, B.N., Yadav, D., Iyengar, N.G.R. (2002) Free vibration of composite cylindrical panels with random material properties, Composite Structures, 58, pp.435-442 https://doi.org/10.1016/S0263-8223(02)00133-2
  20. Vinckenroy G., Wilde W.P. (1995) The use of Monte Carlo techniques in statistical finite element methods for the determination of the structural behavior of composite materials structural components, Composite Structures, 32, pp.247-253 https://doi.org/10.1016/0263-8223(95)00055-0
  21. Yamazaki, F., Shinozuka, M. (1990) Simulation of stochastic fields by statistical preconditioning, Journal of Engineering Mechanics, ASCE, 116(2), pp.268-287 https://doi.org/10.1061/(ASCE)0733-9399(1990)116:2(268)