scholarly journals Closure to “Discussion of ‘Two-Dimensional Rigid-Body Collisions With Friction’” (1993, ASME J. Appl Mech., 60, p. 564–566)

1993 ◽  
Vol 60 (2) ◽  
pp. 566-566
Author(s):  
Yu Wang ◽  
Matthew T. Mason
Keyword(s):  
Rigid Body ◽  
Two Dimensional

Two-Dimensional Rigid-Body Collisions With Friction

1992 ◽  
Vol 59 (3) ◽  
pp. 635-642 ◽  
Author(s):  
Yu Wang ◽  
Matthew T. Mason
Keyword(s):  
Rigid Body ◽  
Graphical Method ◽  
Correct Identification ◽  
Two Dimensional ◽  
Contact Mode ◽  
New Class ◽  
Tangential Impact ◽  
Approach Velocity ◽  
Conservation Principles ◽  
Analytical Expressions

This paper presents an analysis of a two-dimensional rigid-body collision with dry friction. We use Routh’s graphical method to describe an impact process and to determine the frictional impulse. We classify the possible modes of impact, and derive analytical expressions for impulse, using both Poisson’s and Newton’s models of restitution. We also address a new class of impacts, tangential impact, with zero initial approach velocity. Some methods for rigid-body impact violate energy conservation principles, yielding solutions that increase system energy during an impact. To avoid such anomalies, we show that Poisson’s hypothesis should be used, rather than Newton’s law of restitution. In addition, correct identification of the contact mode of impact is essential.

A Method for Generating Desired Contact Pressure Distributions in Experimental Interfacial Studies

1985 ◽  
Vol 107 (3) ◽  
pp. 241-246 ◽  
Author(s):  
M. H. Attia ◽  
L. Kops
Keyword(s):  
Rigid Body ◽  
Contact Pressure ◽  
Flexural Rigidity ◽  
Thermal Contact ◽  
Contact Length ◽  
Wear Testing ◽  
Elastic Response ◽  
Rigid Base ◽  
Two Dimensional ◽  
Pressure Distributions

Computer simulation of the thermal deformation behavior of machine tools requires a priori knowledge of the correlation between the contact pressure distribution and the thermal contact resistance distribution along the structural joint. To establish this correlation experimentally, a method for generating different distributions of contact pressure has been devised in the present work. The method provides also a basic tool toward the satisfaction of the requirements of simulative wear testing. In this paper, the effect of the relative flexural rigidity of two solids in contact on the shape of the distribution of contact pressure is presented as a means for generating desired contact pressure distributions. The theoretical background of the concept is discussed considering two limiting cases: a rigid body on an elastic semi-infinite mass, and an elastic layer on a rigid base. Through a photoelastic analysis, the geometric parameters of contacting bodies, which allow us to generate the desired distributions, have been defined. The results of the analysis were verified by a two-dimensional, plane-stress finite element model. The results indicated that a finite plate, whose dimensions are not less than threefold the contact length can simulate a two-dimensional rigid base or a semi-infinite elastic mass. A change in the height-to-contact length ratio of the contacting beam from 0.5 to 2.5, causes a significant change in its elastic response from a flexural to a rigid body.

Some Implications of Noncoaxiality in Finite Deformations

1973 ◽  
Vol 95 (2) ◽  
pp. 87-93
Author(s):  
T. C. Hsu
Keyword(s):  
Rigid Body ◽  
Linear Transformation ◽  
Metal Forming ◽  
Principal Axis ◽  
Pure Shear ◽  
Finite Deformations ◽  
Two Dimensional ◽  
Body Rotation ◽  
Linear Transformations ◽  
Rectangular Grids

Two-dimensional finite deformations are analyzed by factoring and multiplying the matrices of the linear transformations representing them. A general linear transformation consists of a pure shear, a uniform dilation, and a rigid-body rotation. Coaxiality is defined for finite deformations and its effect on the resultant distortion discussed. Tests for coaxiality are devised for use on rectangular grids which are often employed in metal forming research. Formulas are derived for the initial and final directions of the resultant major principal axis in both equal and unequal noncoaxial pure shears and, in particular, conditions are found for the constancy of distortion in the second deformation.

scholarly journals On the classification and bifurcation of multigerms of maps from surfaces to 3-space

2001 ◽  
Vol 89 (1) ◽  
pp. 57 ◽  
Author(s):  
C. A. Hobbs ◽  
N. P. Kirk
Keyword(s):  
Rigid Body ◽  
Two Dimensional ◽  
Local Models ◽  
Full List ◽  
Rigid Body Motions

The $\mathcal A$-classification of multigerm singularities is discussed, based on the theory of complete transversals. An $\mathcal A$-classification of $r$-multigerms from the plane to 3-space of $\mathcal A-\text{codimension} \leq 6-r$ is carried out and the bifurcation geometry of these singularities analysed. This work has applications to the study of two-dimensional spatial motions, giving local models for the singularities which appear on general trajectories of rigid body motions from the plane to 3-space. In addition, our classification is extensive enough to give the full list of simple multigerm singularities from the plane to 3-space.

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