4020-F2011-HW5Solutions - 1 MSE 4020 HW5-SOLUTION...

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Unformatted text preview: 1 MSE 4020 HW5-SOLUTION 10/03/2011 Problem 1 (a) x axis corresponds to index 1, and y axis corresponds to index 2. Thus, only ! 12 " Thus, ! 11 ! 22 ! 33 ! 23 ! 13 ! 12 " # $ $ $ $ $ $ $ $ $ % & ' ' ' ' ' ' ' ' ' = ! 12 " # $ $ $ $ $ $ $ % & ' ' ' ' ' ' ' = C 11 C 12 C 12 C 12 C 11 C 12 C 12 C 12 C 11 C 44 C 44 C 44 " # $ $ $ $ $ $ $ $ $ % & ' ' ' ' ' ' ' ' ' ( 11 ( 22 ( 33 ) 23 ) 13 ) 12 " # $ $ $ $ $ $ $ $ $ % & ' ' ' ' ' ' ' ' ' * ! 12 = C 44 + ) 12 * G = ! 12 ) 12 = C 44 (b) Stress and state in unrotated coordinate system, ! ! = ! 12 ! 12 " # $ $ $ $ % & ' ' ' ' , ! ( = ) 2 ) 2 " # $ $ $ $ $ $ $ % & ' ' ' ' ' ' ' After transformation to the new coordinate system, it becomes, ! ! ' = " ! !" # 1 = 2 2 2 2 # 2 2 2 2 1 $ % & & & & & & & & ' ( ) ) ) ) ) ) ) ) ! 12 ! 12 $ % & & & & ' ( ) ) ) ) 2 2 # 2 2 2 2 2 2 1 $ % & & & & & & & & ' ( ) ) ) ) ) ) ) ) = #! 12 ! 12 $ % & & & & ' ( ) ) ) ) Similarly for the strain after transformation, 2 ! ' = " ! " # 1 = 2 2 2 2 # 2 2 2 2 1 $ % & & & & & & & & ' ( ) ) ) ) ) ) ) ) * 2 * 2 $ % & & & & & & & ' ( ) ) ) ) ) ) ) 2 2 # 2 2 2 2 2 2 1 $ % & & & & & & & & ' ( ) ) ) ) ) ) ) ) = # * 2 * 2 $ % & & & & & & & ' ( ) ) ) ) ) ) ) In the new coordinate system, using Nye notation gives that !" 12 " 12 # $ % % % % % % % % & ' ( ( ( ( ( ( ( ( == C 11...
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This note was uploaded on 12/05/2011 for the course MSE 4020 at Cornell University (Engineering School).

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4020-F2011-HW5Solutions - 1 MSE 4020 HW5-SOLUTION...

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