• Structural Engineering and Mechanics
• /
• 제86권3호
• /
• pp.349-359
• /
• 2023

This paper presents a technique for determining the optimal number of elements in stochastic finite element analysis based on reliability analysis. Using the change-of-variable perturbation stochastic finite element approach, the probability density function of the dynamic responses of stochastic structures is explicitly determined. This method combines the perturbation stochastic finite element method with the change-of-variable technique into a united model. To further examine the relationships between the random fields, discretization of the random field parameters, such as the variance function and the scale of fluctuation, is also performed. Accordingly, the reliability index is calculated based on the explicit probability density function of responses with Gaussian or non-Gaussian random fields in any number of elements corresponding to the random field discretization. The numerical examples illustrate the effectiveness of the proposed method for a one-dimensional cantilever reinforced concrete column and a two-dimensional steel plate shear wall. The benefit of this method is that the probability density function of responses can be obtained explicitly without the use simulation techniques. Any type of random variable with any statistical distribution can be incorporated into the calculations, regardless of the restrictions imposed by the type of statistical distribution of random variables. Consequently, this method can be utilized as a suitable guideline for the efficient implementation of stochastic finite element analysis of structures, regardless of the statistical distribution of random variables.

• 한국공간정보시스템학회:학술대회논문집
• /
• 한국공간정보시스템학회 2004년도 춘계 학술발표회 논문집 제1권1호(통권1호)
• /
• pp.190-196
• /
• 2004

Thick composite laminated plates is considered in 3D finite-element. To consider continuity of transverse stresses and displacement field, mixed finite-element has been developed by using layerwise theory and the minimum potential energy principle. Mixed finite-element has been enforced through the thick direction, Z, of a laminated plate by considering six degree-of-freedoms per node. Six degree-of-freedoms are three displacement components in the coordinate axes directions and three transverse stress components ${\sigma}_z,\;{\tau}_{xz},\;{\tau}_{yz}$. The model maintain the fundamental elasticity relations that are stress-strain relation and displacement-strain relation, because the transverse stress components invoked as nodal degrees of freedom by using the fundamental elasticity relationship between th components of stress and displacement. Random vibration analysis of the model is performed by computing consistent mass matrix and computing covariance in frequency domain technique.

• Structural Engineering and Mechanics
• /
• 제82권1호
• /
• pp.31-40
• /
• 2022

In structural engineering, the material properties of the structures such as elastic modulus, shear modulus, density, and size may not be deterministic and may vary at different locations. The dynamic response analysis of such structures may need to consider these properties as stochastic. This paper introduces a stochastic finite element method (SFEM) approach to analyze moving loads problems. Firstly, Karhunen-Loéve expansion (KLE) is applied for expressing the stochastic field of material properties. Then the mathematical expression of the random field is substituted into the finite element model to formulate the corresponding random matrix. Finally, the statistical moment of the dynamic response is calculated by the point estimation method (PEM). The accuracy and efficiency of the dynamic response obtained from the KLE-PEM are demonstrated by the example of a moving load passing through a simply supported Euler-Bernoulli beam, in which the material properties (including elastic modulus and density) are considered as random fields. The results from the KLE-PEM are compared with those from the Monte Carlo simulation. The results demonstrate that the proposed method of KLE-PEM has high accuracy and efficiency. By using the proposed SFEM, the random vertical deflection of a high-speed railway (HSR) bridge is analyzed by considering the random fields of material properties under the moving load of a train.

• Structural Engineering and Mechanics
• /
• 제15권4호
• /
• pp.381-394
• /
• 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.

• Computers and Concrete
• /
• 제24권6호
• /
• pp.561-570
• /
• 2019

Understanding the realistic behavior of concrete up to failure under different loading conditions within the framework of damage mechanics and plasticity would lead to an enhanced design of concrete structures. In the present investigation, QR (Quick Response) code based random speckle pattern is used as a non-contact sensor, which is an innovative approach in the field of digital image correlation (DIC). A four-point bending test was performed on RC beams of size 1800 mm × 150 mm × 200 mm. Image processing was done using an open source Ncorr algorithm for the results obtained using random speckle pattern and QR code based random speckle pattern. Load-deflection curves of RC beams were plotted for the results obtained using both contact and non-contact (DIC) sensors, and further, Moment (M)-Curvature (κ) relationship of RC beams was developed. The loading curves obtained were used as input data for material model parameters in finite element analysis. In finite element method (FEM) based software, concrete damage plasticity (CDP) constitutive model is used to predict the realistic nonlinear quasi-static flexural behavior of RC beams for monotonic loading condition. The results obtained using QR code based DIC are observed to be on par with conventional results and FEM results.

