1-9 - 30 Finite Element Analysis and Design 9. For the...

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30 Finite Element Analysis and Design 9. For the stress matrix below, the two principal stresses are given as σ 3 = −3 and σ 1 = 2, respectively. In addition, the two principal stress directions corresponding to the two principal stresses are also given below. 1 0 2 [ ] 0 1 0 2 0 2    , 1 2 5 0 1 5 n and 3 1 5 0 2 5 n (a) What is the normal and shear stress on a plane whose normal vector is parallel to (2, 1, 2)? (b) Calculate the missing principal stress σ 2 and the principal direction n 2 . (c) Write stress matrix in the new coordinates system that is aligned with n 1 , n 2 , and n 3 . Solution: (a) Normal vector: 1 3 {2 1 2} T n Traction vector () 1 3 2 0      n Tn The normal component of the stress vector on the plane can be calculated 2 ( ) 2 1.4444 1.4229 n nn  n n T (b) Using Eq. (0.46) of Chapter 0, the eigen values are governed by 32 1 2 3 0 I I I We can find the coefficients of the above cubic equation from Eq. (0.47) by
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This note was uploaded on 08/22/2011 for the course EML 4500 taught by Professor Staff during the Fall '08 term at University of Florida.

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1-9 - 30 Finite Element Analysis and Design 9. For the...

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