Stochastic Finite Element Buckling Analysis of Laminated Plates With Circular Cutout Under Uniaxial Compression
01 Jul 2007-Journal of Applied Mechanics (American Society of Mechanical Engineers)-Vol. 74, Iss: 4, pp 798-809
TL;DR: In this paper, a generalized stochastic analysis of laminated composite plates, with and without centrally located circular cutouts having random material properties, is presented under uniaxial compressive loading.
Abstract: A generalized stochastic buckling analysis of laminated composite plates, with and without centrally located circular cutouts having random material properties, is presented under uniaxial compressive loading. In this analysis, the layerwise plate model is used to solve both prebuckling and buckling problems. The stochastic analysis is done based on mean centered first-order perturbation technique. The mean buckling strength of composite plates is validated with results available in the literature. It has been observed that the present analysis can predict buckling load accurately even for plates with large cutouts. Micromechanics based approach is used to study the effect of variation in microlevel constituents on the effective macrolevel properties like elastic moduli. Consequently, the effect of uncertainty in these material properties on the buckling strength of the laminated plates is studied. Parametric studies are carried out to see the effect of hole size, layups, and boundary conditions on the mean and variance of plate buckling strength.
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...solid, structural and fluid mechanics, acoustics, heat transfer) [1–4,13–15,18,20,22–29,31,32,37,40,42,44–46,48–51,57–69,72,74, 89,91,92,94–96,99,103,104,106–108,111–113,116–124,126–139,148, 154,155,158,160,162,166,173,175,188,196]....
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References
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TL;DR: In this article, a generic stochastic finite-element method for modeling structures is proposed as a means to analyze and design structures in a probabilistic framework, which is applied in structures discretized with the finite element methodology, and an estimate of the probability of failure based on known and established procedures in second-moment reliability analysis is made with the aid of a transformation to gaussian space of the random variables that define structural reliability.
648 citations
TL;DR: In this article, a finite element method applicable to truss structures for the determination of the probabilistic distribution of the dynamic response has been developed and implemented into a pilot computer code with two-dimensional bar elements.
Abstract: A finite element method applicable to truss structures for the determination of the probabilistic distribution of the dynamic response has been developed. Several solutions have been obtained for the mean and variance of displacements and stresses of a truss structure; nonlinearities due to material and geometrical effects have also been included. In addition, to test this method, Monte Carlo simulations have been used and a new method with implicit and/or explicit time integration and Hermite-Gauss quadrature has also been developed and used. All these methodologies have been implemented into a pilot computer code with two-dimensional bar elements.
375 citations
TL;DR: Some of the different methods available for analysing the effects of randomness of models and data in structural analysis are reviewed to point out some research needs in the field from the authors' point of view.
Abstract: A state of the art on simulation methods in stochastic structural analysis is presented. The purpose of the paper is to review some of the different methods available for analysing the effects of randomness of models and data in structural analysis. While most of these techniques can be grouped under the general name ofMonte Carlo methods, the several published algorithms are more suitable to some objectives of analysis than to others in each case. These objectives have been classified into the foolowing cathegories: (1), TheStatistical Description of the structural scattering, a primary analysis in which the uncertain parameters are treated as random variables; (2) The consideration of the spatial variability of the random parameters, that must then be modelled as Random Fields (Stochastic Finite Elements); (3) The advanced Monte Carlo methods for calculating the usually very low failure probabilities (Reliability Analysis), and, (4), a deterministic technique that depart from the random nature of the above methods, but which can be linked with them in some cases, known as theResponse Surface Method. All of these techniques are critically examined and discussed. The concluding remarks point out some research needs in the field from the authors' point of view.
281 citations
TL;DR: In this paper, the buckling and free-vibration behavior of cross-ply rectangular composite laminates under various boundary conditions was studied. But the bucklings and free vibration properties were not investigated.
Abstract: Analytical and finite-element solutions of the classical, first-order, and third-order laminate theories are developed to study the buckling and free-vibration behavior of cross-ply rectangular composite laminates under various boundary conditions
252 citations
TL;DR: In this article, the differential equation governing buckling of symmetrically laminated composite plates loaded in compression is presented in nondimensiona l form, and a nondimensional parameter is presented that is used to assess when anisotropic bending stiffnesses can be neglected in a buckling analysis.
Abstract: The differential equation governing buckling of symmetrically laminated composite plates loaded in compression is presented in nondimensiona l form. From this equation, nondimensional material coefficients are obtained, and a nondimensional parameter is presented that is used to assess when anisotropic bending stiffnesses can be neglected in a buckling analysis. Results obtained using finite element analyses are presented that show how boundary conditions, aspect ratio, fiber orientation, stacking sequence, and thickness affect the importance of the anisotropic bending stiffnesses.
186 citations