EN222: Mechanics of Solids
Homework 3: Dislocations
Due Thursday February 23, 2006
Division of Engineering
Brown University
1. Set up a symbolic manipulation program to calculate the stresses induced by an edge dislocation
at a depth
h
below the surface of a halfspace, using the method outlined in class.
Note that the
program will need help to evaluate quantities like
0
'( )
z
Ω
.
In Maple, the way to do this is to
calculate the derivative first, and then take the complex conjugates, etc afterwards, as follows
> Omega0 := C*log(z):
> dOmega0 := diff(Omega0,z):
> dOmega0bar := conjugate(subs(z=conjugate(z),dOmega0)):
It is simplest to derive expressions for
'
Ω
,
'
ω
and
''
Ω
in terms of
0
0
,
ω
Ω
and their derivatives by
hand, and then use this procedure to evaluate the formulas for the stress.
To check your solution, check that the boundary conditions are satisfied on the surface of the half
space.
Then plot the variation of strain energy density and stress along the surface of the halfspace
as a function of
1
/
x
h
.
Show results for both
1
0
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 HUAJIANGAO
 Stress, Energy density, displacement field, Engineering Brown University, Point Force, point force solution

Click to edit the document details