• 한국해안해양공학회지
• /
• 제16권1호
• /
• pp.47-55
• /
• 2004

GUI를 이용하여 연안해역에서 항만개발, 방조제 건설, 준설 등의 해상 공사 시 발생하는 부유사(SS)의 이동 및 확산과정을 편리하게 예측할 수 있는 모의시스템(KUSSMOS)을 개발하였다. 모의시스템은 2차원 유한요소모형을 사용하여 해수유동을 모의하고, 입자추적모형을 사용하여 부유사 이송-확산을 모의한다. 군산해역 준설공사에 대해 수립된 시스템을 적용한 결과, 유속과 부유사 농도가 비교적 관측치와 일치하는 양호한 계산결과를 보였다.

• Geomechanics and Engineering
• /
• 제23권1호
• /
• pp.15-30
• /
• 2020

The probabilistic bearing capacity of a strip footing placed on the edge of a purely cohesive reinforced soil slope is computed by combining lower bound finite element limit analysis technique with random field method and Monte Carlo simulation technique. To simulate actual field condition, anisotropic random field model of undrained soil shear strength is generated by using the Cholesky-Decomposition method. With the inclusion of a single layer of reinforcement, dimensionless bearing capacity factor, N always increases in both deterministic and probabilistic analysis. As the coefficient of variation of the undrained soil shear strength increases, the mean N value in both unreinforced and reinforced slopes reduces for particular values of correlation length in horizontal and vertical directions. For smaller correlation lengths, the mean N value of unreinforced and reinforced slopes is always lower than the deterministic solutions. However, with the increment in the correlation lengths, this difference reduces and at a higher correlation length, both the deterministic and probabilistic mean values become almost equal. Providing reinforcement under footing subjected to eccentric load is found to be an efficient solution. However, both the deterministic and probabilistic bearing capacity for unreinforced and reinforced slopes reduces with the consideration of loading eccentricity.

• 한국해양환경ㆍ에너지학회지
• /
• 제12권3호
• /
• pp.124-132
• /
• 2009

하수의 해양방류시스템의 형식과 방류위치 결정을 위해 해수유동모의, 근해역 희석률 모의 그리고 원해역 확산모의가 수행되었다. 방류 후보지점 주변의 조위와 조류는 관측조위 및 조류를 잘 재현하는 2차원 유한요소모형에 의해 수행되었으며, 계산된 조위 및 조류 모의결과에 기초하여 방류 후보지점이 결정되었다. 방류시스템으로는 단일확산관과 다공확산관이 고려되었다. 단일확산관과 다공확산관을 통한 하수 방류의 근역 확산이 CORMIX모형에 의해 검토되었으며, 원역 확산이 2차원 Random-walk 확산모형에 의해 실시되었다. 모의결과로부터 수심, 조류, 방류위치, 방류속도, 확산관 길이 등이 확산범위와 희석률에 미치는 영향이 다각도로 검토되었다.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1996년도 봄 학술발표회 논문집
• /
• pp.173-181
• /
• 1996

In this study, a stochastic finite element model is proposed with a view to consider the uncertainty of physical properties of rock mass in the analysis of structural behavior on underground caverns. Here, the Latin Hypercube Sampling technique, in which can makeup weak points of the Monte Carlo Simulation, is applied for the analysis of underground cavern. The validity of the newly developed computer program has been confirmed in terms of verification examples. And, the applicability of the program to the field has been tested in terms of the analysis of the underground oil storage cavern in korea.

• Structural Engineering and Mechanics
• /
• 제27권2호
• /
• pp.199-222
• /
• 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.