MIT2_094S11_quiz1_sol

MIT2_094S11_quiz1_sol - 2.094 FINITE ELEMENT ANALYSIS OF...

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2.094 F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS S PRING 2008 Quiz #1 - Solution Instructor: Prof. K. J. Bathe Date: 04/03/2008 Problem 1 (10 points) The interpolation functions are 23 6 2 11 (1 ) ; ) ; ) 22 hs s h s s h s =+ = −− = 2 3 6 s S = +1 S = -1 Then, () 1 3 1 6 2 3 4 2 S h R hp d h ⎡⎤ ⎛⎞ ⎢⎥ = ⎜⎟ ⎝⎠ ⎣⎦ s -------------------------------------------------------------------------------------------------------------------------------------- Page 1 of 3 Or 2 6 12 4 1; 1 33 9 hy y h y y h y = = 2 3 6 y y = +3/2 y = -3/2 3/2 2 2 3 3/ 6 4 S h R d h = y -------------------------------------------------------------------------------------------------------------------------------------- Actually 2 3 6 2p 2p 8p 2 2 8 S p R p p =
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Problem 2 (10 points) Page 2 of 3 (a) 22 5 15 5 3 5 2 4 (1 )(1 ) 11 1 ) ; ) 44 4 1 ) ; ) 4 hr s h rsh h h h =− =++ =−+ = − −− = + −− 5 1 4 1 4 1 2 34 5 r s +1 +1 -1 -1 -------------------------------------------------------------------------------------------------------------------------------------- Or 5 12 55 99 1 2 21 1 2 ;11 4 3 4 3 1 2 1 2 43 3 4 3 4 hx y h x yh h x h x h x ⎛⎞ ⎜⎟ ⎝⎠ =+ + + = −− = + 1 2 5 x y +1.5 +1.5 -1.5 -1.5 -------------------------------------------------------------------------------------------------------------------------------------- and 1 p h = (b) 3 0 2 3 0 2 J = ⎢ and 1 2 0 3 2 0 3 J = ⎢
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1 1, x V u B h ⎡⎤ = ⎣⎦ and 1 1, 1, 2 3 1 3 1 3 x x u y x
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MIT2_094S11_quiz1_sol - 2.094 FINITE ELEMENT ANALYSIS OF...

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