Stochastic Meshless Analysis of Elastic-Plastic Cracked Structures

2002 ◽  
Author(s):  
B. N. Rao ◽  
S. Rahman
Keyword(s):  
Finite Element ◽  
Reliability Analysis ◽  
Fracture Initiation ◽  
Crack Size ◽  
J Integral ◽  
Mesh Free ◽  
Reliability Method ◽  
Mesh Free Method ◽  
Cracked Structures ◽  
Probability Of Fracture

This paper presents a stochastic mesh-free method for probabilistic fracture-mechanics analysis of nonlinear cracked structures. The method involves enriched element-free Galerkin formulation for calculating the J-integral; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method (FORM) for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using a virtual crack extension technique. Numerical examples based on mode-I fracture problems have been presented to illustrate the proposed method. The results from sensitivity analysis indicate that the maximum difference between sensitivity of the J-integral calculated using the proposed method and reference solutions obtained by the finite-difference method is about six percent. The results from reliability analysis show that the probability of fracture initiation using the proposed sensitivity and meshless-based FORM are very accurate when compared with either the finite-element-based Monte Carlo simulation or finite-element-based FORM. Since all gradients are calculated analytically, the reliability analysis of cracks can be performed efficiently using meshless methods.

scholarly journals A Numerical Method for SolvingTwo-Dimensional Nonlinear Parabolic ProblemsBased on a Preconditioning Operator

2020 ◽  
Vol 25 (4) ◽  
pp. 531-545
Author(s):  
Amir Hossein Salehi Shayegan ◽  
Ali Zakeri ◽  
Seyed Mohammad Hosseini
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parabolic Problem ◽  
Time Variable ◽  
Two Dimensional ◽  
Helmholtz Operator ◽  
Mesh Free ◽  
Nonlinear Parabolic ◽  
Spline Finite Element ◽  
Mesh Free Method

This article considers a nonlinear system of elliptic problems, which is obtained by discretizing the time variable of a two-dimensional nonlinear parabolic problem. Since the system consists of ill-conditioned problems, therefore a stabilized, mesh-free method is proposed. The method is based on coupling the preconditioned Sobolev space gradient method and WEB-spline finite element method with Helmholtz operator as a preconditioner. The convergence and error analysis of the method are given. Finally, a numerical example is solved by this preconditioner to show the efficiency and accuracy of the proposed methods.

Failure Assessment Diagrams of Semi-Elliptical Surface Crack with Constraint Effect

2007 ◽  
Vol 353-358 ◽  
pp. 1952-1955
Author(s):  
Hyung Yil Lee ◽  
Jin Haeng Lee ◽  
Tae Hyung Kim
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Surface Crack ◽  
J Integral ◽  
Finite Element Analyses ◽  
Constraint Effect ◽  
Failure Assessment ◽  
T Stress ◽  
Cracked Structures ◽  
Constraint Effects

For accurate failure assessment, a second parameter like T-stress describing the constraint is needed in addition to the single parameter J-integral. In this work, selecting the structures of surface-cracked plate and pipe, we perform line-spring finite element modeling, and accompanying elastic-plastic finite element analyses. We then present a framework, which includes the constraint effects in the R6 FAD approach for failure assessment of cracked-structures.

On the Use of Surrogate Models in Reliability-Based Analysis of Dented Pipes

2016 ◽  
Author(s):  
Sherif Hassanien ◽  
Muntaseer Kainat ◽  
Samer Adeeb ◽  
Doug Langer
Keyword(s):  
Finite Element ◽  
Reliability Analysis ◽  
Random Systems ◽  
Probability Of Failure ◽  
Surrogate Models ◽  
Operating Conditions ◽  
Additional Stress ◽  
Internal Stresses ◽  
Stress Risers ◽  
Reliability Method

Pipeline dents lead to changes in the stress/strain state of the pipe body, making it more susceptible to integrity concerns. This susceptibility is especially prevalent in cases where additional stress risers such as crack and/or corrosion features interact with the dented region. While some guidance is available in codes, regulations, and industry best practices, there is substantial room for innovation and improvement to ensure pipeline safety. Existing explicit models are primarily based on experimental correlations and historical findings using simple parameters such as dent depth and location on the pipeline. Moreover, these models are subjected to a substantial uncertainty in both accuracy and precision. This paper presents a state-of-the-art methodology for analyzing dents and dents associated with stress risers through the use of finite element method (FEM) as a mechanical model and reliability analysis to address uncertainties associated with input variables. FEM is used to model the full geometry of dents and any interacting stress risers reported by inline inspection (ILI) to be incorporated into calculations of the internal stresses/strains within the feature. Theoretically, FEM and reliability analysis can be integrated through reliability-based stochastic finite element methodologies due to the absence of closed form mechanical models of dented pipes. However, these methodologies are computationally prohibitive and not suited/designed for frequent integrity analysis. This study aims at further advancing such integration by combining FEM with reliability science to account for pipe properties and measurement uncertainties in order to determine the probability of failure under different operating conditions using surrogate models. This provides the opportunity to more accurately assess the risk posed by ILI reported dent features. Herein, surrogate models refer to the response surface method (RSM) which is considered as a valuable tool for obtaining insight into the behavior of structural random systems at low computational costs. The proposed approach was applied focusing on a plain dent, a dent interacting with a corrosion feature, and a dent interacting with a crack feature. First Order Reliability Method (FORM) is used to evaluate the probability of failure/reliability using the resulting RSM non-linear limit states for each dent feature.

