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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2015, Vol. 9 Issue (2) : 141-153     https://doi.org/10.1007/s11709-014-0286-2
RESEARCH ARTICLE |
Stochastic analysis of laminated composite plate considering stochastic homogenization problem
S. SAKATA(),K. OKUDA,K. IKEDA
Department of Mechanical Engineering, Kinki University, 3-4-1 Kowakae, Higashiosaka, Osaka 577-8502, Japan
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Abstract

This paper discusses a multiscale stochastic analysis of a laminated composite plate consisting of unidirectional fiber reinforced composite laminae. In particular, influence of a microscopic random variation of the elastic properties of component materials on mechanical properties of the laminated plate is investigated. Laminated composites are widely used in civil engineering, and therefore multiscale stochastic analysis of laminated composites should be performed for reliability evaluation of a composite civil structure. This study deals with the stochastic response of a laminated composite plate against the microscopic random variation in addition to a random variation of fiber orientation in each lamina, and stochastic properties of the mechanical responses of the laminated plate is investigated. Halpin-Tsai formula and the homogenization theory-based finite element analysis are employed for estimation of effective elastic properties of lamina, and the classical laminate theory is employed for analysis of a laminated plate. The Monte-Carlo simulation and the first-order second moment method with sensitivity analysis are employed for the stochastic analysis. From the numerical results, importance of the multiscale stochastic analysis for reliability evaluation of a laminated composite structure and applicability of the sensitivity-based approach are discussed.

Keywords stochastic homogenization      multiscale stochastic analysis      microscopic random variation      laminated composite plate     
Corresponding Authors: S. SAKATA   
Online First Date: 08 January 2015    Issue Date: 30 June 2015
 Cite this article:   
S. SAKATA,K. OKUDA,K. IKEDA. Stochastic analysis of laminated composite plate considering stochastic homogenization problem[J]. Front. Struct. Civ. Eng., 2015, 9(2): 141-153.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-014-0286-2
http://journal.hep.com.cn/fsce/EN/Y2015/V9/I2/141
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S. SAKATA
K. OKUDA
K. IKEDA
Fig.1  Schematic view of a laminated plate and its microstructure
fiber (E-glass) matrix (epoxy)
Young’s modulus/GPa 73.0 4.5
Poisson’s ratio 0.22 0.39
Tab.1  Expected values of elastic properties for fiber and matrix
Fig.2  Schematic view of a laminated composite plate. (a) Macroscopic condition; (b) microstructure
Fig.3  Expected values of the equivalent elastic constants of lamina for a microscopic random variation of elastic properties of component materials. (a) Halpin-Tsai; (b) homogenization theory
Fig.4  CV of the equivalent elastic constants of the lamina for a microscopic random variation of elastic properties of component materials. (a) Halpin-Tsai; (b) homogenization theory
Fig.5  CV of the A i j and D i j of a unidirectional fiber reinforced lamina for microscopic random variations. (a) CV of A i j for a microscopic random variation of elastic properties; (b) CV of D i j for a microscopic random variation of elastic properties
Fig.6  Stochastic characteristics of the in-plane strain of a symmetric orthogonal laminated plate along the loading direction. (a) Estimated expectations; (b) estimated CVs
Fig.7  Stochastic characteristics of the deflection of a symmetric orthogonal laminated plate for bending moment. (a) Estimated expectations; (b) estimated CVs
Fig.8  Stochastic characteristics of the in-plane strain along the loading direction for asymmetrical laminated plate
Fig.9  Stochastic characteristics of the deflection for asymmetrical laminated plate
Fig.10  CV of the in-plane strain and deflection of the laminated plate [0/ θ / θ /0]. (a) CV of the in-plane strain along the loading direction; (b) CV of the deflection for the bending moment
Fig.11  CV of the in-plane strain and deflection of the laminated plate [90/ θ / θ /90]
Fig.12  CV of the in-plane strain and deflection of the laminated plate [0/ θ / - θ /0]. (a) CV of the in-plane strain along the loading direction; (b) CV of the deflection for bending moment
Fig.13  CV of the in-plane strain along the loading direction of the laminated plate [0/ θ / - θ /90]. (a) CV of the in-plane strain along the loading direction; (b) CV of the deflection for bending moment
Fig.14  Required coefficients of variance of the microscopic random variable causing CV of the mechanical responses of laminates for random variation of Δ θ = ± 2
Fig.15  Relative error in multiscale stochastic analysis of a symmetric orthogonal laminate plate between the estimated CV with FOSM and the Monte-Carlo simulation
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