• 한국지반공학회논문집
• /
• 제27권10호
• /
• pp.93-104
• /
• 2011

본 연구에서는 댐이나 보와 같은 수리구조물이 설치된 포화 기초지반에서의 구속흐름(confined flow)에 대하여 확률론적 침투해석을 수행하였다. 침투해석은 유한요소법을 이용하였으며 투수계수의 수평방향과 연직방향의 공간적 상관성이 상이한 비등방성을 고려하였다. 지정된 입력 확률분포함수와 자기상관함수(autocorrelation function)를 따르는 2차원의 랜덤필드를 생성하기 위하여 Karhunen-Lo$\grave{e}$ve 전개법을 사용하였으며 생성된 랜덤필드를 이용하여 확률론적 응답을 얻기 위해 Monte Carlo 시뮬레이션을 수행하였다. 이로부터 투수계수의 불확실성과 공간적 변동성이 수리구조물과 기초의 침투로 인한 안정성과 관련된 기초를 통한 유량, 구조물 하부에 작용하는 양압력, 하류 유출면에서의 유출동수경사에 미치는 영향을 연구하였다. 해석결과로부터 투수계수의 확률분포와 자기상관 구조를 만족하는 랜덤필드로 고려하여 공간적 변동을 고려하는 방법은 결정론적 해석이나 투수계수를 하나의 랜덤변수로 고려하는 경우에 나타나지 않는 다양한 지반의 침투거동을 효과적으로 고려할 수 있음을 보여준다.

• 전산구조공학
• /
• 제4권2호
• /
• pp.111-117
• /
• 1991

구조 공학에서의 고유치 문제는 좌굴해석, 진동해석 등 여러분야에 응용되고 있다. 일반적으로 구조물의 좌굴강도 해석에 사용되는 대부분의 변수들은 불확실성을 내포하고 있으므로 확률론적 해석을 수행해야 하지만, 구조물의 좌굴 신뢰성 해석을 위한 극한상태 방정식은 확률변수의 함수로 명확히 표현되지 않으므로 확률 유한 요소법의 사용이 필요하다. 따라서 본 논문에서는 직접미분법에 의해 정식화된 확률 유한요소법을 사용하여 고유치 문제의 신뢰성 해석방법을 정식화 하고, 이를 바탕으로 좌굴 신뢰성 해석을 수행하였으며, 결과의 타당성을 검증하기 위하여 Crude Monte Carlo Method 및 이 방법의 단점을 대폭 보완한 Importance Sampling Method를 사용하였다. 본 논문에 의해 좌굴 신뢰성 해석 방법이 정립됨으로서 신뢰성에 기초한 최적 설계를 수행하는 경우, 시스템 파괴확률로서 소성 파괴확률과 더불어 좌굴 파괴확률의 고려가 가능해졌다.

• Structural Engineering and Mechanics
• /
• 제31권5호
• /
• pp.481-506
• /
• 2009

The present study is concerned with the stochastic linear free vibration study of laminated composite plate embedded with piezoelectric layers with random material properties. The system equations are derived using higher order shear deformation theory. The lamina material properties of the laminate are modeled as basic random variables for accurate prediction of the system behavior. A $C^0$ finite element is used for spatial descretization of the laminate. First order Taylor series based mean centered perturbation technique in conjunction with finite element method is outlined for the problem. The outlined probabilistic approach is used to obtain typical numerical results, i.e., the mean and standard deviation of natural frequency. Different combinations of simply supported, clamped and free boundary conditions are considered. The effect of side to thickness ratio, aspect ratio, lamination scheme on scattering of natural frequency is studied. The results are compared with those available in literature and an independent Monte Carlo simulation.

• Smart Structures and Systems
• /
• 제15권3호
• /
• pp.751-767
• /
• 2015

A new procedure is proposed for assessing probabilistic condition of structures considering effect of measured data uncertainty. In this procedure, multiple Finite Element (FE) models are identified by using weighting vectors that represent the uncertainty conditions of measured data. The distribution of structural parameters is analysed using a Principal Component Analysis (PCA) in relation to uncertainty conditions, and the identified models are classified into groups according to their similarity by using a K-means method. The condition of a structure is then assessed probabilistically using FE models in the classified groups, each of which represents specific uncertainty condition of measured data. Yeondae bridge, a steel-box girder expressway bridge in Korea, is used as an illustrative example. Probabilistic condition of the bridge is evaluated by the distribution of load rating factors obtained using multiple FE models. The numerical example shows that the proposed method can quantify uncertainty of measured data and subsequently evaluate efficiently the probabilistic condition of bridges.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1991년도 가을 학술발표회 논문집
• /
• pp.57-62
• /
• 1991

For the purpose of developing the method for efficiently calculating the design sensitivity and the reliability for the complicated structure such as ship structure, the probabilistic finite element method is introduced to formulate the deterministic design sensitivity analysis method and incorporated with the second moment reliability methods such as MVFOSM, AFOSM and SORM. Also, the probabilistic design sensitivity analysis needed in the reliability-based design is performed. The reliability analysis is carried out for the initial yielding failure, in which the derivative derived in the deterministic desin sensitivity is used. The present PFEM-based reliability method shows good agreement with Monte Carlo method in terms with the variance of response and the associated probability of failure even at the first or first few iteration steps. The probabilistic design sensitivity analysis evaluates explicitly the contribution of each random variable to probability of failure. Further, the reliability index variation can be easily predicted by the variation of the mean and the variance of the random variables.

