• Title/Summary/Keyword: Stochastic finite element method

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Natural frequency of laminated composite plate resting on an elastic foundation with uncertain system properties

  • Lal, Achchhe;Singh, B.N.;Kumar, Rakesh
    • Structural Engineering and Mechanics
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    • v.27 no.2
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    • pp.199-222
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    • 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.

Multi-scale Process-structural Analysis Considering the Stochastic Distribution of Material Properties in the Microstructure (미소 구조 물성의 확률적 분포를 고려한 하이브리드 성형 공정 연계 멀티스케일 구조 해석)

  • Jang, Kyung Suk;Kim, Tae Ri;Kim, Jeong Hwan;Yun, Gun Jin
    • Composites Research
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    • v.35 no.3
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    • pp.188-195
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    • 2022
  • This paper proposes a multiscale process-structural analysis methodology and applies to a battery housing part made of the short fiber-reinforced and fabric-reinforced composite layers. In particular, uncertainties of the material properties within the microscale representative volume element (RVE) were considered. The random spatial distribution of matrix properties in the microscale RVE was realized by the Karhunen-Loeve Expansion (KLE) method. Then, effective properties of the RVE reflecting on spatially varying matrix properties were obtained by the computational homogenization and mapped to a macroscale FE (finite element) model. Morever, through the hybrid process simulation, a FE (finite element) model mapping residual stress and fiber orientation from compression molding simulation is combined with one mapping fiber orientation from the draping process simulation. The proposed method is expected to rigorously evaluate the design requirements of the battery housing part and composite materials having various material configurations.

The Reliability Analysis for Homogeneous Slope Stability Using Stochastic Finite Element Method (확율유한요소법을 이용한 균질 사면의 신뢰성 해석)

  • 조래청;도덕현
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.38 no.5
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    • pp.125-139
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    • 1996
  • This study was performed to provide the design method for soil structure which guarantees proper safety with uncertainty of soil parameters. For this purpose, the effect of uncertainty of soil parameters for slope stability was analyzed by Bishop's simplified method and Monte Carlo simulation(MC). And reliability analysis program, RESFEM, was developed by combining elastic theory, MC, FEM, SFEM, and reliability, which can consider uncertainty of soil parameters. For factor of safety(FS) 1.0 and 1.2 by Bishop's simplified method, the probability of failure(Pf) was analyzed with varying coefficient of variation(c.o.v.) of soil parameters. The Pf increased as c.o.v. of soil parameters increased. This implies that FS is not the absolute index of slope safety, and even if FS is same, it has different Pf according to c.o.v. of soil parameters. The RESFEM was able to express the Pf at each element in slope quantitatively according to uncertainty of soil parameters. The variation of Pf with uncertainty of soil parameters was analyzed by RESFEM, and it was shown that the Pf increased as the c.o.v. of soil parameters increased.

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Probabilistic Behavior of In-plane Structure due to Multiple Correlated Uncertain Material Constants (상호 상관관계가 있는 다중 재료상수의 불확실성에 의한 평면구조의 확률론적 거동)

  • Noh Hyuk-Chun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.18 no.3
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    • pp.291-302
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    • 2005
  • Due to the importance of the parameter in structural response, the uncertain elastic modulus was located at the center of stochastic analysis, where the response variability caused by the uncertain system parameters is pursued. However when we analyze the so-called stochastic systems, as many parameters as possible must be included in the analysis if we want to obtain the response variability that can reach a true one, even in an approximate sense. In this paper, a formulation to determine the statistical behavior of in-plane structures due to multiple uncertain material parameters, i.e., elastic modulus and Poisson's ratio, is suggested. To this end, the polynomial expansion on the coefficients of constitutive matrix is employed. In constructing the modified auto-and cross-correlation functions, use is made of the general equation for n-th moment. For the computational purpose, the infinite series of stochastic sub-stiffness matrices is truncated preserving required accuracy. To demons4rate the validity of the proposed formulation, an exemplary example is analyzed and the results are compared with those obtained by means of classical Monte Carlo simulation, which is based on the local averaging scheme.

Crack identification based on Kriging surrogate model

  • Gao, Hai-Yang;Guo, Xing-Lin;Hu, Xiao-Fei
    • Structural Engineering and Mechanics
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    • v.41 no.1
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    • pp.25-41
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    • 2012
  • Kriging surrogate model provides explicit functions to represent the relationships between the inputs and outputs of a linear or nonlinear system, which is a desirable advantage for response estimation and parameter identification in structural design and model updating problem. However, little research has been carried out in applying Kriging model to crack identification. In this work, a scheme for crack identification based on a Kriging surrogate model is proposed. A modified rectangular grid (MRG) is introduced to move some sample points lying on the boundary into the internal design region, which will provide more useful information for the construction of Kriging model. The initial Kriging model is then constructed by samples of varying crack parameters (locations and sizes) and their corresponding modal frequencies. For identifying crack parameters, a robust stochastic particle swarm optimization (SPSO) algorithm is used to find the global optimal solution beyond the constructed Kriging model. To improve the accuracy of surrogate model, the finite element (FE) analysis soft ANSYS is employed to deal with the re-meshing problem during surrogate model updating. Specially, a simple method for crack number identification is proposed by finding the maximum probability factor. Finally, numerical simulations and experimental research are performed to assess the effectiveness and noise immunity of this proposed scheme.

