1 . 4 G e n e r a l r e v i e w o f modern p l a t e t h e o r i e s The i n c r e a s i n g u s e o f l a m i n a t e d c o m p o s i t e m a t e r i a l s i n d i f f e r e n t branches o f engineering s t i m u l a t e s
the
advances i n the a n a l y s i s o f
l a m i n a t e d beams a n d p l a t e s . E x t e n s i v e r e s e a r c h h a s b e e n c o n d u c t e d i n t h e t h e o r e t i c a l d e v e l o p m e n t s o f new p l a t e t h e o r i e s and , c o n s e q u e n t l y , many i n t e r e s t i n g a p p r o a c h e s have b e e n d e v e l o p e d d u r i n g t h e l a s t decade.
No
a t t e m p t i s made t o r e v i e w modern p l a t e t h e o r i e s i n t h i s b r i e f s e c t i o n . 〔 A literature review in modern plate theories would entail in itself a major piece of work ！ Comprehensive r e v i e w s o f t h e d e v e l o p m e n t s i n t h e a n a l y s i s o f l a m i n a t e d p l a t e s have b e e n r e c e n t l y summarized b y K a p a n i a
et.al description
of plate theories, which are of relevance to this thesis,
is given below. Many of categories,
the existing modern plate namely,
(1) single-layer
theories fall
theory
(SLT)
and
into
two major
(2)
layerwise
expanded
in power
theory (LT). In
the
SLT,
series of the
the
displacement
thickness
components
coordinate
are
z , giving
u(x,y,z) = iio(x,y) +
(x,y) -z + u 2 (x，y”z2 + u 3 (x,y)*z3 + ....
v(x，y,z) = v 0 (x,y) +
(x,y) »2 + v 2 (x，y”z2 + v 3 (x,y)*z3 +• …
w ( x , y , z ) = w o ( x , y ) + w) ( x , y )
(1.1)
2 + w 2 (x’y) .z +. …
The h i g h e s t d e g r e e o f t h e c o o r d i n a t e
z i n the s e r i e s determines the
order o f the corresponding theory. F o r high-order theories, p l a t e s are p h y s i c a l l y t r e a t e d a s 3 - D e l a s t i c b o d i e s . A l l s i x components o f s t r a i n s are
taken
into
consideration.
For
low-order
theories,
however,
t r a n s v e r s e n o r m a l s t r a i n i s u s u a l l y n e g l e c t e d and o n l y t h e o t h e r f i v e s t r a i n components a r e c o n s i d e r e d . A n e x a m p l e o f t h i s i s t h e w e l l - k n o w n f i r s t - o r d e r shear d e f o r m a t i o n t h e o r y due t o H i n d i i n and R e i s s n e r . F o r this
theory,
the
displacement
functions
involve
five
independent
v a r i a b l e s , n a m e l y , t h r e e m i d - p l a n e d i s p l a c e m e n t s a n d two r o t a t i o n s , t h a t is u ( x , y , z ) = u o ( x , y ) + z • (p^ix.y)
v(x,y,2) = vo(x，y) + z • ^ ( x ^ )
(1.2)