It is possible now to consider the case of general
deformation, and to go beyond the WNA.
Given a general
deformation
we should project out (subtract) all the special
components, leaving the normal component,
and only then apply the WNA.
In Fig. 4.8 we demonstrate
this decomposition for the deformation
(CO + W16) and the deformation SX.
Here and elsewhere, all boundary deformation function integrals
(of the form (4.5)) are evaluated using the technique
of Appendix G.
The special deformations constitute a linear space
which is spanned by the basis functions: one dilation, translations,
and
rotations.
(For
they are listed in Table 3.2).
For a general cavity shape these basis functions are not orthogonal.
However, because they are linearly independent,
we can use standard linear algebra to build an orthonormal
basis
of special deformations.
The special (
) and the normal (
) components of any given
deformation
are therefore