From a Geometrical Interpretation of Bramble-Hilbert Lemma to a Probability Distribution for Finite Element Accuracy

2019 ◽  
pp. 3-14
Author(s):  
Joel Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Probability Distribution ◽  
Geometrical Interpretation

scholarly journals PROBABILISTIC FINITE ELEMENT STIFFNESS OF A LATERALLY LOADED MONOPILE BASED ON AN IMPROVED ASYMPTOTIC SAMPLING METHOD

2015 ◽  
Vol 21 (4) ◽  
pp. 503-513 ◽  
Author(s):  
Mohammad Javad Vahdatirad ◽  
Mehdi Bayat ◽  
Lars Vabbersgaard Andersen ◽  
Lars Bo Ibsen
Keyword(s):  
Finite Element ◽  
Probability Distribution ◽  
Sampling Method ◽  
Stochastic Approach ◽  
Undrained Shear Strength ◽  
Finite Element Scheme ◽  
Random Field Theory ◽  
Mechanical Responses ◽  
Laterally Loaded ◽  
Asymptotic Sampling

The mechanical responses of an offshore monopile foundation mounted in over-consolidated clay are calculated by employing a stochastic approach where a nonlinear p–y curve is incorporated with a finite element scheme. The random field theory is applied to represent a spatial variation for undrained shear strength of clay. Normal and Sobol sampling are employed to provide the asymptotic sampling method to generate the probability distribution of the foundation stiffnesses. Monte Carlo simulation is used as a benchmark. Asymptotic sampling accompanied with Sobol quasi random sampling demonstrates an efficient method for estimating the probability distribution of stiffnesses for the offshore monopile foundation.

Application of Reliability Based Design and Assessment to Seismic Evaluations

2010 ◽  
Author(s):  
Maher Nessim ◽  
Nader Yoosef-Ghodsi ◽  
Doug Honegger ◽  
Joe Zhou ◽  
Shanshan Wang
Keyword(s):  
Finite Element ◽  
Probability Distribution ◽  
Natural Gas ◽  
Finite Element Model ◽  
Element Model ◽  
Soil Liquefaction ◽  
Simplified Approach ◽  
Natural Gas Pipelines ◽  
Reliability Based Design ◽  
Ground Deformations

The application of reliability based design and assessment (RBDA) as a basis for seismic evaluations of natural gas pipelines is explored through analysis of a number of representative pipeline examples. To accomplish this, a simplified approach was developed to generate a representative probability distribution of permanent ground deformations due to soil liquefaction. An idealized pipeline alignment through a liquefiable layer under a river was defined, and a number of cases representing NPS12 and NPS36 pipelines in classes 1, 2 and 3 were analyzed using a finite element model. The probability of exceeding the strain limits for pipe body and girth weld were calculated and compared to the reliability targets. The results were used to identify diameter and class combinations that can meet the reliability targets, and to make preliminary conclusions regarding the viability of using RBDA for seismic evaluations.

On generalized binomial laws to evaluate finite element accuracy: preliminary probabilistic results for adaptive mesh refinement

2020 ◽  
Vol 28 (2) ◽  
pp. 63-74
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Error Estimate ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Random Variable ◽  
Geometrical Interpretation ◽  
Relative Accuracy ◽  
Probabilistic Methods

AbstractThe aim of this paper is to provide new perspectives on the relative finite elements accuracy. Starting from a geometrical interpretation of the error estimate which can be deduced from Bramble–Hilbert lemma, we derive a probability law that evaluates the relative accuracy, considered as a random variable, between two finite elements Pk and Pm, k < m. We extend this probability law to get a cumulated probabilistic law for two main applications. The first one concerns a family of meshes, the second one is dedicated to a sequence of simplexes constituting a given mesh. Both of these applications could be considered as a first step toward application for adaptive mesh refinement with probabilistic methods.

scholarly journals Study on Structural Reliability of Prestressed Reinforced Concrete Beam Bridges Based on Full Probability Analysis

2021 ◽  
Vol 1210 (1) ◽  
pp. 012003
Author(s):  
Yubao Liu ◽  
Hanxiong Liu ◽  
Shouyi Sun
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distribution ◽  
Reliability Index ◽  
Limit State ◽  
State Equation ◽  
Distribution Model ◽  
State Equations ◽  
The Monte Carlo Method

Abstract A three dimensional(3D) finite element model is established for a prestressed concrete girder bridge, list the limit state equation and variable probability distribution model, obtain the failure probability and reliability index of the limit state equation based on the Monte-Carlo method, investigate the reliability index’s sensitivity to random variables for limit state equations of bridge bearing capacity. The specific method of the research on the structure reliability index calculation is to select a suitable way that can fit the research’s object among the center point method, the checking-point method, the Monte-Carlo method, the importance sampling method, and so on. Authors use finite element software ANSYS to build model and perform 3D force analysis. According to the results, authors can determine the bridges’ failure modes under the state of 3D stress. Then, authors can list the possible limit state equations related to Stiffness, strength, function, durability, and some character else. After determining the bridge’s structural limit state equation and the probability distribution model of the variables, determine the distribution function of each impact factor and its characteristic parameters through the site survey data and other related data surveys. Then, use the Monte-Carlo method for the calculation of bridge reliability index, obtain the failure probability and reliability index of each limit state equation, analyze the sensitivity of each variable to the reliability index under the ultimate state of the bridge’s bearing capacity. At last, authors give construction quality control plans and suggestions according to the data above.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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