Effect of multiple uncertain material properties on the response variability of in-plane and plate structures

Noh, Hyuk Chun

doi:10.1016/j.cma.2005.06.026

Cited by 20 publications

(6 citation statements)

References 25 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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“…In the present study, stochastic fields f 2 (x, y) and f 3 (x, y) are assumed uncorrelated. However, since cross-correlation between the aforementioned fields has proven to play an important role on the buckling behavior of shell-type structures leading often to a further reduction of the bearing capacity, with respect to the uncorrelated case (Noh and Kwak, 2006;Noh, 2006;Stefanou and Papadrakakis, 2004), the effect of the above mentioned correlation in the optimum design of shell structures will be specifically addressed in follow-up research. The stochastic stiffness matrix of the shell element is derived using the local average method.…”

Section: Stochastic Stiffness Matrixmentioning

confidence: 99%

Optimum design of shell structures with random geometric, material and thickness imperfections

Lagaros

Papadopoulos

2006

International Journal of Solids and Structures

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The optimum design of isotropic shell structures with random initial geometric, material and thickness imperfections is investigated in this paper and a robust and efficient methodology is presented for treating such problems. For this purpose, the concept of an initial ''imperfect'' structure is introduced involving not only geometric deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticity as well as of the thickness of the shell. An efficient reliability-based design optimization (RBDO) formulation is proposed. The objective function is considered to be the weight of the structure while both deterministic and probabilistic constraints are taken into account. The overall probability of failure is taken as the global probabilistic constraint for the optimization procedure. Numerical results are presented for a cylindrical panel, demonstrating the efficiency as well as the applicability of the proposed methodology in obtaining rational optimum designs of imperfect shell-type structures.

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“…Zhang and Ellingwood [17] examined the effect of random material field characteristics on the instability of a simply supported beam on elastic foundation and a frame using perturbation technique. Noh [18] framed stochastic finite element analysis to investigate the effect of multiple uncertain material properties on the response variability of in-plane and plate structures with multiple uncertain material parameters. Keeping in mind the above aspect, in the present work, an HSDT-based probabilistic procedure as proposed by Lal et al [19] and Singh et al [20] is extended to random environments.…”

Section: Introductionmentioning

confidence: 99%

Stochastic nonlinear bending response of laminated composite plates with system randomness under lateral pressure and thermal loading

2010

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In this paper, the effect of sensitivity of randomness in system parameters on the nonlinear transverse central deflection response of laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modelled as basic random variables. A higher order shear deformation theory in the von-Karman sense is used to model the system behavior of the laminated plate. A direct iterative-based C 0 nonlinear finite element method in conjunction with the first-order perturbation technique developed by the authors is extended for thermal problem to obtain the second-order response statistics, i.e., mean and variance of the nonlinear transverse deflection of the plate. Typical numerical results of composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and transverse temperature are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The results have been compared with those available in the literature and an independent Monte Carlo simulation.

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Effect of multiple uncertain material properties on the response variability of in-plane and plate structures

Cited by 20 publications

References 25 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

Optimum design of shell structures with random geometric, material and thickness imperfections

Stochastic nonlinear bending response of laminated composite plates with system randomness under lateral pressure and thermal loading

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