AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

CHAPTER 4
CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK
This thesis demonstrated how to solve an elasticity problem using the Airy
stress function. It showed how the method can be applied to find the stresses and
displacements at any point on a two-dimensional plate subjected to different boundary
conditions. This eventually led to how the Airy stress function can be applied to a two-
phase plate with a circular inclusion in finding the stresses and displacements at any
point.
The problem studied in Chapter 3 further demonstrated how the Airy stress
function is applied to an infinite plate with a circular inclusion. On studying the
graphical representation of the result, it can be seen that all stresses within the inclusion
are constant and the shear stress is zero when subjected to a far-field stress. The
maximum tensile stress occurs at the boundary of the disc intersecting the y-axis and is
decreased along the boundary of the disc as it nears the x-axis. The maximum
compressive stress occurs at the boundary intersecting with the x-axis and decreases as
it nears the y-axis along the interfacing boundary.
thesis:
The following extension is suggested to further exploit the content of the present
a. The boundary conditions can be generalized to include all the stress
components at far fields.
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