Question

4. The three-dimensional state of stress at a point is given by the stress tensor 12 8 101 [ou] = 8 3 4 10 4 7 The principal stresses and the principal directions at the point are given by the eigenvalues and the eigenvectors. I 0 Use the power method for determining value of the largest principal stress. Start with a column vector of ls, and carry out the first four iterations. Also check convergence after fourth iteration

Answer 1

Given that 2 S10 8 3 4 10 4 7 So from the given data lul have to consider the data al followe. The invee dimensional state for alle stress point of followed by the stress tenson, 28.10 A: and S 34 Xo: 10 47 لا --- Ghove matrix x, is Axo the multiplication of and ie 20 0.9523 X, : A Xo 21 0.7142 10 2 8 10 8 3 u 10 47 •B] (ist iteranon) 21 0.95 0.90911 2 S 10 $34 0.71 19.3809 071009 - 10 47 (second iteration) Now Xq = AX, : (by ignore 21) (third itevation) Now X₂ = A xq (by ignore 19.98) (fourth iteration C01909) 2 8 10 8 34 10 47 0.9243 • 18.931 07079 o. Ho 1 2810 19.075 0.91 807 0.7086 8 34 1047 10.92913 Now Xy? A X3 = 0.7079 [ignore 18.931) the edgen value is 19.075 Heration followed. Therefore and it is the

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