Page 196 - Finite Element Analysis with ANSYS Workbench

10.1 Basic Equations 187

These six stress components depend on the six strain
components and temperature. The six strain components are func-
tions of the three displacement components ,u ,v w in the ,x ,y

z directions, respectively. The three displacement components are
solved from the three governing differential equations above.

10.1.2 Related Equations

Boundary conditions for heat transfer problem are: (a)
specified temperature, (b) specified surface heating, (c) surface
convection, and (4) surface radiation. Details of these boundary
conditions are provided in chapter 9.
Boundary conditions for stress analysis of solid pro-
blem are: (a) specified displacements, and (b) specified tractions on
the solid surface. Details of these boundary conditions are
described in chapter 6.
The basic unknowns of the solid problem are the three
displacement components ,u ,v w which are solved from the three
governing differential equations. Since the differential equations
are written in forms of the stress components, the relations between
the stress and displacement components must be provided.
The six stress components can be written in forms of
the six strain components as,

      0 
C



(6 1) (6 6) (6 1)
T

where       xy  xz  
yz 

x
z
y
C
The matrix  is the material elasticity matrix. The total and
thermal strain components are,
  T      xy  xz  

yz 
x
z
y
 T     T    T   T 000  

0

where  is the coefficient of thermal expansion and T is the
difference between the temperature and reference temperature T
ref
for zero stress,
 T  T (, , )  x y z T ref