Static Response of Laminated Composite Plates Resting on Elastic Foundation with Uncertain System Properties

Abstract

Virtually, in all structural systems, there are uncertainties in the system parameters because of real bounds on the quality control and modeling. This paper presents an investigation of the stochastic bending static response of laminated composite plates resting on elastic foundation with uncertain system parameters subjected to static distributed loading. The transverse shear effects have been included in the system equation using higher order shear deformation theory. The interaction between the plate and foundation is included in the formulation with a two-parameter Pasternak model. System parameters such as material properties and foundation stiffness parameters are modeled as independent random variables. A C⁰ finite element method in conjunction with mean centered first-order perturbation technique is outlined to obtain the second-order response statistics of the bending deflection of the plate supported on with and without elastic foundation. The approach has been validated with independent Monte Carlo simulation and other approaches.

Keywords

stochastic bending response random variables composite plate C° finite element method perturbation technique.

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References

Reddy, J.N. and Phan, N.D. (1985). Stability and Vibration of Isotropic, Orthotropic and Laminated Plates according to Higher Order Shear Deformation Theory, Journal of Sound and Vibration, 98(2): 157—170.

Reddy, J.N. (1984). A Simple Higher-order Theory for Laminated Composite Plates, Journal of Applied Mechanics, 51: 745—752.

Latheswary, S. , Valsarajan, K.V. and Rao, V.B.K.S. (2004). Behaviour of Laminated Composite Plates using Higher Shear Deformation Theory, The Institution of Engineers (India)-AS, 10—17.

Setoodes, A.R. and Karmi, G. (2004). Static Free Vibration and Buckling analysis of Anisotropic Thick Laminated Composite Plates on Distributed and Point Elastic Supports using a 3-D Layer-wise FEM, Engineering Structures, 26(2): 211—220.

Shen, H.S. , Zheng, J.J. and Huang, X.L. (2003). Dynamic Response of Shear Deformable Plates under Thermo-mechanical Loading and Resting on Elastic Foundations, Composite Structure, 60(1): 57—66.

Nigam, N.C. and Narayanan, S. (1994). Applications of Random Vibrations, Narosa, New Delhi.

Manohar, C.S. and Ibrahim, R.A. (1999). Progress in Structural Dynamics with Stochastic Dynamic with Stochastic Parameter Variations: 1987—1998 , Applied Mechanics Review, 52: 177—196.

Naveenthraj, B. , Iyengar, N.G.R. and Yadav, D. (1998). Response of Composite Plates with Random Material Properties using FEM and MCS, Advanced Composite Materials, 7: 219—237.

Salim, S. , Yadav, D. and Iyengar, N.G.R. (1993). Analysis of Composite Plates with Random Material Characteristics, Mechanics Research Communications, 20(5): 405—14.

10.

Onkar, A.K. and Yadav, D. (2003). Non-linear Response Statistics of Composite Laminates with Random Material Properties under Random Loading , Composite Structure, 60(4): 375—383.

11.

Zongeen, Z. and Suhaun, C. (1990). The Standard Deviation of the Eigen Solutions for Random Multi Degree Freedom Systems, Journal of Computers and Structures, 39(6): 603—607.

12.

Zhang Y. , Chen, S. , Lue, Q. and Liu, T. ( 1996). Stochastic Perturbation Finite Elements, Computer and Structures, 59(3): 425—429.

13.

Liu.,W.K. , Ted, B. and Mani, A. (1986). A Random Field Finite Elements, International Journal for Numerical Methods in Engineering, 23: 1831—1845.

14.

Zhang, J. and Ellingwood, B. (1993). Effects of Uncertain Material Properties on Structural Stability, Journal of Structural Engineering, 121: 705—716.

15.

Reddy, J.N. (2004). Mechanics of Laminated Composite Plates and Shells Theory and Analysis, Second Edition, CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.

16.

Jones, R.M. (1975). Mechanics of Composite Materials, McGraw-Hill, Kagakusha, Ltd., International Students Edition, Tokyo, Japan.

17.

Shinozuka, M. and Yamazaki, F. (1988). Stochastic Finite Element Analysis: An Introduction, In: S. T. Ariaratnam , G. I. Schuëller and I. Elishakoff (eds), Stochastic Structural Dynamics, Elsevier Science, Amsterdam , pp. 241—291.