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( ( t ) + t E M B E D E q u a t i o n . 3 + E M B E D E q u a t i o n . 3 = f j ( t ) + C j , t ( L j ( j = E M B E D E q u a t i o n . 3 ) ( 1 ) 745AL t - 0DD8:A B>G5: :>=BC@>2 ( j = E M B E D E q u a t i o n . 3 ) . f j ( t ) ( j = E M B E D E q u a t i o n . 3 ) ?@8=OB0 B0:65 2 2845 AB5?5==>3> @O40. H ( j ) ( ( j = E M B E D E q u a t i o n . 3 ) - >?@545;O5BAO 87 CA;>28O =5?@5@K2=>AB8 DC=:F88 f j ( t ) =0 :>=BC@5 L j . 8A. 1 =0;8B8G5A:85 DC=:F88 ( ( z ) 8 ( ( z ) ?@54AB02;5=K 2 2845 A;54CNI8E AB5?5==KE @07;>65=89. E M B E D E q u a t i o n . 3 ( 2 ) Z ( 1 ) ( S ' @8 @5H5=88 MB>9 7040G8 8A?>;L7C5B>1@060NI85 DC=:F88 [ 5 ] . "0:81@07>=5G=>35 4;O >?@545;5=8O :>MDD8F85=B>2 0( 1 ) : , b ( 1 ) : , 5( 1 ) :, q ( 1 ) :, g ( 1 ) :, d ( 1 ) :, f ( 1 ) :, ( 1 ) : , B ( 1 ) :, ( 1 ) : , Q ( 1 ) :, G ( 1 ) :, D ( 1 ) :, F ( 1 ) : ( j = E M B E D E q u a t i o n . 3 ) ?>;CG5=> 1 4 3@C?? A>2>:C?=>AB59 !#. @8 >?@545;5==KE 35>2KE D0:B>@0E , 87 :064>9 ?>;CG5==>9 !# 2K45;O5 =5A:>;L:> ?5@2KE C@02=5=89 8, A>2 @5H0O, =0E>48<K5 25;8G8=K 0( 1 ) : , b ( 1 ) : , 5( 1 ) :, q ( 1 ) :, g ( 1 ) :, d ( 1 ) :, f ( 1 ) :, ( 1 ) : , B ( 1 ) :, ( 1 ) : , Q ( 1 ) :, G ( 1 ) :, D ( 1 ) :, F ( 1 ) : ( j = E M B E D E q u a t i o n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j ( j = E M B E D E q u a t i o n . 3 ) A @048CA0B25@AB88 L j ( j = E M B E D E q u a t i o n . 3 ) :0@B5@ 1;>:5 ?CB52:8 2AB02;5=K F8;8=4@K. =CB@5==85 @048CAK F8;8=4@K ?@8=8<05< 1;87:82>=BC@K 459AB2CNB :CA>G=>- @02=> @0A?@545;5==K5 =03@C7:8 A 8=B5=A82=>ABLN P j ( j = E M B E D E q u a t i o n . 3 ) . 0AAB@5==0O >1;0ABL 872=5 >3@0=8G5=0 ?@OC3>;L=K=BC@>MB>;L7C55 ?@5>1@07>20=88 :0: ?@54K4CI59 7040G8 A2>48BAO : >BKA:0=8N DC=:F89 ( j ( z ( 1 ) ) 8 ( j ( z ( 1 ) ) ( j = E M B E D E q u a t i o n . 3 ) , @53C;O@=KE A>>B25BAB25==> 2 0DD8==> ?@5>1@07>20==KE >1;0ABOE !' j ( j = E M B E D E q u a t i o n . 3 ) . E>45 @5H5=8O 7040G8 ?@5>1@07>20==K5 :>=BC@K L j ' ( j = E M B E D E q u a t i o n . 3 ) >B>1@060NBAO =0 548=8G=KE >:@C6=>ABOE, @0A?>;>65==KE 2> 2A?>30B5;L=KE ?;>A:>ABOE ( j ( j = E M B E D E q u a t i o n . 3 ) . ( j ( t ) + t E M BED Equation.3 + EMBED Equation.3 = fj(t)+Cj , t(Lj (j= EMBED Equation.3 ) (3) (1(t) + t EMBED Equation.3 + EMBED Equation.3 = (j(t) + t EMBED Equation.3 + EMBED Equation.3 Lj (j= EMBED Equation.3 ) (4) EMBED Equation.3 [1 (1(t)-t EMBED Equation.3 - EMBED Equation.3 ]- - EMBED Equation.3 (j(j(t) - t EMBED Equation.3 - E M B E D E q u a t i o n . 3 ) = 2 ( r j , t ( L j ( j = E M B E D E q u a t i o n . 3 ) ( 5 ) 745AL t - 0DD8:A B>G5: :>=BC@>2 L j ( j = E M B E D E q u a t i o n . 3 ) . f j ( t ) ( j = E M B E D E q u a t i o n . 3 ) ?@8=OB0 B0:65 2 2845 AB5?5==>3> @O40 . 8A. 2 =0;8B8G5A:85 DC=:F88 ( ( z ) 8 ( ( z ) ?@54AB02;5=K 2 2845 A;54CNI8E AB5?5==KE @07;>65=89. E M B E D E q u a t i o n . 