MIT2_094S11_hw_7_sol

MIT2_094S11_hw_7_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 Homework 7 - Solution Instructor: Prof. K. J. Bathe Assigned: 04/03/2008 Due: 04/10/2008 Problem 1 (20 points): (a) 00 0 11 0 cos45 sin 45 1 22 sin 45 3 1 3 2 0 42 tt t XR U 3 4 4 ⎤⎡ ⎤ ⎥⎢ °− ° ⎡⎤ == = ⎢⎥ °° ⎣⎦ ⎥⎢ ⎥ ⎦⎣ ⎦ () 1 0 0 22 22 33 t t XX (b) 0 17 5 1 18 9 51 7 2 91 8 tT XXI ε =− = 0 17 18 11 7 0 17 17 71 10 1 7 18 9 5 5 9 t S ⎤⎡ ⎦⎣ 0 0 (1.5)(1)( ) 3 (2)(2)( ) 8 t t V thickness V thickness ρ = Page 1 of 3
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Therefore, 00 0 0 33 0 08 t tt tT t XSX ρ τ = = 22 11 12 33, 8, 0 t ττ = == Hence the Cauchy stress t given by the program is not correct. We can identify the program error by noting that 33 8 20.5 2 + = , 20.5 12.5 33 + = and . Hence a rotation of was wrongly applied. Therefore, 20.5 12.5 8 −= 45 ° T program o e ab v R R = where cos45 sin 45 sin 45 R °− ° = °° Problem 2 (10 points): Since
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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_hw_7_sol - 2.094 FINITE ELEMENT ANALYSIS OF...

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