An introduction to the finite-element method with applications to non-linear problems

1987 ◽  
Vol 30 (1) ◽  
pp. 213
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Non Linear ◽  
Linear Problems ◽  
Element Method

Product Approximation for Non-linear Problems in the Finite Element Method

1981 ◽  
Vol 1 (3) ◽  
pp. 253-266 ◽  
Author(s):  
I. CHRISTIE ◽  
D. F. GRIFFITHS ◽  
A. R. MITCHELL ◽  
J. M. SANZ-SERNA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Non Linear ◽  
Linear Problems ◽  
Element Method

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.

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