scholarly journals Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities

2014 ◽  
Vol 52 (3) ◽  
pp. 1243-1268 ◽  
Author(s):  
Ralf Kornhuber ◽  
Christoph Schwab ◽  
Maren-Wanda Wolf
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Variational Inequalities ◽  
Finite Element Methods ◽  
Multilevel Monte Carlo ◽  
Elliptic Variational Inequalities

Coupling kinetic Monte Carlo and finite element methods to model the strain path sensitivity of the isothermal stress-assisted martensite nucleation in TRIP-assisted steels

2021 ◽  
Vol 154 ◽  
pp. 103707
Author(s):  
Stephen Cluff ◽  
Marko Knezevic ◽  
Michael P. Miles ◽  
David T. Fullwood ◽  
Raja K. Mishra ◽  
...  
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Finite Element Methods ◽  
Strain Path ◽  
Kinetic Monte Carlo

Variation Simulation for Deformable Sheet Metal Assemblies Using Finite Element Methods

1997 ◽  
Vol 119 (3) ◽  
pp. 368-374 ◽  
Author(s):  
S. Charles Liu ◽  
S. Jack Hu
Keyword(s):  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
Sheet Metal ◽  
Finite Element Methods ◽  
Free Form ◽  
Direct Monte Carlo Simulation ◽  
Free Form Surfaces ◽  
Variation Simulation ◽  
Sheet Metal Assembly

Traditional variation analysis methods, such as Root Sum Square method and Monte Carlo simulation, are not applicable to sheet metal assemblies because of possible part deformation during the assembly process. This paper proposes the use of finite element methods (FEM) in developing mechanistic variation simulation models for deformable sheet metal parts with complex two or three dimensional free form surfaces. Mechanistic variation simulation provides improved analysis by combining engineering structure models and statistical analysis in predicting the assembly variation. Direct Monte Carlo simulation in FEM is very time consuming, because hundreds or thousands of FEM runs are required to obtain a realistic assembly distribution. An alternative method, based on the Method of Influence Coefficients, is developed to improve the computational efficiency, producing improvements by several orders of magnitude. Simulations from both methods yield almost identical results. An example illustrates the developed methods used for evaluating sheet metal assembly variation. The new approaches provide an improved understanding of sheet metal assembly processes.

scholarly journals Micro-Macro Simulation of Sintering Process by Combining Monte Carlo and Finite Element Methods

2003 ◽  
Vol 111 (1295) ◽  
pp. 516-520 ◽  
Author(s):  
Ken-ichiro MORI ◽  
Hideaki MATSUBARA ◽  
Nobuhiro NOGUCHI ◽  
Masayoshi SHIMIZU ◽  
Hiroshi NOMURA
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Finite Element Methods ◽  
Sintering Process

scholarly journals A New Approach to Asymptotic Behavior for a Finite Element Approximation in Parabolic Variational Inequalities

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Salah Boulaaras ◽  
Mohamed Haiour
Keyword(s):  
Finite Element ◽  
Asymptotic Behavior ◽  
Variational Inequalities ◽  
Finite Element Approximation ◽  
Uniform Norm ◽  
Element Approximation ◽  
New Approach ◽  
Elliptic Variational Inequalities ◽  
Energy Behavior ◽  
Spatial Approximation

The paper deals with the theta time scheme combined with a finite element spatial approximation of parabolic variational inequalities. The parabolic variational inequalities are transformed into noncoercive elliptic variational inequalities. A simple result to time energy behavior is proved, and a new iterative discrete algorithm is proposed to show the existence and uniqueness. Moreover, its convergence is established. Furthermore, a simple proof to asymptotic behavior in uniform norm is given.

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