• 대한조선학회논문집
• /
• 제57권2호
• /
• pp.80-87
• /
• 2020

As the Arctic sea ice decreases due to various reasons such as global warming, the demand for ships and offshore structures operating in the Arctic region is steadily increasing. In the case of sea ice, the anisotropy is caused by the uncertainty inside the material. For most of the research, nevertheless, estimating the ice load has been treated deterministically. With regard to this, in this paper, a four-point bending strength analysis of an ice specimen was attempted using a stochastic finite element method. First, spatial distribution of the material properties used in the yield criterion was assumed to be a multivariate Gaussian random field. After that, a direct method, which is a sort of stochastic finite element method, and a sensitivity method using the sensitivity of response for random variables were proposed for calculating the probabilistic distribution of ice specimen strength. A parametric study was conducted with different mean vectors and correlation lengths for each material property used in the above procedure. The calculation time was about ten seconds for the direct method and about three minutes for the sensitivity methods. As the cohesion and correlation length increased, the mean value of the critical load and the standard deviation increased. On the contrary, they decreased as the friction angle increased. Also, in all cases, the direct and sensitivity methods yielded very similar results.

• Earthquakes and Structures
• /
• 제4권5호
• /
• pp.527-555
• /
• 2013

This paper proposes probabilistic models for estimating the seismic demands on reinforced concrete (RC) bridges with base isolation. The models consider the shear and deformation demands on the bridge columns and the deformation demand on the isolation devices. An experimental design is used to generate a population of bridges based on the AASHTO LRFD Bridge Design Specifications (AASHTO 2007) and the Caltrans' Seismic Design Criteria (Caltrans 1999). Ground motion records are used for time history analysis of each bridge to develop probabilistic models that are practical and are able to account for the uncertainties and biases in the current, common deterministic model. As application of the developed probabilistic models, a simple method is provided to determine the fragility of bridges. This work facilitates the reliability-based design for this type of bridges and contributes to the transition from limit state design to performance-based design.

• Structural Engineering and Mechanics
• /
• 제85권3호
• /
• pp.369-379
• /
• 2023

Reliability-Based Design Optimization (RBDO) is an appropriate framework for obtaining optimal designs by taking uncertainties into account. Large-scale problems with implicit limit state functions and problems with discrete design variables are two significant challenges to traditional RBDO methods. To overcome these challenges, this paper proposes a hybrid method to perform RBDO of structures that links Firefly Algorithm (FA) as an optimization tool to advanced (finite element) reliability methods. Furthermore, the Genetic Algorithm (GA) and the FA are compared based on the design cost (objective function) they achieve. In the proposed method, Weighted Simulation Method (WSM) is utilized to assess reliability constraints in the RBDO problems with explicit limit state functions. WSM is selected to reduce computational costs. To performing RBDO of structures with finite element modeling and implicit limit state functions, a First-Order Reliability Method (FORM) based on the Direct Differentiation Method (DDM) is utilized. Four numerical examples are considered to assess the effectiveness of the proposed method. The findings illustrate that the proposed RBDO method is applicable and efficient for RBDO problems with discrete and continuous design variables and finite element modeling.

• Steel and Composite Structures
• /
• 제19권1호
• /
• pp.191-208
• /
• 2015

The sensitivity-based finite element model updating method has received increasing attention in damage detection of structures based on measured modal parameters. Finding an optimization technique with high efficiency and fast convergence is one of the key issues for model updating-based damage detection. A new simple and computationally efficient optimization algorithm is proposed and applied to damage detection by using finite element model updating. The proposed method combines the Gauss-Newton method with region truncation of each iterative step, in which not only the constraints are introduced instead of penalty functions, but also the searching steps are restricted in a controlled region. The developed algorithm is illustrated by a numerically simulated 25-bar truss structure, and the results have been compared and verified with those obtained from the trust region method. In order to investigate the reliability of the proposed method in damage detection of structures, the influence of the uncertainties coming from measured modal parameters on the statistical characteristics of detection result is investigated by Monte-Carlo simulation, and the probability of damage detection is estimated using the probabilistic method.

• Smart Structures and Systems
• /
• 제32권3호
• /
• pp.167-177
• /
• 2023

A probabilistic micromechanical framework is proposed to quantify numerically the self-healing capabilities of polymers containing microcapsules. A two-step self-healing process is designed in this study: A probabilistic micromechanical framework based on the ensemble volume-averaging method is derived for the polymers, and a hitting probability model combined with a crack nucleation model is then utilized for encountering microcapsules and microcracks. Using this framework, a series of parametric investigations are performed to examine the influence of various model parameters (e.g., the volume fraction of microcapsules, microcapsule radius, radius ratio of microcracks to microcapsules, microcrack aspect ratio, and scale parameter) on the self-healing capabilities of the polymers. The proposed framework is also implemented into a finite element code to solve the self-healing behavior of tapered double cantilever beam specimens.