3 E M B E D E q u a t i o n . 3 Z ( 1 ) ( S ' E M B E D E q u a t i o n . 3 ( j = E M B E D E q u a t i o n . 3 ) , ( 6 ) @8 @5H5=88 8 MB>9 7040G8 B0:65 8A?>;L7C5B>1@060NI85 DC=:F88. "0:81@07>=5G=>35 4;O >?@545;5=8O :>MDD8F85=B>2 0( j ) : , b ( j ) : , ( j ) : , B ( j ) : ( j = E M B E D E q u a t i o n . 3 ) , 5( 1 ) :, q ( 1 ) :, g ( 1 ) :, d ( 1 ) :, f ( 1 ) :, ( 1 ) : , Q ( 1 ) :, G ( 1 ) :, D ( 1 ) :, F ( 1 ) : ( := E M B E D E q u a t i o n . 3 ) ?>;CG5=> 3 8 3@C?? A>2>:C?=>AB59 !# . @8 >?@545;5==KE 35>2KE D0:B>@0E , 87 :064>9 ?>;CG5==>9 !# 2K45;O5 =5A:>;L:> ?5@2KE C@02=5=89 8, A>2 @5H0O, =0E>48 D>@;>A>20- CAE5;8H28;8 [ 1 ] >?@545;ONBAO :>=5=BK =0?@O65=89 2 :064>9 >1;0AB8 CG8BK20O 0DD8==>5 ?@5>1@07>20=85. 5H5=8O 7040G8 2 ?5@2>38G=> =C;52>B>@K<8 87<5=5=8O1AB20 2 ?5@2>E@0=5=K >1>7=0G5=8O 4;O 8A:>MDD8F85=B>2. "0:81@07>?@545;5=8O :>MDD8F85=B>2 ?>;CG5=> 3 8 3@C?? 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". 3 0 9 . ! 1 . !. 1 4 2 1 4 6 . 0;1852 . . ?@545;5=85 =0?@O65==>3> A>AB>O=8O :>;LF52>3> 1@CA0 A H5@>E>20B>ABLN ?@8 :@CG5=88 ( ( "@C4K X X I 564C=0@. :>=D. ?> B5>@88 >1>;>G5: 8 ?;0AB8=. !0@0B>2: !"#, 2 0 0 5 . !. 1 1 1 1 1 3 . K a l b i e v R . K . R E S E A R C H O F D I S T R I B U T I O N O F P R E S S U R E ( V O L T A G E ) I N M A N Y C Y L I N D E R E N G I N E S O F M A C H I N E S I n a u t o m o b i l e 0n d t r a c t o r o f e n g i n e s o f l i q u i d c o o l i n g w i d e l y a p p l y t h e b l o c k a d e s i g n . T h e t o p p a r t o f t h e b l o c k r e p r e s e n t s m u l t i c o h e r e n t a r e a . L e t ' s c o n s i d e r a t a s k a b o u t e l a s t i c b a l a n c e h o m o g e n e o u s o f t h e b l o c k r e p r e s e n t i n g s e v e n - c o h e r e n t a r e a l i m i t e d o u t s i d e t o a r e c t a n g u l a r , a n d f r o m w i t h i n l o c a t e d b y c i r c l e s c l o s e t o c i r c u l a r w i t h i d e n t i c a l r a d i u s e s . T h u s o n e x t e r n a l a n d i n t e r n a l c o n t o u r s t h e p a r t - i n r e g u l a r i n t e r v a l s d i s t r i b u t e d ( p a r t - i n r e g u l a r i n t e r v a l s a l l o c a t e d ) l o a d i n g s w i t h i n t e n s i t y , a c c o r d i n g l y u n d e r t h e c e n t r a l c o r n e r s w o r k . A t g i v e n o f p r e s s u r e i t i s r e q u i r e d t o d e f i n e ( d e t e r m i n e ) a f i e l d o f p r e s s u r e ( v o l t a g e ) i n t h e s p e c i f i e d a r e a s w i t h t h e a c c o u n t b y a r o u g h n e s s . T h e c o n s i d e r e d a r e a f r o m t h e o u t s i d e i s l i m i t e d t o a r e c t a n g u l a r c o n t o u r . I t i s n e c e s s a r y t o n o t e , t h a t t h e a t t i t u d e ( r e l a t i o n ) o f t h e p a r t i e s o f a r e c t a n g u l a r i s t h o s e , t h a t a t 0f i n t r a n s f o