A Stabilized Low Order Finite Element Method for Three Dimensional Elasticity Problems

2020 ◽  
Vol 13 (2) ◽  
pp. 281-295 ◽  
Author(s):  
global sci
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Element Method ◽  
Low Order

Finite Element Models for Flexible Cosserat Solids

2020 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Minghe Shan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Displacement Vector ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Discrete Equations ◽  
Computation Efficiency ◽  
Elasticity Problems ◽  
Element Method

Abstract The application of the finite element method to the modeling of Cosserat solids is investigated in detail. In two- and three-dimensional elasticity problems, the nodal unknowns are the components of the displacement vector, which form a linear field. In contrast, when dealing with Cosserat solids, the nodal unknowns form the special Euclidean group SE(3), a nonlinear manifold. This observation has numerous implications on the implementation of the finite element method and raises numerous questions: (1) What is the most suitable representation of this nonlinear manifold? (2) How is it interpolated over one element? (3) How is the associated strain field interpolated? (4) What is the most efficient way to obtain the discrete equations of motion? All these questions are, of course intertwined. This paper shows that reliable schemes are available for the interpolation of the motion and curvature fields. The interpolated fields depend on relative nodal motions only, and hence, are both objective and tensorial. Because these schemes depend on relative nodal motions only, only local parameterization is required, thereby avoiding the occurrence of singularities. For Cosserat solids, it is preferable to perform the discretization operation first, followed by the variation operation. This approach leads to considerable computation efficiency and simplicity.

A Quantitative Comparison Between a Low Order Model and a 3D FEM Code for the Study of Thermoacoustic Combustion Instabilities

2011 ◽  
Author(s):  
Giovanni Campa ◽  
Sergio Mario Camporeale ◽  
Anai¨s Guaus ◽  
Julien Favier ◽  
Matteo Bargiacchi ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Quantitative Comparison ◽  
Complex Eigenvalue ◽  
Combustion Instabilities ◽  
Order Model ◽  
Element Method ◽  
Low Order

The study of thermoacoustic combustion instabilities has an important role for safety operation in modern gas turbines equipped with lean premixed dry low emission combustion systems. Gas turbine manufacturers often adopt simulation tools based on low order models for predicting the phenomenon of humming. These simulation codes provide fast responses and good physical insight, but only one-dimensional or two-dimensional simplified schemes can be generally examined. The finite element method can overcome such limitations, because it allows to examine three-dimensional geometries and to search the complex eigenfrequencies of the system. Large Eddy Simulation (LES) techniques are proposed in order to investigate the instability phenomenon, matching pressure fluctuations with turbulent combustion phenomena to study thermoacoustic combustion oscillations, even if they require large numerical resources. The finite element approach solves numerically the Helmholtz equation problem converted in a complex eigenvalue problem in the frequency domain. Complex eigenvalues of the system allow us to identify the complex eigenfrequencies of the combustion system analyzed, so that we can have a valid indication of the frequencies at which thermoacoustic instabilities are expected and of the growth rate of the pressure oscillations at the onset of instability. Through the collaboration among Ansaldo Energia, University of Genoa and Polytechnic University of Bari, a quantitative comparison between a low order model, called LOMTI, and the three-dimensional finite element method has been examined, in order to exploit the advantages of both the methodologies.

A Robust Weak Galerkin Finite Element Method for Linear Elasticity with Strong Symmetric Stresses

2016 ◽  
Vol 16 (3) ◽  
pp. 389-408 ◽  
Author(s):  
Gang Chen ◽  
Xiaoping Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Linear Elasticity ◽  
A Priori ◽  
Three Dimensional ◽  
Weak Galerkin ◽  
Hybridizable Discontinuous Galerkin ◽  
Lame Constant ◽  
Elasticity Problems ◽  
Element Method

AbstractThis paper proposes and analyzes a weak Galerkin (WG) finite element method with strong symmetric stresses for two- and three-dimensional linear elasticity problems on conforming or nonconforming polygon/polyhedral meshes. The WG method uses piecewise-polynomial approximations of degreesk(${\geq 1}$) for the stress,${k+1}$for the displacement, andkfor the displacement trace on the inter-element boundaries. It is shown to be equivalent to a hybridizable discontinuous Galerkin (HDG) finite element scheme. We show that the WG methods are robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the Lamé constant λ. Numerical experiments confirm the theoretical results.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

Sign in / Sign up

Export Citation Format

Share Document