MIT2_092F09_sol_exam1

MIT2_092F09_sol_exam1 - 2.092/2.093 FINITE ELEMENT ANALYSIS...

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2.092/2.093± F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS F ALL 2009± Quiz #1-solution Instructor: Prof. K. J. Bathe TA: Seounghyun Ham Problem 1 (10 points): a) (1) (1) x x u (x)=H U= 1- 0 U 60 60 (2) (2) x x u (x)=H U= 0 1- U 100 100 where [ ] T 1 2 3 U= U U U Therefore, (1) x x H = 1- 0 60 60 (2) x x H = 0 1- 100 100 b) (1) (1) u 1 1 ε (x)= = H U= - x x 60 60 (2) (2) u 1 ε (x)= = H U= 0 - x x 100 (1) 0 U B U = (2) 1 U=B U 100
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1 - x=60± x=60 60 (1)± 60 E - 60 60 0 (4- 20 ) dx K (1) = B (1)T CB (1) dV (1) = B (1)T CB (1) A (1) (x)dx = 1 1 1 x 2 V x=0 x=0 0 0 x=100± x=100 (2) (2)T (2)
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MIT2_092F09_sol_exam1 - 2.092/2.093 FINITE ELEMENT ANALYSIS...

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