Reliability-Based Design Using Simulation for Aluminum Elements

2007 ◽  
Author(s):  
Malek Brahimi ◽  
Sidi Berri ◽  
Joel Lopez
Keyword(s):  
Current Practice ◽  
Limit State ◽  
Good Method ◽  
Probability Of Failure ◽  
State Function ◽  
Limit State Function ◽  
Direct Simulation ◽  
Safety Factors ◽  
Normal Distributions ◽  
Reliability Based Design

Studies of reliability in current practice indicate that reliability based on conventional methods requires a nonlinear transformation to a set of normal distributions, which effectively changes the shape of limit state function. In this paper, the general formulation of safety for aluminum elements and the associated methods of analysis are reviewed. Direct simulation is used to find the probability of failure. It is concluded that direct simulations of safety of aluminum elements of Pr (probability of failure) by failure counting is a good method to achieve acceptable safety factors.

Fatigue Design Margin Evaluation for Carbon and Low-Alloy Steels by Reliability-Based Load and Resistance Factor Method

2011 ◽  
Author(s):  
Masahiro Takanashi ◽  
Makoto Higuchi ◽  
Junki Maeda ◽  
Shinsuke Sakai
Keyword(s):  
Applied Stress ◽  
Limit State ◽  
State Function ◽  
Low Alloy Steels ◽  
Limit State Function ◽  
Safety Factors ◽  
Fatigue Data ◽  
Alloy Steels ◽  
Partial Safety Factors ◽  
Two Parameters

This paper discusses the margins of the design fatigue curve in the ASME Boiler and Pressure Vessel Codes Section III from a reliability analysis point of view. It is reported that these margins were developed so as to cover uncertainties of fatigue data scatter, size effect, and surface condition[1], but the reasons for them remain unclear. In order to investigate the physical implications of the design margin, a probabilistic approach is taken for the collected fatigue data of carbon and low-alloy steels. In this approach, these three parameters are treated as random variables, and an applied stress is also taken into consideration as a random variable. For the analysis, to begin with, a limit state function for fatigue is proposed. Next, reliability index contours of the design fatigue curves for carbon and low-alloy steels are obtained based on the proposed limit state function. The contours indicate that the margins 2 on stress and 20 on life do not provide equal reliability. The margin 20 on life is more conservative and the margin became a minimum near intersections of the design curves with margins 2 on stress and 20 on life. For practical applications, the partial safety factors (PSF) for the target reliability are computed for all materials and several levels of coefficients of variation (COV) of the applied stress. A sensitivity analysis of the PSFs clarifies that only two parameters, the strength (or the life) and the applied stress, are predominant. Thus, the partial safety factors for these two parameters are proposed in a tabular form.

Reliability Analysis by Mean-Value Second-Order Expansion

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Deshun Liu ◽  
Yehui Peng
Keyword(s):  
Saddle Point ◽  
Limit State ◽  
Quadratic Function ◽  
Mean Value ◽  
Second Order ◽  
State Function ◽  
Limit State Function ◽  
Chi Square ◽  
Normal Distributions ◽  
Independent Variables

In this paper, two second-order methods are proposed for reliability analysis. First, general random variables are transformed to standard normal random variables. Then, the limit-state function is additively decomposed into one-dimensional functions, which are then expanded at the mean-value point to second-order terms. The approximated limit-state function becomes the sum of independent variables following noncentral chi-square distributions or normal distributions. The first method computes the probability of failure by the saddle-point approximation. If a saddle-point does not exist, the second method is then used. The second method approximates the limit-state function by a quadratic function with independent variables following normal distributions with the same variances. This treatment leads to a quadratic function that follows a noncentral chi-square distribution. These methods generally produce more accurate reliability approximations than the first-order reliability method (FORM) with 2n + 1 function evaluations, where n is the dimension of the problem. The effectiveness of the proposed methods is demonstrated with three examples, and the proposed methods are compared with the first- and second-order reliability methods (SROMs).

