steel plate analysis by finite elements
TRANSCRIPT
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7/23/2019 Steel Plate Analysis by Finite Elements
1/8
S t e e l P l a t e A n a l y s i s by F i n i t e E l e m e n t s
NORMAN
L.
FIRKINS
T H E F IN I T E E L E M E N T method is becoming a popul ar as
w e l l
as
p r a c t i c a l
way of
a n a l y z i n g p l a t e s , s h e l ls ,
and
r e l a t e d s t r u c t u r e s .
The
t e c h n i q u e
of
m o d e l i n g *
an
elast ic
s t r u c t u r e i n t o an a s s e m b l a g e of d is c r e t e b a r s or sect ions
a n d i n t e r c o n n e c t i n g t h e s e e l e m e n t sby a f in i te num berof
jo in ts or n o d a l p o i n t s is not n e w .
1
Theg r o w t h and de
v e l o p m e n t
of
t h e f in it e e l e m e n t m e t h o d
has
b e e n g r e a t l y
e n h a n c e d by theh i g h s p e e d d i g i t a l c o m p u t e r and m a t r i x
m e t h o d sins t r u c t u r a l m e c h a n i c s .
E x t e n d e d f i n i t e e l e m e n t f o r m u l a t i o n
is
b e i n g c a r r i e d
o n
to
i n c r e a s e
the
p o t e n t i a l
of
t h i s m e t h o d
in the
a r e a s
of p last ici ty , v ibrat ion ,
and
t h r e e - d i m e n s i o n a l s t re s s
a p p l i c a t i o n s .
A l t h o u g h c o n t i n u o u s i n v e s t i g a t i o n
is
b e i n g u n d e r
t a k e n ,
it
m i g h t
be in
o r d e r
to
r e v i e w
the
ba sic finite
e l e m e n t f o r m u l a t i o n
and
p r o v i d e
a
si m p l if i e d m e t h o d
of
e v a l u a t i o n
for the
p r a c t i c i n g e n g i n e e r .
ELEMENT CHARACTERISTICS
I n o r d e r toa n a l y z e ande x p r e s sthee l e m e n t p r o p e r t i e sin
m a t r i x f o r m , c e r t a i n c h a r a c t e r i s t i c s
2
of ane l a s t ic e l e m e n t
m u s t be a s s u m e d , i.e., the m a t e r i a l m a k i n g up the
e l e m e n t m u s t be i s o t r o p i c and h o m o g e n e o u s ; H o o k e ' s
L a w and S a i n t V e n a n t c o m p a t i b i li t y e q u a t i o n s a p p l y
u n d e r s m a l l d e f l e c t i o n t h e o r y .
U s i n g
the
c o o r d i n a t e s
of the
a s s u m e d e l e m e n t
con
figuration in
Fig. 1, the
a r e a
of the
e l e m e n t
may b
e x p r e s s e d
in
d e t e r m i n a t e f o rm
as
A
=V