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MIT2_092F09_sol_exam2

# MIT2_092F09_sol_exam2 - 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 #2-solution Instructor: Prof. K. J. Bathe TA: Seounghyun Ham Problem 1 (10 points): s 1 x f 1 x ⎞⎛ y h i = 1 ( 1 y ) ; h i = 1 ⎟⎜ 1 + . 4 2 4 2 ⎠⎝ 2 s 1 s 1 x h i x , = − ( 1 y ) ; h , = − 1 . i y 8 4 2 f 1 y f 1 x h = − 1 + h , = i , x ; i y 1 8 2 8 2 h s 0 h f 0 H (1) = i s ; H (2) = i f . 0 h i 0 h i U T = [ u i v i ] . s h 0 i x (1) , s B = 0 h i y , (2) f f ; B = h i x , h , i y . s s h h i y , , i x 1 2 M (1) = ρ s H (1)T H (1) dV (1) = ρ s ∫∫ H (1)T H (1) dxdy V (1) -1 -2 1 of 3±

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�� 2 2 M (2) = ρ f H (2)T H (2) dV (2) = ρ f ∫∫ H (2)T H (2) dxdy V (2) -2 -2 1 2 K (1) = B (1)T CB (1) dV (1) = ∫∫ B (1)T CB (1) dxdy V (1) -1 -2 2 2 K (2) = B (2)T β B (2) dV (2) = ∫∫ B (2)T β B (2) dxdy V (2) -2 -2 M=M (1) +M (2) ; K=K (1) +K (2) .
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MIT2_092F09_sol_exam2 - 2.092/2.093 FINITE ELEMENT ANALYSIS...

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