r m a t i o n t h e o u t s i d e c o n t o u r p a s s e s t o a s q u a r e . T h e d e c i s i o n o f t h i s t a s k i s r e d u c e d t o s e a r c h o f f u n c t i o n s r e g u l a r a c c o r d i n g l y i n 0f i n t h e t r a n s f o r m e d a r e a s . A t t h e d e c i s i o n a n d t h i s t a s k a l s o i s u s e d d i s p l a y i n g f u n c t i o n s . F u r t h e r u n d e r t h e f o r m u l a >l >s >v 0- u s E5l i s h v i l i t h e c o m p o n e n t s o f p r e s s u r e ( v o l t a g e ) i n e a c h a r e a t a k i n g i n t o a c c o u n t 0f i n t r a n s f o r m a t i o n a r e d e f i n e d ( d e t e r m i n e d ) . A s a r e s u l t o f t h e a n a l y s i s o f c o n s i d e r e d ( e x a m i n e d ) e x a m p l e s i s e s t a b l i s h e d t h a t , i n e l e m e n t s o f a d e s i g n t h a n l e a v e s a n a p e r t u r e f r o m e a c h o t h e r b y t h a t e s s e n t i a l l y d o e s n o t i n f l u e n c e o f c o n c e n t r a t i o n o f p r e s s u r e ( v o l t a g e ) a r o u n d o f t h e s e a p e r t u r e s . W h e n t h e i n f l u e n c e c o m e s n e a r e r t h e s e i s i n c r e a s e d . I n a c a s e , w h e n d i s t a n c e b e t w e e n a p e r t u r e s i s l e s s t h a n h a l f o f r a d i u s o f a p e r t u r e s o f c o n c e n t r a t i o n o f p r e s s u r e ( v o l t a g e ) i s s e l d o m i n c r e a s e d . I n s u c h c a s e t h e r o u g h n e s s i n t e r n a l s u r f a c e s o f a p e r t u r e s e s s e n t i a l l y i n f l u e n c e s i s i n t e n s e - i s d e f o r m e d a c o n d i t i o n o f e l e m e n t s o f a d e s i g n . T h e r e s u l t s o f n u m e r i c a l e x a m p l e s s h o w , t h a t t h e i n f l u e n c e o f a r o u g h n e s s a n d o t h e r d e f e c t s h a s a n e f f e c t i n c r e a s e o f f a c t o r s o f c o n c e n t r a t i o n o f p r e s s u r e ( v o l t a g e ) , t h i s i n f l u e n c e t a k e s p l a c e i n a s u p e r f i c i a l l a y e r n o t e x c e e d i n g o f t h e t r e b l e d s i z e o f t h e m a x i m a l h o l l o w o r l e d g e . F o r a n e s t i m a t i o n o f d u r a b i l i t y u n i t s a n d d e t a i l s a s m u l t i c o h e r e n t b o d i e s i s f o u n d :0A0B5;L=>5 o f p r e s s u r e ( v o l t a g e ) w o r k i n g n e a r t o a r o u g h c o n t o u r . W i t h t h e p u r p o s e o f a c h i e v e m e n t o f t h e g r e a t e s t d u r a b i l i t y i n c o n s i d e r e d ( e x a m i n e d ) c o m p o u n d d e s i g n s f o r t h e g i v e n i n t e r n a l p r e s s u r e , t h e t e c h n i q u e o f d e f i n i t i o n o f o p t i m u m s i z e s a n d i n t e r n a l p r e s s u r e i s c o n s i d e r e d . 0;1852 . . !! ! / / & +% "/% ( 02B>18;L=KE, B@0:B>@=KE,
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