• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.157-164
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• 1998

An elasto-plastic stochastic finite element method is developed to evaluate the probability of failure of the underground structure. The Mohr-Coulomb failure criteria is adopted for yield condition. The material properties such as the elastic modulus and the cohesion are assumed to be statistically independent random variables which are modeled as spatial stochastic fields. The displacements around the excavated area and the probability of the failure are examined by varying the coefficient of variance for each variables. It is found that the developed procedure can provide the proper probabilistic information about the failure of the underground structure

• Steel and Composite Structures
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• v.26 no.1
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• pp.1-15
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• 2018

This study reported, the effect of random variation in system properties on bending response of single wall carbon nanotube reinforced composite (SWCNTRC) plates subjected to transverse uniform loading is examined. System parameters such as the SWCNT armchair, material properties, plate thickness and volume fraction of SWCNT are modelled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behaviour of the SWCNTRC composite plate. A C0 finite element method in conjunction with the first order perturbation technique procedure developed earlier by the authors for the plate subjected to lateral loading is employed to obtain the mean and variance of the transverse deflection of the plate. The performance of the stochastic SWCNTRC composite model is demonstrated through a comparison of mean transverse central deflection with those results available in the literature and standard deviation of the deflection with an independent First Order perturbation Technique (FOPT), Second Order perturbation Technique (SOPT) and Monte Carlo simulation.

• Structural Engineering and Mechanics
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• v.15 no.4
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• pp.381-394
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• 2003

While constructing multistorey buildings with reinforced concrete framed structures it is a common practice to provide parking space for vehicles at the ground floor level. This floor will generally consist of open frames without any infilled walls and is called an open-storey. From a post disaster damage survey carried out, it was noticed that during the January 26, 2001 Bhuj (Gujarat, India) earthquake, a large number of reinforced concrete framed buildings with open-storey at ground floor level, suffered extensive damage and in some cases catastrophic collapse. This has brought into sharp focus the need to carry out systematic studies on the seismic vulnerability of such buildings. Determination of vulnerability requires realistic structural response estimations taking into account the stochasticity in the loading and the system parameters. The stochastic finite element method can be effectively used to model the random fields while carrying out such studies. This paper presents the details of stochastic finite element analysis of a five-storey three-bay reinforced concrete framed structure with open-storey subjected to standard seismic excitation. In the present study, only the stochasticity in the system parameters is considered. The stochastic finite element method used for carrying out the analysis is based on perturbation technique. Each random field representing the stochastic geometry/material property is discretised into correlated random variables using spatial averaging technique. The uncertainties in geometry and material properties are modelled using the first two moments of the corresponding parameters. In evaluating the stochastic response, the cross-sectional area and Young' modulus are considered as independent random fields. To study the influence of correlation length of random fields, different correlation lengths are considered for random field discretisation. The spatial expectations and covariances for displacement response at any time instant are obtained as the output. The effect of open-storey is modelled by suitably considering the stiffness of infilled walls in the upper storey using cross bracing. In order to account for changes in soil conditions during strong motion earthquakes, both fixed and hinged supports are considered. The results of the stochastic finite element based seismic analysis of reinforced concrete framed structures reported in this paper demonstrate the importance of considering the effect of open-storey with appropriate support conditions to estimate the realistic response of buildings subjected to earthquakes.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.193-213
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• 2017

We investigate an efficient approximation of solution to stochastic Burgers equation driven by an additive space-time noise. We discuss existence and uniqueness of a solution through the Orstein-Uhlenbeck (OU) process. To approximate the OU process, we introduce the Karhunen-$Lo{\grave{e}}ve$ expansion, and sparse grid stochastic collocation method. About spatial discretization of Burgers equation, two separate finite element approximations are presented: the conventional Galerkin method and Galerkin-conservation method. Numerical experiments are provided to demonstrate the efficacy of schemes mentioned above.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.537-549
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• 2001

The effect of partially restrained(PR) connections and the uncertainties in them on the reliability of steel frames subjected to seismic loading is addressed. A stochastic finite element method(SFEM) is proposed combining the concepts of the response surface method(RSM), the finite element method(FEM), the first-order reliability method (FORM), and the iterative linear interpolation scheme. The behavior of PR connections is captured using moment-relative rotation curves, and is represented by the four-parameter Richard model. For seismic excitation, the loading, unloading, and reloading behavior at PR connections is modeled using moment-relative rotation curves and the Masing rule. The seismic loading is applied in the time domain for realistic representation. The reliability of steel frames in the presence of PR connections is calculated considering all major sources of nonlinearity. The algorithm is clarified with the help of an example.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.3
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• pp.373-384
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• 2000

To assess the safety of nonlinear steel frame structures subjected to short duration dynamic loadings, especially seismic loading, a nonlinear time domain reliability analysis procedure is proposed in the context of the stochastic finite element concept. In the proposed algorithm, the finite element formulation is combined with concepts of the response surface method, the first order reliability method, and the iterative linear interpolation scheme. This leads to the stochastic finite element concept. Actual earthquake loading time-histories are used to excite structures, enabling a realistic representation of the loading conditions. The assumed stress-based finite element formulation is used to increase its efficiency. The algorithm also has the potential to evaluate the risk associated with any linear or nonlinear structure that can be represented by a finite element algorithm subjected to seismic loading or any short duration dynamic loading. The algorithm is explained with help of an example and verified using the Monte Carlo simulation technique.

• Structural Engineering and Mechanics
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• v.3 no.3
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• pp.273-287
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• 1995

Stochastic response of systems to random excitation can be estimated by direct integration methods in the time domain such as the stochastic central difference method (SCDM). In this paper, the SCDM is applied to compute the variance and covariance in response of linear and nonlinear structures subjected to random excitation. The accuracy of the SCDM is assessed using two-DOF systems with both deterministic and random material properties excited by white noise. For the former case, closed-form solutions can be obtained. Numerical results also are presented for a simply supported geometrically nonlinear beam. The stiffness of this beam is modeled as a random field, and the beam is idealized by the stochastic finite element method. A perturbation technique is applied to formulate the equations of motion of the system, and the dynamic structural response statistics are obtained in a time domain analysis. The effect of variations in structural parameters and the numerical stability of the SCDM also are examined.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.125-135
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• 2004

Industrial structure systems may have nonlinearity, and are also sometimes exposed to the danger of random excitation. This paper proposes a method to analyze response and reliability design of a complex nonlinear structure system under random excitation. The nonlinear structure system which is subjected to random process is modeled by finite element method. The nonlinear equations are expanded sequentially using the perturbation theory. Then, the perturbed equations are solved in probabilistic methods. Several statistical properties of random process that are of interest in random vibration applications are reviewed in accordance with the nonlinear stochastic problem.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.5
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• pp.29-37
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• 1993

The extension of the weighted integral method in the area of stochastic finite element analysis is presented. The use of weighted integral method in numerical analysis was extended to CST(constant strain triangle) element by Deodatis to calculate the response variability of 2D stochastic systems. In this paper, the extension of the weighted integral method for general plane-elements is represented. It has been shown that the same mesh used in the deterministic FE analysis can be used in the stochastic FE analysis. Furthermore, because the CST element is a special case which has constant strain-displacement matrix the mingling of CST elements with the other quadrilateral elements in the analysis may also be possible.