Application of Partial Safety Factors for Fitness-for-Service Assessment of Pressure Equipment With Local Metal Loss

2017 ◽  
Author(s):  
Takuyo Kaida ◽  
Shinsuke Sakai
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Probability Of Failure ◽  
Pressure Vessels ◽  
Metal Loss ◽  
State Function ◽  
Safety Factors ◽  
Loss Assessment ◽  
Reliability Method ◽  
Partial Safety Factors

Reliability analysis considering data uncertainties can be used to make a rational decision as to whether to run or repair a pressure equipment that contains a flaw. Especially, partial safety factors (PSF) method is one of the most useful reliability analysis procedure and considered in a Level 3 assessment of a crack-like flaw in API 579-1/ASME FFS-1:2016. High Pressure Institute of Japan (HPI) formed a committee to develop a HPI FFS standard including PSF method. To apply the PSF method effectively, the safety factors for each dominant variable should be prepared before the assessment. In this paper, PSF for metal loss assessment of typical pressure vessels are derived based on first order reliability method (FORM). First, a limit state function and stochastic properties of random variables are defined. The properties of a typical pressure vessel are based on actual data of towers in petroleum and petrochemical plants. Second, probability of failure in several cases are studied by Hasofer-Lind method. Finally, PSF’s in each target probability of failure are proposed. HPI published a new technical report, HPIS Z 109 TR:2016, that provide metal loss assessment procedures based on FORM and the proposed PSF’s described in this paper.

scholarly journals Dimensioning of silicone adhesive joints: Eurocode-compliant, mesh-independent approach using the FEM

2020 ◽  
Vol 5 (3) ◽  
pp. 349-369 ◽  
Author(s):  
Micheal Drass ◽  
Michael A. Kraus
Keyword(s):  
Finite Element ◽  
Safety Factor ◽  
Limit State ◽  
Adhesive Joints ◽  
State Function ◽  
Limit State Function ◽  
Element Calculation ◽  
Safety Factors ◽  
Silicone Adhesive ◽  
Level I

Abstract This paper deals with the application of the semi-probabilistic design concept (level I, DIN EN 1990) to structural silicone adhesives in order to calibrate partial material safety factors for a stretch-based limit state equation. Based on the current legal situation for the application of structural sealants in façades, a new Eurocode-compliant design concept is introduced and compared to existing design codes (ETAG 002). This is followed by some background information on semi-probabilistic reliability modeling and the general framework of the Eurocode for the derivation of partial material safety factors at Level I. Within this paper, a specific partial material safety factor is derived for DOWSIL 993 silicone on the basis of experimental data. The data were then further evaluated under a stretch-based limit state function to obtain a partial material safety factor for that specific limit state function. This safety factor is then extended to the application in finite element calculation programs in such a way that it is possible for the first time to perform mesh-independent static calculations of silicone adhesive joints. This procedure thus allows for great optimization of structural sealant design with potentially high economical as well as sustainability benefits. An example for the static verification of a bonded façade construction by means of finite element calculation shows (i) the application of EC 0 to silicone adhesives and (ii) the transfer of the EC 0 method to the finite element method with the result that mesh-independent ultimate loads can be determined.

An Improved Risk Based Design Method Based on a Novel Upper Bound Formulation

2011 ◽  
Author(s):  
Hami Golbayani ◽  
Kazem Kazerounian
Keyword(s):  
Upper Bound ◽  
Design Method ◽  
Limit State ◽  
Probability Of Failure ◽  
Normal Space ◽  
Continuous Limit ◽  
State Function ◽  
Limit State Function ◽  
Engineering Systems ◽  
Reliability Method

In this work, a novel framework is proposed for the risk based design optimization of engineering systems by minimizing the demand on the system components’ accuracy (which directly relates to their cost). The fundamental development of this work is an analytical upper bound for calculating the probability of failure. This is in contrast with First Order Reliability Method (FORM), where a lower bound is used in calculating the probability of failure. FORM is one of the most popular methods for reliability analysis of engineering systems. In this paper, we show that FORM results in an optimistic measure of risk, hence potentially catastrophic in engineering design. A more accurate measure of failure is proposed by utilizing an analytical upper bound for the distribution of reliability index (the length of the most probable point vector to origin). This distribution is a function of the eigenvalues of the linearized limit state function in the normal space which results in a better understanding of failure phenomenon. The proposed formulation is computationally efficient and straightforward to solve, since it only involves finding eigenvalues in each iteration. This algorithm is applicable to any linearizable continuous limit state function with any type of distribution for the design variables. The method is applied to two examples and its accuracy is compared with the Monte Carlo simulation and FORM, demonstrating its effectiveness and value.

