APPENDIX A
DISPLACEMENT FIELD EVALUATION FOR AN ANISOTROPIC ELASTIC
SOLID UNDER GENERALIZED PLANE STRAIN CONDITION
- -- dx
f)Cx
STxy+ dx
x +y dy
aTy+ aoydy
Figure A- 1: Forces acting on a rectangular element with dimension dx x dy in equi-
librium condition.
A generalized plane strain condition has been adopted for an anisotropic
solid applicable to that of an FCC single crystal. [6] Let us consider a rectangular
pipe like element with dimension dx, dy, 1. We assume that this body is under
equilibrium under various forces. If body forces are X, Y per unit volume, then the
equation of equilibrium of force along x and y direction can be written as followed,
Along x-axis.
Ix + aXdy dx axdy + TsY + Txydy\ dx Txydx + Xdxdy = 0 (A.1)