Punch Problems for an Anisotropic Elastic Half-Plane

1996 ◽  
Vol 63 (1) ◽  
pp. 69-76 ◽  
Author(s):  
C. W. Fan ◽  
Chyanbin Hwu
Keyword(s):  
Boundary Value Problems ◽  
Half Plane ◽  
Boundary Value ◽  
Analytical Continuation ◽  
Stroh's Formalism ◽  
Anisotropic Elastic ◽  
Stroh’S Formalism

By combining Stroh’s formalism and the method of analytical continuation, several mixed-typed boundary value problems of an anisotropic elastic half-plane are studied in this paper. First, we consider a set of rigid punches of arbitrary profiles indenting into the surface of an anisotropic elastic half-plane with no slip occurring. Illustrations are presented for the normal and rotary indentation by a flat-ended punch. A sliding punch with or without friction is then considered under the complete or incomplete indentation condition.

The Stroh Formalism

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
General Solution ◽  
Elastic Body ◽  
Three Dimensional ◽  
Anisotropic Elasticity ◽  
Stroh Formalism ◽  
Two Dimensional ◽  
Stroh's Formalism ◽  
Elasticity Problems ◽  
Anisotropic Elastic ◽  
Stroh’S Formalism

In this chapter we study Stroh's sextic formalism for two-dimensional deformations of an anisotropic elastic body. The Stroh formalism can be traced to the work of Eshelby, Read, and Shockley (1953). We therefore present the latter first. Not all results presented in this chapter are due to Stroh (1958, 1962). Nevertheless we name the sextic formalism after Stroh because he laid the foundations for researchers who followed him. The derivation of Stroh's formalism is rather simple and straightforward. The general solution resembles that obtained by the Lekhnitskii formalism. However, the resemblance between the two formalisms stops there. As we will see in the rest of the book, the Stroh formalism is indeed mathematically elegant and technically powerful in solving two-dimensional anisotropic elasticity problems. The possibility of extending the formalism to three-dimensional deformations is explored in Chapter 15.

The half-plane diffraction problem for harmonic time dependence

1959 ◽  
Vol 252 (1270) ◽  
pp. 411-417 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Time Dependence ◽  
Boundary Value Problems ◽  
Half Plane ◽  
Mixed Type ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Two Dimensional ◽  
Conducting Screen ◽  
Plane Diffraction

Green’s functions are obtained for the boundary-value problems of mixed type describing the general two-dimensional diffraction problems at a screen in the form of a half-plane (Sommerfeld’s problem), applicable to acoustically rigid or soft screens, and to the full electromagnetic field at a perfectly conducting screen.

Vibratory Motion of a Body on an Orthotropic Half Plane

1972 ◽  
Vol 39 (4) ◽  
pp. 1033-1040 ◽  
Author(s):  
J. M. Freedman ◽  
L. M. Keer
Keyword(s):  
Boundary Value Problems ◽  
Half Plane ◽  
Previous Investigation ◽  
Boundary Value ◽  
Orthotropic Materials ◽  
Vibratory Motion ◽  
Rocking Motion

Three boundary-value problems for an orthotropic half plane are solved. They correspond to the cases studied in a previous investigation by Karasudhi, Keer, and Lee [9] for a body undergoing independent vertical, horizontal, and rocking motion. Dynamic stiffnesses are computed for three typical orthotropic materials: beryllium, ice, and a steel-mylar composite.

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