ÿþM K - 8
S T A T Y K A U S T R O J Ó W P R T O W Y C H W U J C I U M E S
D l a k r a t o w n i c y p r z e d s t a w i o n e j n a r y s u n k u w y z n a c z y p r z e m i e s z c z e n i a w z Bó w i s i By w p r t a c h
w y w o Ba n e c i |a r e m w Ba s n y m k o n s t r u k c j i .
q s 1 2
q s 1 4
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q s 7
q s 1 q s 5 3
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> w i t h ( L i n e a r A l g e b r a ) :
> m : = 4 ; n : = 1 4 ; e : = 1 1 ; w : = 7 ; # m - w y m i a r w e k t o r a f u n k c j i k s z t a Bt u , n - l i c z b a
w s p ó Br z d n y c h g l o b a l n y c h c a Be j s t r u k t u r y , e - l i c z b a e l e m e n t ó w , w - l i c z b a w z Bó w k r a t o w n i c y
> i n t e r f a c e ( r t a b l e s i z e = n ) :
w e k t o r f u n k c j i k s z t a Bt u d l a p r z e m i e s z c z e D o s i o w y c h ( p u ) i p o p r z e c z n y c h ( p v )
> p u : = V e c t o r ( [ 1 - x / h , 0 , x / h , 0 ] ) ; p v : = V e c t o r ( [ 0 , 1 - x / h , 0 , x / h ] ) ; # h - d Bu g o [
e l e m e n t u
W y z n a c z e n i e m a c i e r z y s z t y w n o [c i K , m a c i e r z y o b r o t u R i w e k t o r a s i B f t y p o w e g o e l e m e n t u p r t o w e g o
h
h
# ëø
" p u " p T öø
u
ìø ÷ø
K = E A ìø d x f = - q 0
õø
+"( s i n ± p u + c o s ± p v ) d x
÷ø
"x "x
!# íø øø
0
0
> p u p r i m : = m a p ( d i f f , p u , x ) ;
> K : = m a p ( i n t , E * A * p u p r i m . T r a n s p o s e ( p u p r i m ) , x = 0 . . h ) ;
> R : = M a t r i x ( [ [ c o s ( a l p h a ) , s i n ( a l p h a ) , 0 , 0 ] , [ - s i n ( a l p h a ) , c o s ( a l p h a ) , 0 , 0 ] ,
[ 0 , 0 , c o s ( a l p h a ) , s i n ( a l p h a ) ] , [ 0 , 0 , - s i n ( a l p h a ) , c o s ( a l p h a ) ] ] ) ;
> f : = - q 0 * m a p ( i n t , s i n ( a l p h a ) * p u + c o s ( a l p h a ) * p v , x = 0 . . h ) ;
W p r o w a d z e n i e d a n y c h o p i s u j c y c h p o s z c z e g ó l n e e l e m e n t y u z u p e Bn i n a p o d s t a w i e r y s u n k u
> d a n e : = t a b l e ( [ 1 = [ 0 , l ] , . . . # t a b l i c a d a n y c h o e l e m e n t a c h : . n u m e r _ e l e m e n t u = [ k t , d Bu g o []
> W : = M a t r i x ( [ [ 1 , 2 , 3 , 4 ] , . . . # m a c i e r z w s k a zn i k ó w w s p ó Br z d n y c h w z Bo w y c h
W y z n a c z e n i e m a c i e r z y s z t y w n o [c i , m a c i e r z y o b r o t u i w e k t o r ó w s i B p o s z c z e g ó l n y c h e l e m e n t ó w
> f o r i t o e d o
K | | i : = e v a l ( K , h = d a n e [ i ] [ 2 ] ) ;
R | | i : = e v a l ( R , a l p h a = d a n e [ i ] [ 1 ] ) ;
f | | i : = e v a l ( f , [ a l p h a = d a n e [ i ] [ 1 ] , h = d a n e [ i ] [ 2 ] ] ) ;
e n d d o :
O b r ó t m a c i e r z y s z t y w n o [c i i w e k t o r ó w s i B p o s z c z e g ó l n y c h e l e m e n t ó w d o u k Ba d u g l o b a l n e g o
K = R T K R f g = R T f
g
> f o r i t o e d o
K g | | i : = T r a n s p o s e ( R | | i ) . K | | i . R | | i ;
f g | | i : = T r a n s p o s e ( R | | i ) . f | | i ;
e n d d o :
Z Bo |e n i e m a c i e r z y s z t y w n o [c i i w e k t o r a s i B c a Be j s t r u k t u r y
e e
T T
K s = K B i f s = f g i
"B i g i "B i
i = 1 i = 1
> f o r i t o e d o B | | i : = M a t r i x ( 4 , n ) e n d d o :
> f o r i t o e d o
f o r j t o m d o B | | i [ j , W [ i , j ] ] : = 1 e n d d o ; # - m a c i e r z e l o g i c z n e
e n d d o ;
> K s : = e v a l ( a d d ( T r a n s p o s e ( B | | i ) . K g | | i . B | | i , i = 1 . . e ) ) : # m a c i e r z s z t y w n o [c i
c a Be j s t r u k t u r y
> f s : = e v a l ( a d d ( T r a n s p o s e ( B | | i ) . f g | | i , i = 1 . . e ) ) ; # w e k t o r s i B c a Be j s t r u k t u r y