Probabilistic Fracture Mechanics Using Fractal Finite Element Method

2008 ◽  
Author(s):  
R. M. Reddy ◽  
B. N. Rao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Mixed Mode ◽  
Fracture Parameter ◽  
Shape Sensitivity ◽  
Probabilistic Fracture Mechanics ◽  
Reliability Method ◽  
Cracked Structures ◽  
Element Method

This paper presents probabilistic fracture-mechanics analysis of linear-elastic cracked structures subjected to mixed-mode (modes I and II) loading conditions using fractal finite element method (FFEM). The method involves FFEM for calculating fracture response characteristics; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using continuum shape sensitivity analysis. Numerical examples based on mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that the predicted failure probability based on the proposed formulation of the sensitivity of fracture parameter is accurate in comparison with the Monte Carlo simulation results. Since all gradients are calculated analytically, reliability analysis of cracks can be performed efficiently using FFEM.

Finite Element Reliability Analysis of Steel Containment Vessels with Corrosion Damage

2015 ◽  
Vol 10 (3) ◽  
pp. 527-534 ◽  
Author(s):  
Xiaolei Wang ◽  
◽  
Dagang Lu ◽  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Reliability Analysis ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Power Plants ◽  
Corrosion Damage ◽  
Element Analysis ◽  
Containment Vessel ◽  
Reliability Method

Containment vessels, which contain any radioactive materials that would be released from the primary system in an accident, are the last barrier between the environment and the nuclear steam supply system in nuclear power plants. Assessing the probability of failure for the containment building is essential to level 2 PSA studies of nuclear power plants. Degradation of containment vessels of some nuclear power plants has been observed in many countries, so it is important to study how the corrosion has adverse effects on the capacity of containment vessels. Conventionally, the reliability analysis of containment vessels can be conducted by using Monte Carlo Simulation (MCS) or Latin Hypercube Sampling (LHS) with the deterministic finite element analysis. In this paper, a 3D finite element model of an AP1000 steel containment vessel is constructed using the general-purpose nonlinear finite element analysis program ABAQUS. Then the finite element reliability method (FERM) based on the first order reliability method (FORM) is applied to analyze the reliability of the steel containment vessel, which is implemented by combining ABAQUS and MATLAB software platforms. The reliability and sensitivity indices of steel containment vessels under internal pressure with and without corrosion damage are obtained and compared. It is found that the FERM-based procedure is very efficient to analyze reliability and sensitivity of nuclear power plant structures.

Finite Element Study of Settlement of Cement Mixing Composite Foundation and Non-Probabilistic Reliability Analysis

2014 ◽  
Vol 638-640 ◽  
pp. 675-679 ◽  
Author(s):  
Huan Sheng Mu ◽  
Ling Gao
Keyword(s):  
Finite Element ◽  
Reliability Analysis ◽  
Load Transfer ◽  
Soft Soil ◽  
Probabilistic Method ◽  
Three Dimensional ◽  
Element Model ◽  
Composite Foundation ◽  
Reliability Method ◽  
Three Dimensional Finite Element

This paper presents a non-probabilistic method for reliability analysis of cement mixing composite foundations. First, the load transfer mechanism of composite foundations is described. Then a three-dimensional finite element model of cement mixing composite foundation under embankment is built. The settlement of subgrade is analyzed. Finally, a non-probabilistic reliability method is used to investigate the settlement reliability. The results show that the cement mixing composite foundation can significantly improve the compressibility of soft soil.

Failure Assessment Diagrams of Semi-Elliptical Surface Crack with Constraint Effect

2007 ◽  
Vol 353-358 ◽  
pp. 98-101
Author(s):  
Hyung Yil Lee ◽  
Jin Haeng Lee ◽  
Tae Hyung Kim
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Surface Crack ◽  
J Integral ◽  
Finite Element Analyses ◽  
Constraint Effect ◽  
Failure Assessment ◽  
T Stress ◽  
Cracked Structures ◽  
Constraint Effects

For accurate failure assessment, a second parameter like T-stress describing the constraint is needed in addition to the single parameter J-integral. In this work, selecting the structures of surface-cracked plate and pipe, we perform line-spring finite element modeling, and accompanying elastic-plastic finite element analyses. We then present a framework, which includes the constraint effects in the R6 FAD approach for failure assessment of cracked-structures.

