Random homogenization analysis for heterogeneous materials with full randomness and correlation in microstructure based on finite element method and Monte-carlo method

2014 ◽  
Vol 54 (6) ◽  
pp. 1395-1414 ◽  
Author(s):  
Juan Ma ◽  
Jie Zhang ◽  
Liangjie Li ◽  
Peter Wriggers ◽  
Shahab Sahraee
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Heterogeneous Materials ◽  
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 $\{\phi_j\}_{j \ge 1}$.

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