STUDY ON FINITE ELEMENT METHOD FOR DYNAMIC PROBLEMS INVOLVING CONTACT ACOUSTIC NONLINEARITY

2018 ◽  
Vol 74 (2) ◽  
pp. I_115-I_123
Author(s):  
Kazushi KIMOTO
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Problems ◽  
Acoustic Nonlinearity ◽  
Contact Acoustic Nonlinearity ◽  
Element Method

On the New Equations for the Lateral Dynamics of a Rail-Tie Structure

1987 ◽  
Vol 109 (2) ◽  
pp. 180-185 ◽  
Author(s):  
A. D. Kerr ◽  
M. A. El-Sibaie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Close Agreement ◽  
Natural Frequencies ◽  
Dynamic Problems ◽  
Lateral Dynamics ◽  
Dynamic Analyses ◽  
Lateral Plane ◽  
Element Method

The accuracy of the new equations for the rail-tie structure, derived by Kerr and Zarembski and recently generalized for dynamic problems by Kerr and Accorsi, is studied. This is done by comparing the natural frequencies based on the new equations with those calculated using a finite element method for a range of fastener stiffness values and a variety of rail spacings. The comparison revealed very close agreement. The findings confirm the suitability of the new equations for dynamic analyses of cross-tie tracks in the lateral plane.

AN EXPLICIT SMOOTHED FINITE ELEMENT METHOD (SFEM) FOR ELASTIC DYNAMIC PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340002 ◽  
Author(s):  
X. Y. CUI ◽  
G. Y. LI ◽  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Integration ◽  
Internal Force ◽  
Dynamic Problems ◽  
Central Difference ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Central Difference Method ◽  
Element Method

This paper presents an explicit smoothed finite element method (SFEM) for elastic dynamic problems. The central difference method for time integration will be used in presented formulations. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. In present method, the problem domain is first divided into elements as in the finite element method (FEM), and the elements are further subdivided into several smoothing cells. Cell-wise strain smoothing operations are used to obtain the stresses, which are constants in each smoothing cells. Area integration over the smoothing cell becomes line integration along its edges, and no gradient of shape functions is involved in computing the field gradients nor in forming the internal force. No mapping or coordinate transformation is necessary so that the element can be used effectively for large deformation problems. Through several examples, the simplicity, efficiency and reliability of the smoothed finite element method are demonstrated.

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