193 Appendix
Through-thickness
integrals
F o r r e g i o n I , i n t e g r a t i o n o f the product of l a y e r w i s e c u b i c shape f u n c t i o n s can be w r i t t e n a s , nl I = I I;
"128 99 [M]
where
[M] d z = h./1680
-36
19
648 - 8 1 - 3 6 m.
648
99 128^
The
summation
is
carried
out
with
arrangement i n t h e t h i c k n e s s c o - o r d i n a t e .
due
regard
to
the
Other i n t e g r a l s o f the
nodal cu b ic
shape f u n c t i o n s a r e a s f o l l o w s .
[M],
[M] d z = 1/80
-40
-57
57
0
-24
81
7
-24
24
-7
-81
24*
0
-57
57
40
148 -189 5 4 - 1 3 [M]’ [M]’dz = l/40h. T
432-297 sym.
54
432 -189 148
For region the product
of
transformation
II, with reference the global-local of
the
integral
to equation
(9.3a),
integration of
interpolation can be written as of
layerwise
cubic
shape
the
functions,
that is
I k l= 1 i=1 where I
J
[M] T [M] d z {6 i } l h .
denotes the integral of the product of the k-th and l-th terms kI of the global-local interpolation.