MIT2_094S11_hw_3_sol

# MIT2_094S11_hw_3_sol - 2.094 FINITE ELEMENT ANALYSIS OF...

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Page 1 of 4 2.094 F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS S PRING 2008 Homework 3 - Solution Instructor: Prof. K. J. Bathe Assigned: 02/21/2008 Due: 02/28/2008 Problem 1 (10 points): From the plane strain condition,   ( 1 )0 z z xx z z yy E   ) ( x zz x yy The strains are     27 ( 11 ) ) 4.766 (1 ( 71 1 0 ) xx z xx yy xx y z y EE      28 ( ) ) 4.333 ( 31 1 0 ) yy z yy xx yy x z x 7 2(1 8.6667 1) 10 xy xy xy E G The displacements in the four-node element can be written as 0 1 2 3 ( , ) u x y a a x a y a xy 0 1 2 3 ( , ) v x y b b x b y b xy (*Note that you can also use the following form of displacements as in the class. 1 1 2 2 3 3 4 4 ( , ) ( , ) ( , ) ( , ) ( , ) u x y h x y u h x y u h x y u h x y u 1 1 2 2 3 3 4 4 ( , ) ( , ) ( , ) ( , ) ( , ) v x y h x y v h x y v h x y v h x y v But, then equations are slightly complicate to solve. Please see attached sample solution which uses this method)

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Page 2 of 4 Then, 7 13 4.7667 10 xx u a a y x
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MIT2_094S11_hw_3_sol - 2.094 FINITE ELEMENT ANALYSIS OF...

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