AXISYMMETRIC BENDING OF CIRCULAR SANDWICH PLATE ON ELASTIC FOUNDATION WITH COMPLICATED STRUCTURE - Sergey Mikhaylovich Ayzikovich; Sergey Sergeyevich Volkov; Avetik Vardanovich Melkonyan (Advanced Engineering Research, 2014)
T h e a p p r o xim a t e clo s e d - fo r m s olu tio n t o t h e p r o ble m o n a cir c ula r m ultila y e r ( s a n d wic h ) c o n s t a n t -t hic k n e s s pla t e b e n din g o n a n ela s tic fo u n d a tio n wit h a c o m plic a t e d s tr u c t u r e is o b t ain e d. T h e pla t e is b e n t u n d e r t h e a xis y m m e t ric dis trib u t e d lo a d , a n d t h e fo u n d a tio n r e a c tio n . T h e ela s tic fo u n d a tio n is a u nifo r mly ir r e g ula r in t hic k n e s s la y e r ( c o a tin g ) b a s e d o n a h o m o g e n e o u s h alf- s p a c e ( s u b s tr a t e ). Y o u n g’s m o d ulu s v alu e a t t h e in t e rf a c e o f t h e c o a tin g a n d t h e s u b s tr a t e h a s a sig nific a n t le a p. T w o diff e r e n t c a s e s o f t h e b o u n d a r y c o n ditio n s a r e c o n sid e r e d f o r t h e pla t e : fix e d a n d fr e e e d g e c o n ditio n s . T h e c o n s t r u c t e d a p p r o xim a t e a n aly tic al s olu tio n t o t h e p r o ble m is e ff e c tiv e f o r a wid e r a n g e o f b o t h g e o m e t ric ( t h e in h o m o g e n e o u s la y e r t hic k n e s s a n d t h e pla t e r a diu s ) a n d p h y sic al p a r a m e t e r s ( pla t e fle xibilit y , a n d ela s tic p r o p e r tie s o f t h e c o a tin g a n d t h e s u b s t r a t e ). T h e c o n t a c t p r o ble m is r e d u c e d t o t h e s y s t e m o f t h e in t e g r o diff e r e n tial e q u a tio n s olu tio n t h r o u g h t h e in t e g r al tr a n s fo r m a tio n m e t h o d . T h e o b t ain e d fo r m ula s c a n b e u s e d fo r c alc ula tin g t h e c o n t a c t in t e r a c tio n c h a r a c t e ris tic s b e t w e e n a m ultila y e r pla t e a n d a f o u n d a tio n wit h a c o m ple x s t r u c t u r e in v a rio u s c a s e s o f t h e b o u n d a r y c o n ditio n s, a n d v a rio u s lo a d s a p plie d t o t h e pla t e.