EN0175-21

EN0175-21 - EN0175 11 / 16 / 06 Continue on the problem of...

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Unformatted text preview: EN0175 11 / 16 / 06 Continue on the problem of circular hole under uniaxial tension (remote). Stress concentration occurs at a r = , 2 = . T T 3 a Governing equation is: 2 2 = The stress components in polar coordinates are: 2 2 2 1 1 + = r r r rr = r r r 1 2 2 r = Boundary conditions are: @ a r = , = = r rr @ = r , 1 1 e e T v v = ( ) 2 cos 1 2 + = = T e e r r rr v v ( ) 2 cos 1 2 = T 2 sin 2 T r = Therefore, the boundary condition at infinity can be decomposed into two parts. Part I: 1 EN0175 11 / 16 / 06 @ = r , 2 T rr = = . For this part, we have previously obtained the solution as = 2 2 1 2 r a T rr + = 2 2 1 2 r a T = r Part II: @ = r , 2 cos 2 T rr = , 2 cos 2 T = , 2 sin 2 T r = These expressions suggests ( ) 2 cos r f = . Inserting it into gives 2 2 = ( ) 4 d d 1 d d 4 d d 1 d d 2 2 2 2 2 2 = + + r f r r r r r r r r Assume: ( ) ( ) ( ) ( ) 4 , 2 , 2 , 2 2 4 = = + = r r f ( ) 4 2 3 4 2 2 1 C r C r C r C r f + + + = Using boundary conditions: @ a r = , = = r rr @ = r , 2 cos 2 T rr = , 2 sin 2 T r = We can determine the constant coefficients as 2 EN0175 11 / 16 / 06 T C 4 1 1 = , , 2 = C T a C 4 3 4 1 = , T a C 2 4 2 1 = Adding the solution to part I, the complete solutions of stress components are: 2...
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This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.

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EN0175-21 - EN0175 11 / 16 / 06 Continue on the problem of...

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