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Unformatted text preview: Problem 1. (i) Write the three linear equations you will use to determine the corresponding principal direction. (ii) Solve the above equations to determine the principal direction. If there are multiple principal directions for σ n =1, then show them in a parametric form. Solution ( - )-- ( - ) ( - ) = 3 1 20 2 3 1 000 1 1 nxnynz 000 The first two equations are the same:-= → = 2nx 2ny 0 nx ny The last equation does not yield any useful information. Hence n z is arbitrary, say n z = α . Then the direction cosines of the principal stress direction take the form: +∝ , , 12 21 1 α where -∞≤ ≤+∞ α Some examples of the principal stress directions (eigen vectors) α n x n y n z-∞-1 1 1 ½ 2/3 2/3 1/3 +∞ +1...
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This note was uploaded on 06/07/2011 for the course EML 4507 taught by Professor Kim during the Fall '11 term at University of Florida.
- Fall '11
- Finite Element Analysis