scholarly journals An Energy-Based Limit State Function for Estimation of Structural Reliability in Shock Environments

2013 ◽  
Vol 20 (5) ◽  
pp. 933-950 ◽  
Author(s):  
Michael A. Guthrie
Keyword(s):  
Reliability Index ◽  
Structural Reliability ◽  
Limit State ◽  
Element Model ◽  
Monte Carlo Analysis ◽  
State Function ◽  
Limit State Function ◽  
Qualitative Comparison ◽  
Structural Capacity ◽  
Mass Spring

limit state function is developed for the estimation of structural reliability in shock environments. This limit state function uses peak modal strain energies to characterize environmental severity and modal strain energies at failure to characterize the structural capacity. The Hasofer-Lind reliability index is briefly reviewed and its computation for the energy-based limit state function is discussed. Applications to two degree of freedom mass-spring systems and to a simple finite element model are considered. For these examples, computation of the reliability index requires little effort beyond a modal analysis, but still accounts for relevant uncertainties in both the structure and environment. For both examples, the reliability index is observed to agree well with the results of Monte Carlo analysis. In situations where fast, qualitative comparison of several candidate designs is required, the reliability index based on the proposed limit state function provides an attractive metric which can be used to compare and control reliability.

LIMIT AND SHAKEDOWN ANALYSIS UNDER UNCERTAINTY

2014 ◽  
Vol 11 (03) ◽  
pp. 1343008 ◽  
Author(s):  
MANFRED STAAT
Keyword(s):  
Structural Reliability ◽  
High Reliability ◽  
Limit State ◽  
Mathematical Optimization ◽  
Element Model ◽  
General Purpose ◽  
State Function ◽  
Limit State Function ◽  
Shakedown Analysis ◽  
Definition Of

Structural reliability analysis is based on the concept of a limit state function separating failure from safe states of a structure. Upper and lower bound theorems of limit and shakedown analysis are used for a direct definition of the limit state function for failure by plastic collapse or by inadaptation. Shakedown describes an asymptotic and therefore time invariant structural behavior under time variant loading. The limit state function and its gradient are obtained from a mathematical optimization problem. The method is implemented into a general purpose finite element model (FEM) code. Combined with first-order methods/second-order methods (FORM/SORM) robust and precise analyses can be performed for structures with high reliability. This approach is particularly effective because the sensitivities which are needed by FORM/SORM are derived from the solution of the deterministic problem.

An Efficient Response Surface Method Using Givens Transformation for Structural Reliability Analysis

2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Mathematical Techniques ◽  
Input Variables ◽  
Improved Accuracy

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.

Advances of a FEM for the Failure Probability Evaluation of Masonry Vehicular Bridge Support Piers

2012 ◽  
Vol 538-541 ◽  
pp. 580-585
Author(s):  
Luis Horacio Martínez-Mártinez ◽  
Gustavo Mendoza-Chavez ◽  
David Joaquin Delgado-Hernandez ◽  
David De León Escobedo ◽  
Elia Mercedes Alonso Guzmán ◽  
...  
Keyword(s):  
Risk Analysis ◽  
Structural Engineering ◽  
Limit State ◽  
Element Model ◽  
Failure Criteria ◽  
Point Of View ◽  
Structural Safety ◽  
State Function ◽  
Limit State Function ◽  
Risk Magnitude

One of the responsibilities of a Civil Engineer is to make decisions regarding preservation of infrastructure; therefore, there have been established concepts such as risk and risk analysis. Risk analysis, is a methodology applied to determine and evaluate the risk magnitude. From the structural engineering point of view, it is required that any structure become secure, this means that the capacity to withstand external actions (strength) will be higher than these actions (loads). In order to determine the structural safety, it is required to define the failure of the structure that it is not strongly related with the collapse of the structure; the failure criteria needs to be fixed depending on the use of the building and the consequences associated with the interruption of services provided by the facility. The failure then, is calculated by means of a limit state function in where it is established the failure criteria; failure is reached when a specific condition (strength) is surpassed by the actions over the structure. The present work aims to propose a preliminary Finite Element Model (FEM) that represents a pier used as support for vehicular bridges. This FEM is required for the assessment of mechanical behavior of the structure that will be used for the determination of the limit state function needed for risk assessment. Most of the simulations with FEM presented in literature are very used for modeling of masonry walls, but it is not usual to model structures such as bridge piers.

