Generalized buckling analysis of laminated plates with random material properties using stochastic finite elements

Onkar, Amit Kumar; Upadhyay, C. S.; Yadav, D.

doi:10.1016/j.ijmecsci.2006.01.002

Cited by 50 publications

(16 citation statements)

References 24 publications

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“…It is nowadays generally recognized that an accurate prediction of the buckling behavior of shells requires a realistic description of all uncertainties involved in the problem and that such task is realizable only in the framework of a robust Stochastic Finite Element Method (SFEM) formulation that can efficiently and accurately handle geometric as well as physical nonlinearities of shell-type structures (Choi and Noh, 2000;Graham and Siragy, 2001;Argyris et al, 2002b;Papadrakakis, 2004, 2005;Stefanou and Papadrakakis, 2004;Lagaros and Papadopoulos, 2006;Noh, 2006;Onkar et al, 2006;Papadopoulos and Iglesis, 2007). The analysis of such structures has been carried out in a probabilistic context through the application of the Finite Element method in conjunction with the Monte Carlo Simulation, incorporating realistic descriptions of the uncertainties involved in geometric (Bielewicz and Górski, 2002;Schenk and Schuëller, 2003), material and thickness imperfections Papadrakakis, 2004, 2005), as well as boundary conditions (Papadopoulos and Iglesis, 2007;Schenk and Schuëller, 2007).…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties

Papadopoulos

Stefanou

Papadrakakis

2009

International Journal of Solids and Structures

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a b s t r a c tIn this paper, the effect of material and thickness spatial variation on the buckling load of isotropic shells with random initial geometric imperfections is investigated. To this purpose, a random spatial variability of the elastic modulus as well as of the thickness of the shell is introduced in addition to the random initial geometric deviations of the shell structure from its perfect geometry. The main novelty of this paper compared to previous works is that a non-Gaussian assumption is made for the distribution of the two aforementioned uncertain parameters i.e. the modulus of elasticity and the shell thickness which are described by two-dimensional uni-variate (2D-1V) homogeneous non-Gaussian stochastic fields. The initial geometric imperfections are described as a 2D-1V Gaussian non-homogeneous stochastic field with properties derived from corresponding experimental measurements. Numerical examples are presented focusing on the influence of the non-Gaussian assumption on the variability of the buckling load, which is calculated by means of the Monte Carlo Simulation method. It is shown that the choice of the marginal probability distribution for the description of the material and thickness variability is crucial since it affects significantly the statistics of the buckling load of imperfection sensitive shell-type structures.

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Section: Introductionmentioning

confidence: 99%

Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties

Papadopoulos

Stefanou

Papadrakakis

2009

International Journal of Solids and Structures

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“…Najafizadeh and Eslami [151] used classical plate theory (CLPT) to investigate the buckling behavior of clamped and simply supported circular FGM plate. Onkar et al [152,153] presented the generalized buckling of laminated composite plate with random material properties using classical plate theory (CLPT) combined with First order shear deformation theory (FSDT). Samsamshariat et al [154] studied buckling behavior of FGM plates under uniaxial compression and biaxial compression and tension, using CLPT and HSDT.…”

Section: Bending and Stability Analysis Of Fg Platesmentioning

confidence: 99%

Recent development in modeling and analysis of functionally graded materials and structures

Gupta

Talha

2015

Progress in Aerospace Sciences

400

115

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“…Equation 22 is the nonlinear free vibration problem which is random in nature, being dependent on the system properties. Consequently, the nonlinear natural frequency (ω nl ) and its mode shape are random in nature.…”

Section: Governing Equationmentioning

confidence: 99%

“…For the MCS approach, the samples are generated using Mat Lab to fit the desired mean and SD. These samples are used in response equation (22), which is solved repeatedly, adopting conventional eigenvalue procedure, to generate a sample of the nonlinear fundamental frequency. The number of samples used for MCS approach is 10,000 based on satisfactory convergence of the results.…”

Section: Standard Deviation Of Nonlinear Fundamental Frequencymentioning

confidence: 99%

“…Yadav and Verma [19,20] investigated the free vibration of composite circular cylindrical shells with random material properties employing CLT and FOPT for obtaining the second order statistics natural frequencies. Onkar et al [21,22] have investigated the non-linear free vibration and buckling analysis of laminated composite plate with random material properties using the classical laminate theory. Tripathi et al [23] investigated the free vibration response of laminated composite conical shells with random material properties using FEM in conjunction with FOPT based on HSDT.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic nonlinear free vibration of laminated composite plates resting on elastic foundation in thermal environments

Lal

Singh

2008

Comput Mech

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This paper presents the nonlinear free vibration analysis of laminated composite plates resting on elastic foundation with random system properties in thermal environments. System parameters are modeled as basic random variables for accurate prediction of system behavior. A C 0 nonlinear finite element based on HSDT in von Karman sense is used to descretize the laminate. A direct iterative method in conjunction with first-order perturbation technique is outlined and applied to solve the stochastic nonlinear generalized eigenvalue problem. The developed stochastic procedure is successfully used for thermally induced nonlinear free vibration problem with a reasonable accuracy. Numerical results for various combinations of boundary conditions, geometric parameters, amplitude ratios, foundation parameters and thermal loading have been compared with those available in literature and an independent MCS. Some new results are also presented which clearly demonstrate the importance of the randomness in the system parameters on the response of the structures.

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Generalized buckling analysis of laminated plates with random material properties using stochastic finite elements

Cited by 50 publications

References 24 publications

Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties

Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties

Recent development in modeling and analysis of functionally graded materials and structures

Stochastic nonlinear free vibration of laminated composite plates resting on elastic foundation in thermal environments

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