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Unformatted text preview: (1) A prismatic, isotropic, homogenous, linear elastic, circular cylinder:b r a, c x 3 c , is shown below. This structure has a displacement vector feld u where the components oF displacement are given below in the given Cartesian coordinate system. Here , , , and are given, small, positive constants. Here is Poisson s ratio. Assume that b=0 (the cylinder is solid)and that the displacement feld is provided below u 1 ( x 1 , x 2 , x 3 ) = 2 ( x 3 2 x 2 2 + x 1 2 ) x 1 x 3 x 2 2 ( c x 3 )( x 1 2 x 2 2 ) x 3 3 6 + c x 3 2 2 u 2 ( x 1 , x 2 , x 3 ) = x 1 x 2 x 2 + x 3 x 1 ( c x 3 ) x 1 x 2 u 3 ( x 1 , x 2 , x 3 ) = x 1 x 3 + x 3 + ( 3 4 + 2 ) a 2 x 1 + 1 4 ( x 1 3 3 x 1 x 2 2 ) + x 1 x 2 2 + x 3 x 1 ( c x 3 2 ) or each oF the Following scenarios: (i) What are the stresses inside the body? Provide an equation and some type oF plot that describes an (i) What are the stresses inside the body?...
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This note was uploaded on 04/01/2008 for the course AERO 315 taught by Professor Roe during the Winter '08 term at University of Michigan.
 Winter '08
 Roe

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