Added effect of uncertain geometrical parameter on the response variability of Mindlin plate

  • Noh, Hyuk Chun;Choi, Chang Koon
    • Structural Engineering and Mechanics
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    • v.20 no.4
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    • pp.477-493
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    • 2005
  • In case of Mindlin plate, not only the bending deformation but also the shear behavior is allowed. While the bending and shear stiffness are given in the same order in terms of elastic modulus, they are in different order in case of plate thickness. Accordingly, bending and shear contributions have to be dealt with independently if the stochastic finite element analysis is performed on the Mindlin plate taking into account of the uncertain plate thickness. In this study, a formulation is suggested to give the response variability of Mindlin plate taking into account of the uncertainties in elastic modulus as well as in the thickness of plate, a geometrical parameter, and their correlation. The cubic function of thickness and the correlation between elastic modulus and thickness are incorporated into the formulation by means of the modified auto- and cross-correlation functions, which are constructed based on the general formula for n-th joint moment of random variables. To demonstrate the adequacy of the proposed formulation, a plate with various boundary conditions is taken as an example and the results are compared with those obtained by means of classical Monte Carlo simulation.

An improved approach for multiple support response spectral analysis of a long-span high-pier railway bridge

  • Li, Lanping;bu, Yizhi;Jia, Hongyu;Zheng, Shixiong;Zhang, Deyi;Bi, Kaiming
    • Earthquakes and Structures
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    • v.13 no.2
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    • pp.193-200
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    • 2017
  • To overcome the difficulty of performing multi-point response spectrum analysis for engineering structures under spatially varying ground motions (SVGM) using the general finite element code such as ANSYS, an approach has been developed by improving the modelling of the input ground motions in the spectral analysis. Based on the stochastic vibration analyses, the cross-power spectral density (c-PSD) matrix is adopted to model the stationary SVGM. The design response spectra are converted into the corresponding PSD model with appropriate coherency functions and apparent wave velocities. Then elements of c-PSD matrix are summarized in the row and the PSD matrix is transformed into the response spectra for a general spectral analysis. A long-span high-pier bridge under multiple support excitations is analyzed using the proposed approach considering the incoherence, wave-passage and site-response effects. The proposed approach is deemed to be an efficient numerical method that can be used for seismic analysis of large engineering structures under SVGM.

Stochastic Simulation of Groundwater Flow in Heterogeneous Formations: a Virtual Setting via Realizations of Random Field (불균질지층내 지하수 유동의 확률론적 분석 : 무작위성 분포 재생을 통한 가상적 수리시험)

  • Lee, Kang-Kun
    • Journal of the Korean Society of Groundwater Environment
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    • v.1 no.2
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    • pp.90-99
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    • 1994
  • Heterogeneous hydraulic conductivity in a flow domain is generated under the assumption that it is a random variable with a lognormal, spatially-correlated distribution. The hydraulic head and the conductivity in a groundwater flow system are represented as a stochastic process. The method of Monte Carlo Simulation (MCS) and the finite element method (FEM) are used to determine the statistics of the head and the logconductivity. The second moments of the head and the logconductivity indicate that the cross-covariance of the logconductivity with the head has characteristic distribution patterns depending on the properties of sources, boundary conditions, head gradients, and correlation scales. The negative cross-correlation outlines a weak-response zone where the flow system is weakly responding to a stress change in the flow domain. The stochastic approach has a potential to quantitatively delineate the zone of influence through computations of the cross-covariance distribution.

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Improved Response Surface Method Using Modified Selection Technique of Sampling Points (개선된 평가점 선정기법을 이용한 응답면기법)

  • 김상효;나성원;황학주
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1993.10a
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    • pp.248-255
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    • 1993
  • Recently, due to the increasing attention to the structural safety under uncertain environments, many researches on the structural reliability analysis have been peformed. Some useful methods are available to evaluate performance reliability of structures with explicit limit states. However, for large structures, in which structural behaviors can be analyzed with finite element models and the limit states are only expressed implicitly, Monte-Carlo simulation method has been mainly used. However, Monte-Carlo simulation method spends too much computational time on repetitive structural analysis. Many alternative methods are suggested to reduce the computational work required in Monte-Carlo simulation. Response surface method is widely used to improve the efficiency of structural reliability analysis. Response surface method is based on the concept of approximating simple polynomial function of basic random variables for the limit state which is not easily expressed in explicit forms of design random variables. The response surface method has simple algorithm. However, the accuracy of results highly depends on how properly the stochastic characteristics of the original limit state has been represented by approximated function, In this study, an improved response surface method is proposed in which the sampling points for creating response surface are modified to represent the failure surface more adequately and the combined use of a linear response surface function and Rackwitz-Fiessler method has been employed. The method is found to be more effective and efficient than previous response surface methods. In addition more consistent convergence is achieved, Accuracy of the proposed method has been investigated through example.

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Numerical Research about Asymmetric Growth of Cancer, Angiogenesis and Hemodynamics (암의 비대칭적 성장, 혈관생성 및 혈류역학에 대한 수치적 연구)

  • Kim, Y.S.;Shim, E.B.
    • Proceedings of the KSME Conference
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    • 2007.05b
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    • pp.2951-2954
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    • 2007
  • Tumor hemodynamics in vascular state is numerically simulated using pressure node solution. The tumor angiogenesis pattern in our previous study is used for the geometry of vessel networks. For tumor angiogenesis, the equation that governed angiogenesis comprises a tumor angiogenesis factor (TAF) conservation equation in time and space, which is solved numerically using the Galerkin finite element method. A stochastic process model is used to simulate vessel formation and vessel. In this study, we use a two-dimensional model with planar vessel structure. Hemodynamics in vessel is assumed as incompressible steady flow with Newtonian fluid properties. In parent vessel, arterial pressure is assigned as a boundary condition whereas a constant terminal pressure is specified in tumor inside. Kirchhoff's law is applied to each pressure node to simulate the pressure distribution in vessel networks. Transient pressure distribution along with angiogenesis pattern is presented to investigate the effect of tumor growth in tumor hemodynamics.

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