Literature Review : ON THE STABILITY OF EXPLICIT METHODS FOR THE NUMERICAL INTEGRATION OF THE EQUATIONS OF MOTION IN FINITE ELEMENT METHODS Fu, C. C. Intl. Numer. Methods Engr. 4, 95-107 (Jan. /Feb. 1972) Refer to Abstract No. 72-550

1973 ◽  
Vol 5 (1) ◽  
pp. 69-70
Author(s):  
W.H. Armstrong
Keyword(s):  
Finite Element ◽  
Literature Review ◽  
Numerical Integration ◽  
Finite Element Methods ◽  
Equations Of Motion ◽  
Explicit Methods ◽  
The Stability

scholarly journals Inverse Nonlinear Finite Element Methods for Surgery Simulation and Image Guidance

2008 ◽  
Author(s):  
Philip Pratt
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Equations Of Motion ◽  
Nonlinear Finite Element ◽  
Weighted Sums ◽  
Global Coordinate System ◽  
Surgery Simulation ◽  
Explicit Integration ◽  
Time Step ◽  
Nonlinear Finite Element Methods

Nonlinear finite element methods are described in which cyclic organ motion is implied from 4D scan data. The equations of motion corresponding to an explicit integration of the total Lagrangian formulation are reversed, such that the sequence of node forces which produces known changes in displacement is recovered. The forces are resolved from the global coordinate system into systems local to each element, and at every simulation time step are expressed as weighted sums of edge vectors. In the presence of large deformations and rotations, this facilitates the combination of external forces, such as tool-tissue interactions, and also positional constraints. Applications in the areas of surgery simulation and minimally invasive robotic interventions are discussed, and the methods are illustrated using CT images of a pneumatically-operated beating heart phantom.

scholarly journals Instability Threshold of a Rigid Rotor-Tilting Pad Journal Bearings System

1997 ◽  
Vol 3 (3) ◽  
pp. 199-213 ◽  
Author(s):  
Stefano Pagano ◽  
Ernesto Rocca ◽  
Michele Russo ◽  
Riccardo Russo
Keyword(s):  
Differential Equations ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Stable Operation ◽  
Rigid Rotor ◽  
Tilting Pad ◽  
The Stability ◽  
Tilting Pad Journal Bearings ◽  
Rotor Axis

The stability of a rigid rotor supported on radial tilting pad journal bearings is analysed. This study has been tackled both for small unbalance values by linearising the equations of motion, and also in the case where, because of the high unbalance value, the rotor axis describes orbits with an amplitude such that the system's non-linearity cannot be ignored. In both cases the system's stable operation maps have been obtained and verified through numerical integration of the differential equations of motion.

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