U S I N G M O V I N G L E A S T S Q U A R E S A P P R O X I M A T I O N F U N C T I O N I N T H E F I N I T E V O L U M E M E T H O D F O R T H E C A L C U L A T I O N O F T H E S T R E S S I N T E N S I T Y F A C T O R O F T H E C R A C K E D B E N D I N G

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A m r a e i A.; F a l l a h N.

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Journal: Sharif Journal of Civil Engineering Year:2019 | Volume:35-2 | Issue:2.2 Page(s): 3-15

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Title

U S I N G M O V I N G L E A S T S Q U A R E S A P P R O X I M A T I O N F U N C T I O N I N T H E F I N I T E V O L U M E M E T H O D F O R T H E C A L C U L A T I O N O F T H E S T R E S S I N T E N S I T Y F A C T O R O F T H E C R A C K E D B E N D I N G

Author(s)

A m r a e i A. | F a l l a h N. | Issue Writer Certificate

Keywords

Reissner cracked plateQ1

stress intensity factorQ2

moving least squaresQ1

Abstract

D u e t o c y c l i c n a t u r e o f a p p l i e d p r e s s u r e o n e n g i n e e r i n g s t r u c t u r e s l i k e a i r p l a n e f u s e l a g e s, s t o r a g e t a n k s, a n d s h i p h u l l s, m e m b e r s e v o l v i n g t h e t h r o u g h c r a c k, r e s u l t s i n t h e s u d d e n f a i l u r e; s o-c a l l e d a s f a t i g u e f r a c t u r e. I n v e s t i g a t i o n o f t h i s t y p e o f f r a c t u r e i s a n i m p o r t a n t i s s u e f o r a s u c c e s s f u l d e s i g n o f t h e s e s t r u c t u r e s. O n t h e o t h e r h a n d, t h e f i n i t e v o l u m e m e t h o d (F V M) a s a w e l l-k n o w n m e t h o d i n t h e c o m p u t a t i o n a l m e c h a n i c s, i s f o u n d a s a p o w e r f u l m e t h o d f o r t h e b e n d i n g a n a l y s i s o f b e a m s a n d p l a t e s, w i t h n o m a t t e r o f t h i c k n e s s v a r i e s f r o m v e r y t h i n t o m o d e r a t e l y t h i c k b e a m s a n d p l a t e s. U s u a l l y i n t h i s m e t h o d, a c c o r d i n g t o t h e c l a s s i c a p p r o x i m a t i o n o f t h e f i e l d v a r i a b l e s, t h e d i s p l a c e m e n t a t a f a v o r i t e p o i n t o n t h e f a c e o f c o n t r o l v o l u m e i s a p p r o x i m a t e d l i n e a r l y i n t e r m s o f d i s p l a c e m e n t o f c e l l c e n t e r s a d j a c e n t t o t h a t f a c e. H o w e v e r, a c c u r a c y o f t h e a p p r o x i m a t i o n c a n b e i n c r e a s e d b y u s i n g o f t h e h i g h e r-o r d e r a p p r o x i m a t i o n t e c h n i q u e s l i k e M o v i n g L e a s t S q u a r e s (M L S) a p p r o x i m a t i o n w h i c h i s w e l l s u i t e d i n t h e m e s h f r e e m e t h o d s. I n t h i s r e s e a r c h t h e M L S a p p r o x i m a t i o n i s u s e d i n t h e f i n i t e v o l u m e m e t h o d, a n d t h e R e i s s n e r p l a t e w i t h a t h r o u g h-t h e-t h i c k n e s s c r a c k (t h r o u g h c r a c k) i s a n a l y z e d f o r t h e c o m p u t a t i o n o f t h e s t r e s s i n t e n s i t y f a c t o r s (S I F s) a t t h e c r a c k t i p. F i r s t, t h e i n f l u e n c e o f t h e s i z e o f s u p p o r t d o m a i n a s o n e o f t h e k e y p a r a m e t e r o f t h e M L S a p p r o x i m a t i o n i s i n v e s t i g a t e d. B y u s i n g o f t h e o b t a i n e d v a l u e o f t h e s u p p o r t d o m a i n s i z e, t h e S I F v a l u e s o f s e v e r a l b e n c h m a r k c r a c k e d p l a t e s a r e c a l c u l a t e d. T h e o b t a i n e d r e s u l t s c o m p a r e d w i t h t h e v a l u e s o b t a i n e d b y t h e o t h e r a n a l y t i c a l a n d n u m e r i c a l m e t h o d s p r e s e n t e d i n l i t e r a t u r e w h e r e g o o d a g r e e m e n t c a n b e s e e n. T h e s e c o m p a r i s o n s i n d i c a t e t h e c a p a b i l i t y o f t h e p r e s e n t e d F V M f o r s t u d y i n g o f t h e c r a c k e d p l a t e s. F u r t h e r m o r e, t h e s i z e o f s u p p o r t d o m a i n f o u n d i n t h i s r e s e a r c h c a n b e c o n s i d e r e d a s t h e c o n v e n i e n t v a l u e s f o r t h e F V M a n a l y s i s o f c r a c k e d p l a t e i n t h e f u t u r e r e s e a r c h e s.

