scholarly journals Error control in FORM reliability analysis

2012 ◽  
Author(s):  
Laurent Gallimard
Keyword(s):  
Finite Element ◽  
Error Control ◽  
Sampling Technique ◽  
Error Estimator ◽  
The Finite Element Method ◽  
Element Mesh ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
Importance Sampling Technique

This paper deals with the failure probability error induced by the coupling between the first-order reliability method (FORM) and the Finite Element Method (FEM). A FEM error estimator based on the concept of error in constitutive relation associated with goal-oriented error estimation is proposed. Furthermore an importance sampling technique is used to compute the error due to the FORM approximation. Both these errors are used to choose a finite element mesh adapted to the problem.

scholarly journals Reliability Analysis of Reinforced Concrete Frame by Finite Element Method with Implicit Limit State Functions

Buildings ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 119 ◽  
Author(s):  
Marin Grubišić ◽  
Jelena Ivošević ◽  
Ante Grubišić
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reinforced Concrete ◽  
Reliability Analysis ◽  
Numerical Models ◽  
Limit State ◽  
First Order Reliability Method ◽  
First Order ◽  
Knowledge Based ◽  
Reliability Method

Since the prediction of the seismic response of structures is highly uncertain, the need for the probabilistic approach is clear, especially for the estimation of critical seismic response parameters. Considering the uncertainties present in the material and geometric form of reinforced concrete (RC) structures, reliability analyses using the Finite Element Method (FEM) were performed in the context of Performance-Based Earthquake Engineering (PBEE). This study presented and compared the possibilities of nonlinear modelling of the reinforced concrete (RC) planar frame and its reliability analysis using different numerical methods, Mean-Value First-Order Second-Moment (MVFOSM), First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM) and Monte Carlo simulation (MCS). The calibrated numerical models used were based on the previous experimental test of a planar RC frame subjected to cyclic horizontal load. Numerical models were upgraded by random variable (RV) parameters for reliability analysis purposes and, using implicit limit state function (LSF), pushover analyses were performed by controlling the horizontal inter-storey drift ratio (IDR). Reliability results were found to be sensitive to the reliability analysis method. The results of reliability analysis reveal that, in a nonlinear region, after exceeding the yield strength of the longitudinal reinforcement, the cross-sectional geometry parameters were of greater importance compared to the parameters of the material characteristics. The results also show that epistemic (knowledge-based) uncertainties significantly affected dispersion and on the median estimate parameter response. The MCS sampling method is recommended, but the First-Order Reliability Method (FORM) applied on a response model can be used with good accuracy. Reliability analysis using the FEM proved to be suitable for the direct implementation of geometric and material nonlinearities to cover epistemic (knowledge-based) uncertainties.

An accuracy analysis method for first-order reliability method

2018 ◽  
Vol 233 (12) ◽  
pp. 4319-4327 ◽  
Author(s):  
Zhenzhong Chen ◽  
Zihao Wu ◽  
Xiaoke Li ◽  
Ge Chen ◽  
Guangfeng Chen ◽  
...  
Keyword(s):  
Structural Reliability ◽  
Nonlinear Problems ◽  
Accuracy Analysis ◽  
Analysis Method ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Level ◽  
Reliability Method ◽  
Value Range ◽  
Crashworthiness Design

The first-order reliability method is widely used for structural reliability analysis; however, its accuracy would become worse for nonlinear problems. This paper proposes the accuracy analysis method of the first-order reliability method, which considers the worst cases when using the first-order reliability method and gives the possible value range of the probability of safety. The accuracy analysis method can evaluate the reliability level of the first-order reliability method when the failure surfaces are nonlinear. The calculation formula for the possible value range of the probability of safety is proposed, and its trend as the dimensions and reliability rise is also discussed in this paper. A numerical example and a honeycomb crashworthiness design are presented to validate the accuracy of the first-order reliability method, and the results show that they are located within the possible value range proposed in this paper.

The Qualification of Safety Critical Structures by Finite Element Analytical Methods

1996 ◽  
Vol 210 (2) ◽  
pp. 203-207 ◽  
Author(s):  
A J Morris
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Control ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Method Error ◽  
Safety Critical ◽  
Critical Situation ◽  
Error Treatment

The paper introduces the concept of certifying or qualifying structures in a safety critical situation using the finite element method. Error control and error treatment methods for this purpose are discussed together with the associated role of testing. The underlying methodology follows the principles laid down in the SAFESA (SAFE Structural Analysis) method which is described in outline.

Sensitivity of Vessel Responses to Environmental Contours of Extreme Sea States

2015 ◽  
Author(s):  
Curtis Armstrong ◽  
Christopher Chin ◽  
Irene Penesis ◽  
Yuriy Drobyshevski
Keyword(s):  
Case Studies ◽  
Return Period ◽  
Significant Wave Height ◽  
Peak Period ◽  
First Order Reliability Method ◽  
First Order ◽  
Long Wave ◽  
Contour Lines ◽  
Reliability Method ◽  
Extreme Responses

A comparative study of two methods for the generation of the environmental contours is presented investigating the sensitivity of the predicted extreme vessel responses to the type of the contour lines. Two approaches for the generation of environmental contours of the significant wave height and peak period are compared: the Inverse First Order Reliability Method (IFORM) and Constant Probability Density (CPD) approach. Case studies include several global responses of a ship-shaped weather-vaning vessel and a semisubmersible platform. The case studies reveal that the differences between the IFORM and CPD contours are more pronounced in the range of long wave periods. Vessel responses which are less sensitive to long wave periods exhibit less difference (less than 1.0%) in their maximum values between the two types of contours. In contrast, responses which are sensitive to long wave periods show significantly larger differences of up to 7.0%. Uncertainties also exist in the predicted extreme responses where the environmental contour and the response isoline behave tangentially. Differences between the extreme responses produced by the two contours generally decrease with an increase in return period; however exceptions exist due to the tangential behaviour. It is advised that these sensitivities should be taken into consideration when the environmental contours are used in the design.

scholarly journals Safety parameters calibration in the structural design of sewer liners

2018 ◽  
Vol 45 ◽  
pp. 00096
Author(s):  
Arkadiusz Szot
Keyword(s):  
Analytical Solutions ◽  
Structural Design ◽  
Safety Index ◽  
Safety Factors ◽  
Load Bearing Capacity ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
Safety Parameters ◽  
Global Safety Factor

The article concerns aspects of safety in the process of designing continuous polymer liners used to strengthen and seal sewers and drains. The issues of safety coefficients, the variability of basic loadbearing parameters of liners and the problem of sensitivity of analytical solutions describing load-bearing capacity are discussed. The currently used magnitude of safety factors has been verified. The results of an examination on the safety index of liners for strengthening sewers has been presented in the paper. The necessity for the verification of current concepts of liner safety normalisation was herein addressed. A postulation to abandon the analogy of liners for newly constructed pipes was formulated. Calculations using the Hasofer-Lind safety index (First Order Reliability Method) were performed in some cases. A verification and evaluation of the global safety factor for sewer liners were herein carried out.

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