On Certain Approximations in the Finite-Element Method

1971 ◽  
Vol 38 (1) ◽  
pp. 58-61 ◽  
Author(s):  
R. W. McLay
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Variational Principle ◽  
Lagrange Multipliers ◽  
Restricted Problem ◽  
Generalized Variational Principle ◽  
The Finite Element Method ◽  
Element Method

Approximations made outside of the variational principle used in the finite-element method are examined for a restricted problem in elasticity. They are shown to be rigorous from the standpoint of a generalized variational principle in which Lagrange multipliers are utilized. The convergence of the Ritz solution to the exact solution is demonstrated. The bound is shown to be a function of the quality of both the displacement functions and other approximate functions in the analysis.

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.

Smoothed particle hydrodynamics versus finite element method for blast impact

2013 ◽  
Vol 61 (1) ◽  
pp. 111-121 ◽  
Author(s):  
T. Jankowiak ◽  
T. Łodygowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Smoothed Particle Hydrodynamics ◽  
Concrete Slab ◽  
The Finite Element Method ◽  
Particle Hydrodynamics ◽  
Mesh Density ◽  
Smoothed Particle ◽  
Element Method

Abstract The paper considers the failure study of concrete structures loaded by the pressure wave due to detonation of an explosive material. In the paper two numerical methods are used and their efficiency and accuracy are compared. There are the Smoothed Particle Hydrodynamics (SPH) and the Finite Element Method (FEM). The numerical examples take into account the dynamic behaviour of concrete slab or a structure composed of two concrete slabs subjected to the blast impact coming from one side. The influence of reinforcement in the slab (1, 2 or 3 layers) is also presented and compared with a pure concrete one. The influence of mesh density for FEM and the influence of important parameters in SPH like a smoothing length or a particle distance on the quality of the results are discussed in the paper

Application of the Finite Element Method (FEM) through GFAS Software to the study of a tunnel

2021 ◽  
Vol 4 (2) ◽  
pp. 001
Author(s):  
Maurizio Ponte ◽  
◽  
Filippo Catanzariti ◽  
Gloria Campilongo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Simulation ◽  
Theoretical Method ◽  
The Finite Element Method ◽  
Tunnel Excavation ◽  
Analysis System ◽  
Quality Of Products ◽  
Element Method

Computational simulation is widely used in companies to perform analysis and improve the quality of products and projects. Most of these analyses are carried out using software that uses the Finite Element Method, which allows to obtain answers to numerous engineering problems. In this study, two examples of application to the study of tunnels of the Finite Element Method using the Geostru Software "GFAS - Geotechnical F.E.M. Analysis System" are proposed. The case of a tunnel excavated inside a granite rock massif was analyzed, first determining the state of stresses in the cavity contour through a theoretical method and comparing these results with those obtained in the software. Then, by means of finite element modeling, the settlements induced by the excavation were determined. Finally, the problem of tunnel excavation in a viscoplastic rock mass is presented and the authors propose a comparison of the analytical and numerical method.

Reconstruction of the Main Cylinder of Carding Machine-Optimization of Dimensions with the Use of the Finite Element Method

2012 ◽  
Vol 59 (2) ◽  
pp. 199-211 ◽  
Author(s):  
Piotr Danielczyk ◽  
Jacek Stadnicki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parametric Design ◽  
Optimal Solution ◽  
The Finite Element Method ◽  
Deflection Amplitude ◽  
Textile Technology ◽  
Carding Machine ◽  
Element Method

Reconstruction of the Main Cylinder of Carding Machine-Optimization of Dimensions with the Use of the Finite Element MethodThe following paper presents the solution to the problem of searching the best shape - structural form of the bottoms and optimal dimensions of the main cylinder of the carding machine with consideration to the criterion of minimal deflection amplitude. The ANSYS package of the Finite Element Method has been used for the analysis. Polak-Ribery conjugate gradient method has been applied for searching the optimal solution, basing on the parametric model of the cylinder written with the use ofAnsys Parametric Design Language.As a result of the performed analyses, reduction of maximum deflection value at approximately 80% has been obtained. Optimal cylinder dimensions enable application of a new textile technology - microfibre carding and improvement in the quality of traditional carding technology of woollen and wool-like fibres.

Convergence of the Finite Element Method in the Theory of Elasticity

1968 ◽  
Vol 35 (2) ◽  
pp. 274-278 ◽  
Author(s):  
M. W. Johnson ◽  
R. W. McLay
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Principle ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Careful Consideration ◽  
Stress Singularities ◽  
The Finite Element Method ◽  
Element Method

The foundations of the theory of the finite element method as it applies to linear elasticity are investigated. A particular boundary-value problem in plane stress is considered and the variational principle for the finite element method is shown to be equivalent to it. Mean and uniform convergence of the finite element solution to that of the boundary-value problem is demonstrated with careful consideration given to the stress singularities. A counterexample is presented in which a set of functions, admissible to the variational principle, is shown not to converge.

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