SampleExam1 - stress components on all surfaces of the...

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AE 220 – EXAM #1 MONDAY SEPTEMBER 29, 2003, 9:00 am-9:50 am INSTRUCTIONS: THERE ARE TWO (2) QUESTIONS IN THIS EXAM CLOSED BOOKS AND NOTES EQUATION SHEETS HANDED OUT IN CLASS ARE ALLOWED CALCULATORS ARE NOT ALLOWED WRITE ALL ANSWERS IN THE BOOKLET PROVIDED DO NOT HAND IN ANY OF YOUR OWN PAPER
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1. (40 points) If a and B are a vector and a two tensor field respectively, then use indicial notation to prove the following identity: ± . B T a ( ) = a . ± . B ( ) + B . ± a ( )
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2. (60 points) Find the boundary conditions (i.e. relation between traction and
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Unformatted text preview: stress components) on all surfaces of the hollow circular cylinder (inner radius a, outer radius b) shown below in both (i) Cartesian coordinates and (ii) cylindrical coordinates, where P , P and P i are normal tractions and q a shear traction. Note: the loading shown on the cross sectional figure on the right hand side acts over the entire length L and over the entire circumference. P L P i P o q Loading on cylindrical surfaces P...
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