scholarly journals Reliability Estimation for Highway Bridges

2020 ◽  
Author(s):  
Nafiseh Kiani
Keyword(s):  
Reliability Index ◽  
Structural Reliability ◽  
Limit State ◽  
Highway Bridges ◽  
Reliability Estimation ◽  
State Function ◽  
Limit States ◽  
Resistance Factors ◽  
Load And Resistance Factors ◽  
Reliability Methods

Structural reliability analysis is necessary to predict the uncertainties which may endanger the safety of structures during their lifetime. Structural uncertainties are associated with design, construction and operation stages. In design of structures, different limit states or failure functions are suggested to be considered by design specifications. Load and resistance factors are two essential parameters which have significant impact on evaluating the uncertainties. These load and resistance factors are commonly determined using structural reliability methods. The purpose of this study is to determine the reliability index for a typical highway bridge by considering the maximum moment generated by vehicle live loads on the bridge as a random variable. The limit state function was formulated and reliability index was determined using the First Order Reliability Methods (FORM) method.

A Structural Reliability Approach to Management of Defective Spiral Welding in a ‘Legacy’ Pipeline

2010 ◽  
Author(s):  
Michael Gardiner ◽  
Ross Michie ◽  
Gerardo Douce
Keyword(s):  
Structural Reliability ◽  
Buenos Aires ◽  
Limit State ◽  
State Function ◽  
Operating Pressure ◽  
Limit State Function ◽  
Line Pipe ◽  
Failure Frequency ◽  
Failure Point ◽  
Weld Root

Metrogas SA operates a natural gas distribution concession within the Greater Buenos Aires region of Argentina. In August 2007 a failure occurred on a section of the 22-bar system that dates from the early 1960s and, as such, was ‘inherited’ by Metrogas at privatization. The line pipe in this part of the system is spirally welded and at the failure point the spiral weld root was found to have been incomplete. Subsequent investigations showed that incomplete spiral welds were also present at other locations in the same section of the system. This paper describes some of the steps taken to investigate the incident of 2007 and to manage the threat from other defective spiral welds in the same pipeline section. We present a limit state model for through-wall failure of such features and show how this was used to help understand the incident. We also discuss modeling of uncertainties in parameters of the model and look at results from a probabilistic structural reliability implementation of the limit state function, which allowed the failure frequency of other defective spiral welds in this section to be predicted for various reductions of the operating pressure. Metrogas was then able to use these quantified reliability data to make a responsible, informed decision to keep the affected section in downrated service.

scholarly journals Hybrid Reliability Analysis for Spacecraft Docking Lock with Random and Interval Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Zhang ◽  
Jiwei Qiu ◽  
Pidong Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Simple Problem ◽  
State Function ◽  
Limit State Function ◽  
Interval Variables ◽  
Reliability Method ◽  
Hybrid Reliability

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis with hybrid variables, that is, random and interval variables. This method can significantly improve the computational efficiency for the abovementioned hybrid reliability analysis (HRA), while generally providing sufficient precision. In the proposed procedure, the hybrid problem is reduced to standard reliability problem with the polar coordinates, where an n-dimensional limit-state function is defined only in terms of two random variables. Firstly, the linear Taylor series is used to approximate the limit-state function around the design point. Subsequently, with the approximation of the n-dimensional limit-state function, the new bidimensional limit state is established by the polar coordinate transformation. And the probability density functions (PDFs) of the two variables can be obtained by the PDFs of random variables and bounds of interval variables. Then, the interval of failure probability is efficiently calculated by the integral method. At last, one simple problem with explicit expressions and one engineering application of spacecraft docking lock are employed to demonstrate the effectiveness of the proposed methods.

