Design and Analysis of Laminates: Special Cases and Symmetry
Explore the design and analysis of laminates with special cases and symmetry, presented by Dr. Autar Kaw from the University of South Florida. Learn about different laminate configurations and their properties for composite materials.
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Presentation Transcript
Chapter 5 Design and Analysis of Laminates Special Cases of Laminates Dr. Autar Kaw Department of Mechanical Engineering University of South Florida, Tampa, FL 33620 Courtesy of the Textbook Mechanics of Composite Materials by Kaw
0 [ / 30 / 60 S] 0 x N A A A 0 11 12 16 x = 0 y N A A A 30 12 22 26 y 0 xy N A A A 16 26 66 xy 60 30 M D D D 11 12 16 x x 0 = M D D D 12 22 26 y y M D D D 16 26 66 xy xy
0 [ / 90 / 0 / 90 ] 2 0 90 0 N 0 0 A A B B x 11 12 11 12 x 0 N 0 0 A 0 A B B 90 y 12 22 0 12 0 22 0 y 0 N A B xy 66 0 66 0 xy = 0 M B B D D x 11 12 11 12 x 90 M 0 0 B B D D y 12 0 22 0 12 0 22 0 y M B D xy 66 66 xy
If laminates consistes of an even number of plies : -40 = A = 0 A 40 16 26 -40 40 If laminates consistes of number odd an of plies : [ 40 / 40 / 40 / 40 ] Laminate = B symmetric, is [ A ] , 0 A and D , , , 0 D 16 26 16 26
[ 45 / 60 / 60 / 45 ] 45 0 N 0 A A B B B x 11 12 11 12 16 x 0 60 N 0 A 0 A B B B y 12 22 0 12 22 26 y 0 -60 N A B B B xy 66 16 26 66 0 xy = M B B B D D -45 x 11 12 16 11 12 x M 0 B B B D D y 12 22 26 12 0 22 0 y M B B B D xy 16 26 66 66 xy
30 [ / 40 / 30 / 30 / 30 / 40 ] 30 40 0 N 0 A A B B B x 11 12 11 12 16 x 0 -30 N 0 A 0 A B B B y 12 22 0 12 22 26 y 0 N 30 A B B B xy 66 16 26 66 xy = M B B B D D D -30 x 11 12 16 11 12 16 x M B B B D D D y 12 22 26 12 22 26 y -40 M B B B D D D xy 16 26 66 16 26 66 xy
E E 1 0 2 2 1 - - 0 0 0 E E 1 A B = 0 h, = 0 0 0 , 2 2 1 - 0 - 0 0 0 0 E + 1 ( 2 ) E E 0 2 2 12 1 ( E ) 12 1 ( ) - - E D = 3 0 h 2 2 12 1 ( ) 12 1 ( ) - - E 0 0 + 24 1 ( )
Examples : = A A 11 22 , 0 [ / 60 ], = = , 0 and A A 16 26 0 [ / 45 / 90 ] and , S A A = 11 12 A 0 [ / 36 / 72 / 36 / 72 ] 66 2
