3. Part II A unit square OABC is distorted to OA'B'C' in three ways, as shown in Fig. P5.12. In each of the cases, write

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3 Part Ii A Unit Square Oabc Is Distorted To Oa B C In Three Ways As Shown In Fig P5 12 In Each Of The Cases Write 1 (314.4 KiB) Viewed 37 times

3. Part II A unit square OABC is distorted to OA'B'C' in three ways, as shown in Fig. P5.12. In each of the cases, write down the displacement field u₁, ₂ of every point in the square as a function of the location (a,, a₂) of the point in the original position. Then determine the strains E, e. Assume that u, = 0 and that u₁, u, are independent of x, and a,. In Cases (b) and (c), assume that the lengths of OA, OA', OC, and OC' are all 1. Also, obtain the simplified expressions of the strains e, if €₁, ₂, 0, are infinitesimal. mation X2,02 X2, 02 Abb 18 (b) €2 (a) 1. Solve Problem 3 above by Mathematica. 8 -€₁ X₁, 0₁ X2,02 X₁, 0₁ (c) 8' X₁, 0₁