• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.6
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• pp.727-737
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• 2010

Together with the Young's modulus the Poisson's ratio is another independent material parameter that governs the behavior of a structural system. Therefore, it is meaningful to evaluate separately the influence of the parameter on the random response of the structural system. To this end, a formulation dealing with the spatial randomness in the Poisson's ratio in laminated composite plates is proposed. The main idea of the paper is to transform the fraction form of the constitutive coefficients into the expanded form in an ascending order of the stochastic field function. To validate the adequacy of the formulation, a square plate is chosen and the computation results are compared with those obtained using conventional Monte Carlo simulation. It is observed that the results show good agreement with those by the Monte Carlo simulation(MCS).

• Steel and Composite Structures
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• v.11 no.2
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• pp.115-130
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• 2011

Considering the randomness of material parameters in the laminated composite plate, a scheme of stochastic finite element method to analyze the displacement response variability is suggested. In the formulation we adopted the concept of the weighted integral where the random variable is defined as integration of stochastic field function multiplied by a deterministic function over a finite element. In general the elastic modulus of composite materials has distinct value along an individual axis. Accordingly, we need to assume 5 material parameters as random. The correlations between these random parameters are modeled by means of correlation functions, and the degree of correlation is defined in terms of correlation coefficients. For the verification of the proposed scheme, we employ an independent analysis of Monte Carlo simulation with which statistical results can be obtained. Comparison is made between the proposed scheme and Monte Carlo simulation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1920-1929
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• 1994

The stochastic finite element method(SFEM) based structural optimal design is presented. Random system response including uncertainties for the design variable is calculated with first order perturbation method. A method for calculating the sensitivity coefficients is developed using the equilibrium equation and first-order perturbed equation. Numerical results are presented for a truss, frame and plate structures with displacement and stress constraints. The sensitivity calculation proposed here is compared with finite difference method. A nonlinear programming technique is used to solve the problem. The procedure is easily incorporated with existing deterministic structural optimization.

• Structural Engineering and Mechanics
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• v.27 no.2
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• pp.199-222
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• 2007

Composite laminated structures supported on elastic foundations are being increasingly used in a great variety of engineering applications. Composites exhibit larger dispersion in their material properties compared to the conventional materials due to large number of parameters associated with their manufacturing and fabrication processes. And also the dispersion in elastic foundation stiffness parameter is inherent due to inaccurate modeling and determination of elastic foundation properties in practice. For a better modeling of the material properties and foundation, these are treated as random variables. This paper deals with effects of randomness in material properties and foundation stiffness parameters on the free vibration response of laminated composite plate resting on an elastic foundation. A $C^0$ finite element method has been used for arriving at an eigen value problem. Higher order shear deformation theory has been used to model the displacement field. A mean centered first order perturbation technique has been employed to handle randomness in system properties for obtaining the stochastic characteristic of frequency response. It is observed that small amount of variations in random material properties and foundation stiffness parameters significantly affect the free vibration response of the laminated composite plate. The results have been compared with those available in the literature and an independent Monte Carlo simulation.

• Journal of Korean Association for Spatial Structures
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• v.1 no.1 s.1
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• pp.109-115
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• 2001

Composite materials also known as fiber reinforced plastics have been developed and used in many engineering applications due to their outstanding mechanical properties. Laminated plates as structural components that are made of in composite material are widely used. Therefore, nonlinear response of laminated composite plates modeled with finite elements and excited by stochastic loading is studied. The classical laminated plate theory is used to account for the variation of strains through the thickness for modeling laminated thin plates. Approximate nonlinear random vibration analysis is performed using the method of equivalent linearization to account for material non-linearity.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.857-864
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• 2006

Due to the difficulties in numerical generation of random fields that satisfy not only the probabilistic distribution but the spectral characteristics as well. it is relatively hard to find an exact response variability of a structural response with a specific random field which has its features in the spatial and spectral domains. In this study. focusing on the fact that the random field assumes a constant over the domain under consideration when the correlation distance tends to infinity, a semi-theoretical solution of response variability is proposed for in-plane and plate bending structures. In this procedure, the probability density function is used directly resulting in a semi-exact solution for the random field in the state of random variable. It is particularly noteworthy that the proposed methodology provides response variability for virtually any type of probability density functions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.335-345
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• 2008

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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.27-32
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• 2008

The laminated composite materials have been applied to various mechanical structures due to their high performance to weight ratios. In this study, we suggest a stochastic finite element scheme for the probabilistic analysis of the composite laminated plates. The composite materials consist of two different materials which constitute the matrix and fiber. The material properties in the major and minor directions are determined depending on the volume fraction of these two materials. In this study, the elastic modulus and shear modulus are considered as random and the effect of these random properties on the behavior of the composite plate is investigated. We adopt the weighted integral scheme in the formulation, which has been recognized as the most accurate method in the statistical methodologies. For verification of the proposed scheme, Monte Carlo analysis is also performed for the comparison with the proposed scheme.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.529-541
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• 2006

This work gives an application of stochastic techniques for the optimization of stiffened plates in vibration. The search strategy consists of substituting, for finite element calculations in the optimization process, an approximate response from a Rayleigh-Ritz method. More precisely, the paper describes the use of a Rayleigh-Ritz method in creating function approximations for use in computationally intensive design optimization based on genetic algorithms. Two applications are presented; their deal with the optimization of stiffeners on plates by varying their positions, in order to maximize some natural frequencies, while having well defined dimensions. In other words, this work gives the fundamental idea of using a Ritz approximation to the response of a plate in vibration instead of finite element analysis.

• Smart Structures and Systems
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• v.9 no.6
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• pp.505-534
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• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).