Second-Order Reliability Method Based on Edgeworth Expansion With Application to Reliability-Based Design Optimization

2019 ◽  
Author(s):  
Rami Mansour ◽  
Mårten Olsson
Keyword(s):  
Design Optimization ◽  
Limit State ◽  
Probability Of Failure ◽  
Second Order ◽  
State Function ◽  
Reliability Based Design Optimization ◽  
First Order ◽  
Reliability Based Design ◽  
Statistical Measures ◽  
Reliability Method

Abstract In the Second-Order Reliability Method, the limit-state function is approximated by a hyper-parabola in standard normal and uncorrelated space. However, there is no exact closed form expression for the probability of failure based on a hyper-parabolic limit-state function and the existing approximate formulas in the literature have been shown to have major drawbacks. Furthermore, in applications such as Reliability-based Design Optimization, analytical expressions, not only for the probability of failure but also for probabilistic sensitivities, are highly desirable for efficiency reasons. In this paper, a novel Second-Order Reliability Method is presented. The proposed expression is a function of three statistical measures: the Cornell Reliability Index, the skewness and the Kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the Most Probable Point. Furthermore, analytical sensitivities with respect to mean values of random variables and deterministic variables are presented. The sensitivities can be seen as the product of the sensitivities computed using the First-Order Reliability Method and a correction factor. The proposed expressions are studied and their applicability to Reliability-based Design Optimization is demonstrated.

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.

Development of Ultimate Strength Evaluation Method for Piping Subjected to Seismic Loads

2013 ◽  
Author(s):  
Hideo Machida ◽  
Hiromasa Chitose ◽  
Tatsuhiro Yamazaki
Keyword(s):  
Power Plants ◽  
Evaluation Method ◽  
Failure Modes ◽  
Limit State ◽  
Seismic Loading ◽  
Earthquake Resistance ◽  
State Function ◽  
Limit State Function ◽  
Input Acceleration ◽  
Resistance Tests

This paper reports the results of the study on the failure modes and limit loads of piping in nuclear power plants subjected to cyclic seismic loading. By investigating the past fracture tests and earthquake resistance tests, it became clear that dominant failure mode of piping was fatigue, and the effect of ratchet strain was negligible. Until now, the stress generated with the acceleration of an earthquake was classified into the primary stress. However, the relationship between the input acceleration and the seismic response displacement of the pipe observed from earthquake resistance tests is non-linear, and increasing rate of displacement is lower than that of input acceleration in elastic-plastic stress condition. Therefore, the seismic loading can be treated as displacement controlled loading. To evaluate the reliability-based critical acceleration, a limit state function was defined taking the variations in the fatigue strength or some parameters into consideration. By using the limit state function, the reliability was evaluated for the typical piping of boiling water reactor (BWR) plants subjected to cyclic seismic loading, and a partial safety factors were calculated. Based on these results, a fatigue curve corresponding to the target reliability was proposed.

A New Reliability Evaluation Algorithm Using Response Surface Methodology Combined With Space Mapping Technique

2006 ◽  
Author(s):  
Lixin Zhang ◽  
Zhijun Jian ◽  
Zhaohui Xu
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Limit State ◽  
Space Mapping ◽  
Mapping Technique ◽  
State Function ◽  
Limit State Function ◽  
New Approach ◽  
Successive Response ◽  
Evaluation Algorithm

A new method is proposed to tackle the huge computation cost involved in Successive Response Surface Methodology applied to the reliability analysis, in which Space Mapping technique is combined with Response Surface Methodology. While the new approach is performed, the limit state function is only fitted at the first iteration; at other iterations Space Mapping technique is employed to map the original limit state function into the new ones. Experimental design, corresponding model evaluations and response surface fitting of the limit state function are not done repetitively as what we do while SRSM is used, which leads to the great cutting down of computational efforts.

Sign in / Sign up

Export Citation Format

Share Document