4103q5.1.091

4103q5.1.091 - MEEG 4103 Quiz 5.1.091 (20 points) It is...

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MEEG 4103 Quiz 5.1.091 (20 points) It is known that the total strain energy per unit volume u at a point P of a machine part is given by ( ) 222 1 2 3 12 23 31 1 2 2 u E σσσ ν σ σσ  = ++− + +  Making use of this formula, derive ( a ) the strain energy per unit volume u v associated with only the volume change at P , ( b ) the distortion strain energy per unit volume u d at P . --------------------------------------------------------------------------------------------------------------------------------------- ( a ) 123 av 3 ++ = ( ) 1 2 3 av 22 2 av av av 2 1 3 2 (3 ) (3 ) 6 uu EE E σσσσ νσ = = = = = −= = v ( ) 1 2 3 2 6 u E = +++ + + v ( b ) d u = v ( ) ( ) ( ) ( ) 1 2 3 1 2 3 1 2 3 1 2 3 3( ) 6 1 ( )2
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