MIT2_094S11_quiz2_sol

# MIT2_094S11_quiz2_so - 2.094 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS SPRING 2008 Quiz#2 Solution Instructor Prof K J Bathe Date Problem 1(10

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2.094 F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS S PRING 2008 Quiz #2 - Solution Instructor: Prof. K. J. Bathe Date: 05/13/2008 Problem 1 (10 points) a) 0 73 4 cos30 sin 30 7 / 6 0 12 9 sin 30 0 8 / 9 74 3 12 9 t X °− ° ⎡⎤ == ⎢⎥ °° ⎣⎦ b) () 00 0 2 0 13 0 11 72 17 22 0 162 tt t t T XXI U I ε =− = = 0 13 13 10 0 72 72 01 0 1 7 1 7 162 162 001 / 2 t SE E ⎛⎞ ⎜⎟ −− ⎝⎠ c) 0 0 4 1 3 7 0 12 9 72 12 12 17 det 7343 4 7 44 3 3 0 162 12 9 9 12 99 12 9 t t t t t t t TT E XSX X E ρ τ ⋅+ = Page 1 of 3

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Problem 2 (10 points) The governing equation we need is ij j V i ed V τ =ℜ By substituting () ,, 2 ij ij i j j i ij ij pv p ve δμ δ μ = =− + + + , 2 ij ij ij ij ii VV V V e e p dV e dV τμ ∫∫ In the following calculations, we need to know the interpolation function and its derivatives only at the node 1.
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## This note was uploaded on 02/24/2012 for the course MECHANICAL 2.094 taught by Professor Klaus-jürgenbathe during the Spring '11 term at MIT.

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MIT2_094S11_quiz2_so - 2.094 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS SPRING 2008 Quiz#2 Solution Instructor Prof K J Bathe Date Problem 1(10

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