R e d u k c j a m a c i e r z y s z t y w n o [c i , w e k t o r a s i B i w e k t o r a p r z e m i e s z c z e D
> K r : = S u b M a t r i x ( K s , [ 3 . . 7 , 9 . . n ] , [ 3 . . 7 , 9 . . n ] ) ; # z r e d u k o w a n a m a c i e r z s z t y w n o [c i
> f r : = S u b V e c t o r ( f s , [ 3 . . 7 , 9 . . n ] ) ; # z r e d u k o w a n y w e k t o r s i B
> q s : = V e c t o r ( n , s y m b o l = q ) : # w e k t o r p r z e m i e s z c z e D w z Bo w y c h c a Be j s t r u k t u r y
> q r : = S u b V e c t o r ( q s , [ 3 . . 7 , 9 . . n ] ) ; # z r e d u k o w a n y w e k t o r p r z e m i e s z c z e D w z Bo w y c h
R o z w i z a n i e u k Ba d u r ó w n a D: K r . w r = f r
> r o z : = s o l v e ( c o n v e r t ( K r . q r - f r , s e t ) , c o n v e r t ( q r , s e t ) ) ;
> a s s i g n ( r o z ) ;
> q [ 1 ] , q [ 2 ] , q [ 8 ] : = 0 , 0 , 0 ; # w i z y n a Bo |o n e n a u k Ba d
> q s : = V e c t o r ( [ s e q ( q [ i ] , i = 1 . . n ) ] ) : # w e k t o r w y l i c z o n y c h p r z e m i e s z c z e D w z Bo w y c h
W y l i c z e n i e s i B w p o s z c z e g ó l n y c h p r t a c h ( r o z w i z a n i e s y m b o l i c z n e )
f i = K i R i B i q s
> f o r i t o e d o
f | | i : = s i m p l i f y ( K | | i . R | | i . B | | i . q s ) :
e n d d o :
D a n e l i c z b o w e
> A : = 0 . 0 0 1 ; g : = 9 . 8 1 ; r h o : = 8 0 0 0 ; q 0 : = r h o * g * A ; E : = 2 e 1 1 ; l : = 1 ;
W a r t o [c i s i B w p o s z c z e g ó l n y c h p r t a c h
> f o r i t o e d o e v a l f ( f | | i [ 3 ] ) ; e n d d o ;
W i z u a l i z a c j a w y n i k ó w
> q p : = e v a l f ( 1 0 0 0 0 * q s ) : # p r z e s k a l o w a n y w e k t o r p r z e m i e s z c z e D w z Bo w y c h
G e o m e t r i a k r a t o w n i c y ( w s p ó Br z d n e p o s z c z e g ó l n y c h w z Bó w )
> P 1 : = [ 0 , 0 ] ; P 2 : = [ l , 0 ] ; P 3 : = [ 2 * l , 0 ] ; P 4 : = [ 3 * l , 0 ] ; P 5 : = [ l / 2 , l * s q r t ( 3 ) / 2 ] ;
P 6 : = [ 3 / 2 , l * s q r t ( 3 ) / 2 ] ; P 7 : = [ 5 / 2 , l * s q r t ( 3 ) / 2 ] ;
R y s u n e k k r a t o w n i c y p r z e d o b c i |e n i e m
> q 1 : = p l o t ( [ [ P 1 , P 2 ] , [ P 2 , P 3 ] , [ P 3 , P 4 ] , [ P 1 , P 5 ] , [ P 2 , P 5 ] , [ P 2 , P 6 ] , [ P 3 , P 6 ] ,
[ P 3 , P 7 ] , [ P 5 , P 6 ] , [ P 6 , P 7 ] , [ P 4 , P 7 ] ] , c o l o r = r e d , a x e s = n o n e , s c a l i n g = c o n s t r a i n
e d ) :
D o d a n i e p r z e m i e s z c z e D p o s z c z e g ó l n y c h w z Bó w d o i c h w s p ó Br z d n y c h
> j : = 0 :
f o r i t o w d o
P | | i [ 1 ] : = P | | i [ 1 ] + q p [ i + j ] :
P | | i [ 2 ] : = P | | i [ 2 ] + q p [ i + 1 + j ] :
j : = j + 1 :
e n d d o :
R y s u n e k k r a t o w n i c y p o o b c i |e n i u
> q 2 : = p l o t ( [ [ P 1 , P 2 ] , [ P 2 , P 3 ] , [ P 3 , P 4 ] , [ P 1 , P 5 ] , [ P 2 , P 5 ] , [ P 2 , P 6 ] ,
[ P 3 , P 6 ] , [ P 3 , P 7 ] , [ P 5 , P 6 ] , [ P 6 , P 7 ] , [ P 4 , P 7 ] ] , c o l o r = b l u e , a x e s = n o n e ,
s c a l i n g = c o n s t r a i n e d ) :
> p l o t s [ d i s p l a y ] ( { q 1 , q 2 } ) ;
> u n a s s i g n ( ' q ' ) ;
Z a d a n i e
W y l i c z y p r z e m i e s z c z e n i a w z Bó w i s i By w p r t a c h k r a t o w n i c y z a m o c o w a n e j n a o b u p o d p o r a c h
n i e p r z e s u w n y c h . K r a t o w n i c a o b c i |o n a j e s t c i |a r e m w Ba s n y m ( w a r t o [ q 0 j a k w p o p r z e d n i m z a d a n i u )
o r a z s i B s k u p i o n o w a r t o [c i P = 1 0 0 0 N , p r z y Bo |o n d o w z Ba I I .
q s 1 2
q s 1 4
q s 1 0
V I
1 0 1 1 V I I
V
q s 9 q s 1 1
q s 1 3
6 8 9
5 7
4
q s 4
q s 6
q s 8
q s 2
I V
I
q s 7
q s 1 q s 5 3
q s 3
1 2
I I I I I
P
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