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APA: Copy

A‌m‌r‌a‌e‌i, A., & F‌a‌l‌l‌a‌h, N.. (2019). U‌S‌I‌N‌G M‌O‌V‌I‌N‌G L‌E‌A‌S‌T S‌Q‌U‌A‌R‌E‌S A‌P‌P‌R‌O‌X‌I‌M‌A‌T‌I‌O‌N F‌U‌N‌C‌T‌I‌O‌N I‌N T‌H‌E F‌I‌N‌I‌T‌E V‌O‌L‌U‌M‌E M‌E‌T‌H‌O‌D F‌O‌R T‌H‌E C‌A‌L‌C‌U‌L‌A‌T‌I‌O‌N O‌F T‌H‌E S‌T‌R‌E‌S‌S I‌N‌T‌E‌N‌S‌I‌T‌Y F‌A‌C‌T‌O‌R O‌F T‌H‌E C‌R‌A‌C‌K‌E‌D B‌E‌N‌D‌I‌N‌G. SHARIF: CIVIL ENINEERING, 35-2(2.2 ), 3-15. SID. https://sid.ir/paper/127902/en

Vancouver: Copy

A‌m‌r‌a‌e‌i A., F‌a‌l‌l‌a‌h N.. U‌S‌I‌N‌G M‌O‌V‌I‌N‌G L‌E‌A‌S‌T S‌Q‌U‌A‌R‌E‌S A‌P‌P‌R‌O‌X‌I‌M‌A‌T‌I‌O‌N F‌U‌N‌C‌T‌I‌O‌N I‌N T‌H‌E F‌I‌N‌I‌T‌E V‌O‌L‌U‌M‌E M‌E‌T‌H‌O‌D F‌O‌R T‌H‌E C‌A‌L‌C‌U‌L‌A‌T‌I‌O‌N O‌F T‌H‌E S‌T‌R‌E‌S‌S I‌N‌T‌E‌N‌S‌I‌T‌Y F‌A‌C‌T‌O‌R O‌F T‌H‌E C‌R‌A‌C‌K‌E‌D B‌E‌N‌D‌I‌N‌G. SHARIF: CIVIL ENINEERING[Internet]. 2019;35-2(2.2 ):3-15. Available from: https://sid.ir/paper/127902/en

IEEE: Copy

A. A‌m‌r‌a‌e‌i, and N. F‌a‌l‌l‌a‌h, “U‌S‌I‌N‌G M‌O‌V‌I‌N‌G L‌E‌A‌S‌T S‌Q‌U‌A‌R‌E‌S A‌P‌P‌R‌O‌X‌I‌M‌A‌T‌I‌O‌N F‌U‌N‌C‌T‌I‌O‌N I‌N T‌H‌E F‌I‌N‌I‌T‌E V‌O‌L‌U‌M‌E M‌E‌T‌H‌O‌D F‌O‌R T‌H‌E C‌A‌L‌C‌U‌L‌A‌T‌I‌O‌N O‌F T‌H‌E S‌T‌R‌E‌S‌S I‌N‌T‌E‌N‌S‌I‌T‌Y F‌A‌C‌T‌O‌R O‌F T‌H‌E C‌R‌A‌C‌K‌E‌D B‌E‌N‌D‌I‌N‌G,” SHARIF: CIVIL ENINEERING, vol. 35-2, no. 2.2 , pp. 3–15, 2019, [Online]. Available: https://sid.ir/paper/127902/en

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