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# hw_01 - Due In class Friday September 7 2007 Name For...

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Unformatted text preview: Due: In class, Friday September 7, 2007 Name For instructor or TA use only: Problem Score Points 1 10 2 20 3 10 4 10 5 10 6 10 7 20 8 10 ME 521 Fall Semester, 2007 Homework Set # 1 Professor J. M. Cimbala Total: 100 1 . (10 pts) The components ( u , v , w ) of vector u G satisfy the following six equations, where C and D are simply scalar constants: uu = 2 C- 3 D uv = 2 C vv = 2 C- 3 D uw = 2 C ww = 2 C- 3 D vw = 2 C Rewrite these equations as a single expression in tensor notation ( one equation in tensor notation should be equivalent to all six of the above equations ). 2 . (20 pts) The three invariants of a symmetric second-order tensor, A ij , are: I 1 = A 11 + A 22 + A 33 I 2 = A 11 A 22 + A 22 A 33 + A 33 A 11- A 12 2- A 23 2- A 31 2 I 3 = det ( A ij ) [determinant of the matrix A ij ] Rewrite I 1 and I 2 in standard tensor notation, simplified as much as possible. 3 . (10 pts) Text problem 1.2 . Also, sketch a two-dimensional fluid element at that location, and draw all the stresses acting ....
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