Macromechanical Analysis of a Lamina Engineering Constants
Explore the application of stresses to find engineering constants of an angle lamina in the field of composite materials engineering, as presented by Dr. Autar Kaw from the University of South Florida. This detailed analysis covers various aspects of lamina behavior and properties.
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Presentation Transcript
Chapter 2 MacromechanicalAnalysis of a Lamina Engineering Constants Part 6 Dr. AutarKaw Department of Mechanical Engineering University of South Florida, Tampa, FL 33620 Courtesy of the Textbook Mechanics of Composite Materials by Kaw
= = 0 0 0 , , x y xy S S S 11 12 16 x x 0 = S S S y y 12 22 26 0 S S S xy 16 26 66 xy (a) FIGURE 2.23 Application of stresses to find engineering constants of an angle lamina
= S = = S S y x 12 x x x 16 xy 11 S 1 1 1 y 12 = x = x = E xy x m E E S S S 1 1 x x 16 xy 11 x 11
= = 0 0 0 , , x y xy 0 S S S 11 12 16 x x = S S S y y 12 22 26 0 S S S xy 16 26 66 xy (b) FIGURE 2.23 Application of stresses to find engineering constants of an angle lamina
= = S S = S y y y 22 26 xy x y 12 1 S 1 1 y = x E 12 = y = y yx S m E E S S y 22 1 1 y 26 xy y 22 yx xy = E E y x
= = 0 0 0 , , x y xy 0 S S S 11 12 16 x x 0 = S S S y y 12 22 26 S S S xy 16 26 66 xy (c) FIGURE 2.23 Application of stresses to find engineering constants of an angle lamina
y S = = = S S xy 26 xy x xy 66 xy 16 1 1 1 1 1 xy xy = = = = xy = G m E E m E E xy S S S 1 1 1 1 x x y y 16 26 xy 66
S S S 11 12 16 x x = 1 S S S m y y 12 22 26 xy x E E E 1 x x S S S xy 16 26 66 xy x x 1 m xy y = y y E E E y 1 x xy xy 1 m m x y G E E 1 xy 1
1 = S 11 Ex ( ) 4 2 2 4 2 = + + + S c S S s c S s 11 12 66 22 1 1 2 1 12 4 2 2 4 = + + c s c s G E E E 1 1 2 12
1 = S 22 Ey 4 2 2 4 2 ( ) = + S + + S s S c s S c 11 66 22 12 1 2 1 1 12 4 2 2 4 = + + + s c s c G E E E 1 1 2 12
1 = S 66 Gxy ( ) ( ) 2 2 4 4 2 2 2 4 = + + + S S S S s c S s c 11 22 12 66 66 2 2 4 1 1 ( ) + + 2 2 4 4 2 12 = + + s c s c E E G G E 1 12 2 1 12
= mx E S 1 16 1 c ( ) ( ) 3 3 2 2 2 2 = sc S s S S S S S E 11 12 66 12 66 22 2 2 1 2 2 1 12 12 3 3 = + s + + c c s E 1 G G E E E E 1 1 2 1 12 12
= my E S 1 26 ( ) ( ) 3 3 2 2 2 2 = c s S S S s S S S c E 1 11 12 66 22 12 66 2 2 1 2 2 1 + 12 12 3 3 = c+ + s s c E 1 G G E E E E 1 1 2 1 12 12
