Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach

1988 ◽  
Author(s):  
C. R. Rao
Keyword(s):  
Geometric Approach ◽  
Generalized Inverses ◽  
Projection Operators ◽  
Linear Transformations

A Geometric Approach to Homology Theory

1976 ◽  
Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson
Keyword(s):  
Geometric Approach ◽  
Homology Theory

A GEOMETRIC APPROACH TO DISSIPATION AND ITS APPLICATION TO DISSIPATIVE NUCLEAR DYNAMICS

1984 ◽  
Vol 45 (C6) ◽  
pp. C6-87-C6-94
Author(s):  
H. Reinhardt ◽  
R. Balian ◽  
Y. Alhassid
Keyword(s):  
Geometric Approach ◽  
Nuclear Dynamics

Computer Modeling of a Tire under Cornering Loads

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves
Keyword(s):  
Finite Element Analysis ◽  
Geometric Approach ◽  
Lateral Force ◽  
Slip Angle ◽  
Element Analysis ◽  
Pressure Distributions ◽  
Slip Effects ◽  
Improved Accuracy ◽  
Nonlinear Geometric ◽  
Good Agreement

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

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