每年出版 6 期
ISSN 打印: 2152-5080
ISSN 在线: 2152-5099
Indexed in
APPLICATION OF THE λ NEUMANN-MONTE CARLO METHODOLOGY FOR QUANTIFICATION OF THE UNCERTAINTY OF THE PROBLEM OF STOCHASTIC BENDING OF KIRCHHOFF PLATES
摘要
This paper proposes to apply the λ Neumann-Monte Carlo method to obtain the estimates of the statistical moments of the solution for stationary Kirchhoff plate bending problems, with uncertainty about the mechanical and material properties associated with plate stiffness. The approximate solutions represent the stochastic displacement processes. For uncertainty modeling, parameterized stochastic processes will be used. The consistency of the approximate solutions will be based on studies on the existence and uniqueness of the theoretical solutions to this problem. The uncertainty will be quantified by estimating the statistical moments of the stochastic transverse displacement processes. The Monte Carlo simulation method is used to evaluate the performance of the proposed methodology.
-
Ang, A.H.S. and Tang, W.H., Probability Concepts in Engineering Planning and Design, Volume II: Decision, Risk and Reliability, Hoboken, NJ: John Wiley & Sons, 1984.
-
Ghanem, R. and Spanos, P.D., Stochastic Finite Elements: A Spectral Approach, New York: Dover, 1991.
-
Yamazaki, F., Shinozuka, M., and Dasgupta, G., Neumann Expansion for Stochastic Finite Element Analysis, j. Eng. Mech, 114(8):1335-1354, 1988.
-
Chakraborty, S. and Dey, S.S., A Stochastic Finite Element Dynamic Analysis of Structures with Uncertain Parameters, Int. J. Mech. Sci., 40(11):1071-1087, 1998.
-
Lei, Z. and Qiu, C., Neumann Dynamic Stochastic Finite Element Method of Vibration for Structures with Stochastic Parameters to Random Excitation, Comput. Struct., 77(6):651-657, 2000.
-
Chakraborty, S. and Sarkar, S.K., Analysis of a Curved Beam on Uncertain Elastic Foundation, Finite Elements Anal. Des., 36(1):73-82, 2000.
-
Araujo, J.M. and Awruch, A.M., On Stochastic Finite Elements for Structural Analysis, Comput. Struct., 52(3):461-469,1994.
-
Chakraborty, S. and Dey, S.S., Stochastic Finite Element Simulation of Random Structure on Uncertain Foundation under Random Loading, Int. J. Mech. Sci., 38(11):1209-1218,1996.
-
Chakraborty, S. and Bhattacharyya, B., An Efficient 3D Stochastic Finite Element Method, Int. J. Solids Struct., 39(9):2465- 2475, 2002.
-
Li, C.F., Feng, Y.T., and Owen, D.R.J., Explicit Solution to the Stochastic System of Linear Algebraic Equations, Comput. Methods Appl. Mech. Eng., 195(44-47):6560-6576, 2006.
-
Avila da Silva Jr., C.R. and Beck, A.T., New Method for Efficient Monte Carlo-Neumann Solution of Linear Stochastic Systems, Probab. Eng. Mech, 40:90-96, 2015.
-
Love, A.E.H., On the SmallFree Vibrations and Deformations ofElastic Shells, Philos. Trans. R. Soc, A, 179:491-549,1888.
-
Reddy, J.N., Theory and Analysis of Elastic Plates and Shells, Boca Raton, FL: CRC Press, Taylor and Francis, 2007.
-
Bauchau, O.A. and Craig, J.I., Structural Analysis with Applications to Aerospace Structures, Dordrecht, the Netherlands: Springer, 2009.
-
Necas, J., Direct Methods in the Theory of Elliptic Equations, Springer Monographs in Mathematics, Heidelberg, Germany: Springer, 2012.
-
Brenner, S.C. and Scott, L.R., The Mathematical Theory of Finite Element Methods, New York: Springer-Verlag, 1994.
-
Kreyszig, E., Introductory Functional Analysis with Applications, New York: Wiley, 1978.
-
Rao, M.M. and Swift, J.R., Probability Theory with Applications, 2nd ed., New York: Springer, 2010.
-
Saad, Y., Iterative Methods for Sparse Linear Systems, Boston: PWS Publishing Co., 1996.
-
Quarteroni, A., Sacco, R., and Saleri, F., Numerical Mathematics, New York: Springer-Verlag, 2000.
-
Golub, G.H. and Van Loan, C.F., Matrix Computations, Baltimore, MD: Johns Hopkins University Press, 2012.
-
Nocedal, J. and Wright, S.J., Numerical Optimization, New York: Springer, 1999.