Probabilistic Analysis of Cracked Structures With Uncertainty Parameters

2008 ◽  
Vol 33-37 ◽  
pp. 223-228 ◽  
Author(s):  
Ahmad Kamal Ariffin ◽  
M.R.M. Akramin ◽  
Syifaul Huzni ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali
Keyword(s):  
Finite Element Analysis ◽  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
Failure Probability ◽  
Probabilistic Analysis ◽  
Crack Size ◽  
Probability Of Failure ◽  
Element Analysis ◽  
Cracked Structures

This paper presents a probabilistic approach for fracture mechanics analysis of cracked structures. The objective of this work is to calculate the rigidity of cracked structures based on failure probability. The methodology consists of cracked structures modelling, finite element analysis with adaptive mesh, sampling of cracked structure including uncertainties factors and probabilistic analysis using Monte Carlo method. Probabilistic analysis represents the priority of proceeding either suitable to repair the structures or it can be justified that the structures are still in safe condition. Therefore, the combination of finite element and probabilistic analysis represents the failure probability of the structures by operating the sampling of cracked structures process. The uncertainty of the crack size can produce a significant effect on the probability of failure, particularly for the crack size with large coefficient of variation. The probability of failure caused by uncertainties relates to loads and material properties of the structure are estimated using Monte Carlo simulation technique. Numerical example is presented to show that probabilistic analysis based on Monte Carlo simulation provides accurate estimates of failure probability. The comparisons of simulation result, analytical solution and relevant numerical results obtained from other previous works shows that the combination of finite element analysis and probabilistic analysis based on Monte Carlo simulation provides accurate estimation of failure probability.

scholarly journals Performance and Risk Assessment of Soil-Structure Interaction Systems Based on Finite Element Reliability Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Quan Gu
Keyword(s):  
Risk Assessment ◽  
Finite Element ◽  
Reliability Analysis ◽  
Soil Structure ◽  
Soil Structure Interaction ◽  
Structure Interaction ◽  
Analysis Methods ◽  
Reliability Method ◽  
Reliability Methods ◽  
Time Invariant

In the context of performance-based earthquake engineering, reliability method has been of significant importance in performance and risk assessment of structures or soil-structure interaction (SSI) systems. The finite element (FE) reliability method combines FE analysis with state-of-the-art methods in reliability analysis and has been employed increasingly to estimate the probability of occurrence of failure events corresponding to various hazard levels (e.g., earthquakes with various intensity). In this paper, crucial components for FE reliability analysis are reviewed and summarized. Furthermore, recent advances in both time invariant and time variant reliability analysis methods for realistic nonlinear SSI systems are presented and applied to a two-dimensional two story building on layered soil. Various time invariant reliability analysis methods are applied, including the first-order reliability method (FORM), importance sampling method, and orthogonal plane sampling (OPS) method. For time variant reliability analysis, an upper bound of the failure probability is obtained from numerical integration of the mean outcrossing rate (MOCR). The MOCR is computed by using FORM analysis and OPS analysis. Results by different FE reliability methods are compared in terms of accuracy and computational cost. This paper provides valuable insights for reliability based probabilistic performance and risk assessment of SSI systems.

scholarly journals A Study of Probabilistic FEMs for a Slope Reliability Analysis Using the Stress Fields

2015 ◽  
Vol 9 (1) ◽  
pp. 196-206 ◽  
Author(s):  
Khaled Farah ◽  
Mounir Ltifi ◽  
Hedi Hassis
Keyword(s):  
Finite Element ◽  
Slope Stability ◽  
Perturbation Method ◽  
Spatial Variation ◽  
Reliability Analysis ◽  
Young Modulus ◽  
Soil Strength ◽  
Cumulative Distribution ◽  
Strength Parameters ◽  
Reliability Method

In this paper, the applicability and the effectiveness of the probabilistic finite element methods (FEMs) such as the perturbation method, and the Spectral Stochastic Finite Element Method (SSFEM) applied to the reliability analysis of the slope stability have been studied. The results were checked by the Monte Carlo simulation and a direct coupling ap-proach combining the deterministic finite elements code and First Order Reliability Method (FORM) algorithm. These methods are presented considering the spatial variation of soil strength parameters and Young modulus. The random field is used to describe the spatial variation. Also, the reliability analysis is conducted using a performance function formulat-ed in terms of the stochastic stress mobilized along the sliding surface. The present study shows that the perturbation method and SSFEM can be considered as practical methods to conduct a second moment analysis of the slope stability taking into account the spatial variability of soil properties since good results are obtained with acceptable estimated rela-tive errors. Finally, the perturbation method is performed to delimit the location of the critical probabilistic sliding surfac-es and to evaluate the effect of the correlation length of soil strength parameters on the safety factor. In addition, the two methods are used to estimate the probability density and the cumulative distribution function of the factor of safety.

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