Study of Computation for Structural Reliability Index Based on Penalty Function Method

2014 ◽  
Vol 635-637 ◽  
pp. 443-446 ◽  
Author(s):  
Hai Tao Lu ◽  
Yu Ge Dong ◽  
Fang Ying Wu
Keyword(s):  
Unconstrained Optimization ◽  
Penalty Function ◽  
Reliability Index ◽  
Function Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Penalty Function Method ◽  
Design Point ◽  
Reliability Method

According to the geometric meaning of the structural reliability index, an unconstrained optimization model with structural reliability index and design point is obtained by exterior penalty function method. The Powell method, golden section method and extrapolation method are used to solve the unconstrained optimization problem. The proposed method not has to deal with the any derivative of the limited state function, and can been used to obtain structural reliability index and design point of the strong nonlinear limit state function, which first-order reliability method (FORM) may fail to converge. Three examples are given to compare penalty function method with the difference methods. The results show that the given method is simply, effective and precise enough.

scholarly journals A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

2020 ◽  
Vol 11 (1) ◽  
pp. 346
Author(s):  
Pidong Wang ◽  
Lechang Yang ◽  
Ning Zhao ◽  
Lefei Li ◽  
Dan Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Function ◽  
Strong Nonlinearity ◽  
Limit State Function ◽  
Practical Applications ◽  
Uncertain Variables ◽  
Practical Engineering

(1) Background: in practical applications, probabilistic and non-probabilistic information often simultaneously exit. For a complex system with a nonlinear limit-state function, the analysis and evaluation of the reliability are imperative yet challenging tasks. (2) Methods: an improved second-order method is proposed for reliability analysis in the presence of both random and interval variables, where a novel polar transformation is employed. This method enables a unified reliability analysis taking both random variables and bounded intervals into account, simplifying the calculation by transforming a high-dimension limit-state function into a bivariate state function. The obtained nonlinear probability density functions of two variables in the function inherit the statistic characteristics of interval and random variables. The proposed method does not require any strong assumptions and so it can be used in various practical engineering applications. (3) Results: the proposed method is validated via two numerical examples. A comparative study towards a contemporary algorithm in state-of-the-art literature is carried out to demonstrate the benefits of our method. (4) Conclusions: the proposed method outperforms existing methods both in efficiency and accuracy, especially for cases with strong nonlinearity.

Seismic Reliability Analysis of Complex Structure

2012 ◽  
Vol 446-449 ◽  
pp. 2321-2325
Author(s):  
Zhi Yong Zhang ◽  
Wen Bo Huang ◽  
Yue Fa Zhou ◽  
Tian Shu Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Complex Structure ◽  
State Function ◽  
Limit State Function ◽  
Seismic Reliability ◽  
Element Method

The seismic reliability analysis of complex structure is carried out based on the response surface method and finite element method. Firstly, the appropriate design points are selected based on the mean values and standard deviations of the basic random variables. Secondly, the finite element method is employed to obtain the values of the limit state function of the complex structure. Thirdly, with selected design points and the obtained values of the limit state function of the complex structure, a polynomial function is constructed to approximate the original implicit limit state function. Then, with the established explicit polynomial limit state function and available methods of structural reliability analysis, the seismic reliability of the complex structure is estimated. Numerical analyses show that the established method is simple to use for the evaluation of the reliability analysis of complex structure.

Influence Research of Correlation of Random Variables on Structural Reliability

2011 ◽  
Vol 243-249 ◽  
pp. 245-250
Author(s):  
Yan Feng Fang ◽  
Li Yan Chen ◽  
Hua Xi Gao
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Equation ◽  
Maximum Intensity ◽  
State Function ◽  
Sampling Techniques ◽  
Limit State Function

In this paper, the influence of correlation of variables on structural reliability is discussed. Using importance, condition and duality sampling techniques of Monte Carlo method, accepted accuracy can be obtained. For the limit state function, the correlation of random variables will influence structural reliability, and the influence can be described. For the case of positive correlation, reliability will increase as the the correlation coefficient raise. For the case of negative correlation, reliability will drop as the correlation coefficient raise. The level of influence depends on the slope of limit state equation in standardized coordinate. When k=1, the influence attains maximum intensity for both cases.

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