Finite Plane Strain of Incompressible Elastic Solids by the Finite Element Method

1968 ◽  
Vol 19 (3) ◽  
pp. 254-264 ◽  
Author(s):  
J. Tinsley Oden
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Strain ◽  
Simple Shear ◽  
Finite Elasticity ◽  
The Finite Element Method ◽  
Finite Plane ◽  
Elastic Solids ◽  
Non Linear ◽  
Element Method

SummaryThe finite element method is extended to the problem of finite plane strain of elastic solids. A highly elastic body subjected to two-dimensional deformations is represented by an assembly of triangular elements of finite dimension. The displacement fields within each element are approximated by linear functions of the local coordinates. Non-linear stiffness relations involving generalised node forces and displacements are derived from energy considerations. For demonstration purposes, the non-linear stiffness equations are applied to the problems of finite simple shear and generalised shear. For finite simple shear, it is shown that these relations are in exact agreement with finite elasticity theory. Convergence rates of finite element representations of these problems are briefly examined.

Combining regression trees and the finite element method to define stress models of highly non-linear mechanical systems

2009 ◽  
Vol 44 (6) ◽  
pp. 491-502 ◽  
Author(s):  
R Lostado ◽  
F J Martínez-De-Pisón ◽  
A Pernía ◽  
F Alba ◽  
J Blanco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Systems ◽  
Regression Trees ◽  
Support Vector ◽  
The Finite Element Method ◽  
Multiple Contacts ◽  
Non Linear ◽  
Instance Space ◽  
Element Method

This paper demonstrates that combining regression trees with the finite element method (FEM) may be a good strategy for modelling highly non-linear mechanical systems. Regression trees make it possible to model FEM-based non-linear maps for fields of stresses, velocities, temperatures, etc., more simply and effectively than other techniques more widely used at present, such as artificial neural networks (ANNs), support vector machines (SVMs), regression techniques, etc. These techniques, taken from Machine Learning, divide the instance space and generate trees formed by submodels, each adjusted to one of the data groups obtained from that division. This local adjustment allows good models to be developed when the data are very heterogeneous, the density is very irregular, and the number of examples is limited. As a practical example, the results obtained by applying these techniques to the analysis of a vehicle axle, which includes a preloaded bearing and a wheel, with multiple contacts between components, are shown. Using the data obtained with FEM simulations, a regression model is generated that makes it possible to predict the contact pressures at any point on the axle and for any condition of load on the wheel, preload on the bearing, or coefficient of friction. The final results are compared with other classical linear and non-linear model techniques.

scholarly journals Non-linear analysis and warping of tubular pipe conveyors by the finite element method

2007 ◽  
Vol 46 (1-2) ◽  
pp. 95-108 ◽  
Author(s):  
J.J. del Coz Díaz ◽  
P.J. García Nieto ◽  
J.A. Vilán Vilán ◽  
A. Martín Rodríguez ◽  
J.R. Prado Tamargo ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Linear Analysis ◽  
The Finite Element Method ◽  
Non Linear ◽  
Element Method

Non-linear thermal analysis of light concrete hollow brick walls by the finite element method and experimental validation

2006 ◽  
Vol 26 (8-9) ◽  
pp. 777-786 ◽  
Author(s):  
J.J. del Coz Díaz ◽  
P.J. García Nieto ◽  
A. Martín Rodríguez ◽  
A. Lozano Martínez-Luengas ◽  
C. Betegón Biempica
Keyword(s):  
Finite Element Method ◽  
Thermal Analysis ◽  
Finite Element ◽  
Experimental Validation ◽  
The Finite Element Method ◽  
Non Linear ◽  
Hollow Brick ◽  
Element Method

Analyses of Axisymmetric Upsetting and Plane-Strain Side-Pressing of Solid Cylinders by the Finite Element Method

1971 ◽  
Vol 93 (2) ◽  
pp. 445-454 ◽  
Author(s):  
C. H. Lee ◽  
Shiro Kobayashi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plastic Zone ◽  
Plane Strain ◽  
Deformation Characteristics ◽  
Stress Distributions ◽  
The Finite Element Method ◽  
Percent Reduction ◽  
Zone Development ◽  
Element Method

Detailed studies of the deformation characteristics in axisymmetric upsetting and plane-strain side-pressing were attempted by the finite element method. Solutions were obtained up to a 33 percent reduction in height in axisymmetric upsetting and up to a 19 percent reduction in height in side-pressing, under conditions of complete sticking at the tool-workpiece interface. Load-displacement curves, plastic zone development, and strain and stress distributions were presented, and some of the computed solutions were compared with those found experimentally.

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