An Ultra Weak Finite Element Method as an Alternative to a Monte Carlo Method for an Elasto-Plastic Problem with Noise

2009 ◽  
Vol 47 (5) ◽  
pp. 3374-3396 ◽  
Author(s):  
Alain Bensoussan ◽  
Laurent Mertz ◽  
Olivier Pironneau ◽  
Janos Turi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Element Method

Structural Reliability Analysis for UAV Center Wing Based on Stochastic Finite Element

2014 ◽  
Vol 684 ◽  
pp. 208-212 ◽  
Author(s):  
Da Qian Zhang ◽  
Xin Ping Fu ◽  
Xiao Dong Tan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Engineering Application ◽  
Reliability Design ◽  
Structure Reliability ◽  
Element Method

In general it is difficult to obtain the results directly during process of structural reliability designing because of the complexity of the structure. It can calculate the structure reliability and failure probability effectively according to the combination of finite element method and theory of reliability. This paper introduces a method of structure reliability based on finite element method, summarizes a common method which has an important engineering application value to calculate the reliability such as using Monte-Carlo method to calculate reliability analysis combining with finite element method, recommends a common used software to reliability design and shows the process of using the software to reliability analysis.

The Strength Reliability Analysis of Periodically Symmetric Struts Supports of Gas Turbine Based on Monte-Carlo Method

2011 ◽  
Vol 311-313 ◽  
pp. 1977-1981 ◽  
Author(s):  
Ya Xin Zhang ◽  
Bin Bin Li ◽  
Mamtimin Geni
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Reliability Analysis ◽  
Gas Turbine ◽  
Maximum Stress ◽  
Random Variables ◽  
Probabilistic Distribution ◽  
Element Method

Due to the limitations of dimension and experiment cost, the reliability analysis of PSSS (Periodic Symmetric Struts Support ) mainly depend on reliability simulation. Inlet temperature, inlet velocity and inlet pressure of the thermal channel are the major random variables impacting PASS. In this paper, it generates 120 groups random variables by using stochastic finite element method ,which combined finite element software and Monte Carlo method. Temperature distribution is obtained based on fluid-structure interaction analysis with each group of variables as boundary condition, then thermal stress distribution is obtained by using steady state thermal analysis. After that, the maximum stress value of each group are extracted out, and the curve fitting for the probabilistic distribution curve of the stress was carried on. Then the function of the probabilistic distribution of maximum stress was got. According to the stress - strength interference model, the reliability calculation of PSSS was carried out, which can provides some reference data for the reliability analysis of the heavy--duty gas turbine.. This shows that by using finite element method and the monte carlo method to carry out structure strength reliability analysis of maximum stress area is feasible.

scholarly journals MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM

2021 ◽  
Author(s):  
Dong T.P. Nguyen ◽  
Dirk Nuyens
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Convergence Rates ◽  
Higher Order ◽  
Elliptic Pdes ◽  
Infinite Dimensional ◽  
Quasi Monte Carlo ◽  
Higher Order Convergence ◽  
Element Method

We introduce the \emph{multivariate decomposition finite element method} (MDFEM) for elliptic PDEs with lognormal diffusion coefficients, that is, when the diffusion coefficient has the form $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\bsy) = \sum_{j \ge 1} y_j \, \phi_j$ with $y_j \sim \calN(0,1)$ and a given sequence of functions $\{\phi_j\}_{j \ge 1}$. We use the MDFEM to approximate the expected value of a linear functional of the solution of the PDE which is an infinite-dimensional integral over the parameter space. The proposed algorithm uses the \emph{multivariate decomposition method} (MDM) to compute the infinite-dimensional integral by a decomposition into finite-dimensional integrals, which we resolve using \emph{quasi-Monte Carlo} (QMC) methods, and for which we use the \emph{finite element method} (FEM) to solve different instances of the PDE.   We develop higher-order quasi-Monte Carlo rules for integration over the finite-di\-men\-si\-onal Euclidean space with respect to the Gaussian distribution by use of a truncation strategy. By linear transformations of interlaced polynomial lattice rules from the unit cube to a multivariate box of the Euclidean space we achieve higher-order convergence rates for functions belonging to a class of \emph{anchored Gaussian Sobolev spaces} while taking into account the truncation error. These cubature rules are then used in the MDFEM algorithm.   Under appropriate conditions, the MDFEM achieves higher-order convergence rates in term of error versus cost, i.e., to achieve an accuracy of $O(\epsilon)$ the computational cost is $O(\epsilon^{-1/\lambda-\dd/\lambda}) = O(\epsilon^{-(p^* + \dd/\tau)/(1-p^*)})$ where $\epsilon^{-1/\lambda}$ and $\epsilon^{-\dd/\lambda}$ are respectively the cost of the quasi-Monte Carlo cubature and the finite element approximations, with $\dd = d \, (1+\ddelta)$ for some $\ddelta \ge 0$ and $d$ the physical dimension, and $0 < p^* \le (2 + \dd/\tau)^{-1}$ is a parameter representing the sparsity of $\{\phi_j\}_{j \ge 1}$.

scholarly journals Monte Carlo Simulation for Exploring Mechanical Properties of Porous Materials Based on Scaled Boundary Finite Element Method

2022 ◽  
Vol 12 (2) ◽  
pp. 575
Author(s):  
Guangying Liu ◽  
Ran Guo ◽  
Kuiyu Zhao ◽  
Runjie Wang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
Porous Materials ◽  
Influencing Factors ◽  
Random Models ◽  
Scaled Boundary Finite Element ◽  
Element Method

The existence of pores is a very common feature of nature and of human life, but the existence of pores will alter the mechanical properties of the material. Therefore, it is very important to study the impact of different influencing factors on the mechanical properties of porous materials and to use the law of change in mechanical properties of porous materials for our daily lives. The SBFEM (scaled boundary finite element method) method is used in this paper to calculate a large number of random models of porous materials derived from Matlab code. Multiple influencing factors can be present in these random models. Based on the Monte Carlo simulation, after a large number of model calculations were carried out, the results of the calculations were analyzed statistically in order to determine the variation law of the mechanical properties of porous materials. Moreover, this paper gives fitting formulas for the mechanical properties of different materials. This is very useful for researchers estimating the mechanical properties of porous materials in advance.

scholarly journals Monte Carlo-Based Finite Element Method for the Study of Randomly Distributed Vacancy Defects in Graphene Sheets

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Liu Chu ◽  
Jiajia Shi ◽  
Eduardo Souza de Cursi ◽  
Xunqian Xu ◽  
Yazhou Qin ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Natural Frequencies ◽  
Vacancy Defect ◽  
Honeycomb Lattice ◽  
Graphene Sheets ◽  
Pristine Graphene ◽  
Vacancy Defects ◽  
Element Method

This paper proposed an effective stochastic finite element method for the study of randomly distributed vacancy defects in graphene sheets. The honeycomb lattice of graphene is represented by beam finite elements. The simulation results of the pristine graphene are in accordance with literatures. The randomly dispersed vacancies are propagated and performed in graphene by integrating Monte Carlo simulation (MCS) with the beam finite element model (FEM). The results present that the natural frequencies of different vibration modes decrease with the augment of the vacancy defect amount. When the vacancy defect reaches 5%, the regularity and geometrical symmetry of displacement and rotation in vibration behavior are obviously damaged. In addition, with the raise of vacancy defects, the random dispersion position of vacancy defects increases the variance in natural frequencies. The probability density distributions of natural frequencies are close to the Gaussian and Weibull distributions.

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