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Unformatted text preview: AE 321 Homework 6 Solution 1. (a) Given: z y x 3 2 z y x x E 3 2 x x x x E x x x E 6 5 6 5 1 x x E x x E 5 6 6 where the slope is 5 6 6 E . (b) assumptions: linear, elastic, isotropic, homogeneous 2 2 2 1 2 1 1 1 2 1 2 1 kk ij ij kk ii ij ij kk ij ij ij ij ij E E W E E E E W 2. For a linearly elastic isotropic material starting from kk ij ij ij 2 (4.1) show that E ij 1 ij ij kk (4.2) To this end, we first determine kk in terms of kk from (4.1) by setting k j i to yield 2 3 3 2 kk kk kk kk kk kk 2 3 1 (4.3) Now by solving (4.1) for ij and substituting from (4.3), we obtain the inverse form of the and substituting from (4....
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 Spring '08
 Dutton,J

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