Browse > Article

A Formulation for Response Variability of Plates Considering Multiple Random Parameters  

Noh, Hyuk-Chun (세종대학교 토목환경공학과)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.20, no.6, 2007 , pp. 789-799 More about this Journal
Abstract
In this paper, we propose a stochastic finite element formulation which takes into account the randonmess in the material and geometrical parameters. The formulation is proposed for plate structures, and is based on the weighted integral approach. Contrary to the case of elastic modulus, plate thickness contributes to the stiffness as a third-order function. Furthermore, Poisson's ratio is even more complex since this parameter appears in the constitutive relations in the fraction form. Accordingly, we employ Taylor's expansion to derive decomposed stochastic field functions in ascending order. In order to verify the proposed formulation, the results obtained using the proposed scheme are compared with those in the literature and those of Monte Carlo analysis as well.
Keywords
stochastic finite element method; random parameter; response variability; correlation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Chakraborty, S., Bhattacharyya, B. (2002) An efficient 3D stochastic finite element method, International Journal of Solids and Structures 39, pp.2465-2475   DOI   ScienceOn
2 Ghanem, R. Spanos, P.D. (1991) Stochastic Finite Elements: A Spectral Approach, Spingar-Verlag, New York
3 Lawrence, M.A. (1987) Basis random variables in finite element analysis, International Journal for Numerical Methods in Engineering, 24, pp.1849-1863   DOI   ScienceOn
4 Spanos P.D., Beer M., Red-Horse J. (2007) Karhunen-loeve expansion of stochastic processes with a modified exponential covariance kernel, Journal of Engineering Mechanics-ASCE, 133 (7). pp.773-779   DOI   ScienceOn
5 Vanmarcke E.H., Grigoriu, M. (1983) Stochastic finite element analysis of simple beams, Journal of Engineering Mechanics. ASCE, 109(5). pp.1203-1214   DOI
6 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   DOI   ScienceOn
7 Graham, L., Deodatis, G. (1998) Variability response functions for stochastic plate bending problems, Structural Safety, 20, pp.167-188   DOI   ScienceOn
8 최창근, 노혁천 (1990) 가중적분법을 이용한 반무한영역의 추계론적 유한요소해석, 한국전산구조공학회 논문집, 12(2). pp.129-140
9 Kaminski, M. (2007) Generalized perturbation-based stochastic finite element method in elastostatics, Computers & Structures, 85(10), pp.586-594   DOI   ScienceOn
10 Ghanem, R. Spanos, P.D. (1990) Polynomial chaos in stochastic finite-elements, Journal of applied Mechanics-Transactions of the ASME, 57(1), pp. 197-202   DOI
11 Sohueuller , G.I. (2007) On the treatment of uncertainties in structural mechanics and analysis, Computers and Structures, 85(5-6). pp.235-243   DOI   ScienceOn
12 Schueuller , G.I. (2001) Computational Stochastic Mechanics-Recent Advances, Computers and Structures, 79. pp.2225-2234   DOI   ScienceOn
13 Hisada, T., Noguchi, H. (1989) Development of a nonlinear stochastic FEM and its application, In Ang AH-S. Shinozuka M, Schueuller GI, editors. Structural Safety and Reliability, Proc of the 5th ICOSSAR. San Francisco: ASCE
14 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
15 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   DOI   ScienceOn