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AE321_Theory - AE 321 Theoretical questions Last update 1...

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1 Q1. AE 321 AE 321 - “Theoretical questions” Last update: September 29, 2008 1) Vector calculus: TRUE/FALSE a) The inner product of two vectors is a vector b) The gradient of a scalar fi eld is a vector c) The divergence of a vector fi eld is a vector d) The curl of a vector fi eld is a vector 2) Indicial notation: how many expressions/equations are denoted by (a) D i , j B j (b) C ij + D ji (c) B ii (no sum) (d) C ij , j B j (e) ± ij = C ijkl ² kl (f) C pq , r U pr = B q
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2 Q1. AE 321 3) Let a , u and W be a scalar, vector and two-tensor field, respectively. Describe the following quantities in both vector/tensor and indicial notations: a) Gradient of a b) Divergence of u c) Curl of u d) Gradient of W e) W is symmetric f) W is skew-symmetric g) V is the inverse of W 4) With ± ij denoting the Kronecker delta, simplify/compute a) A mnop ± om ± np b) ± ij ± ij c) ± ij ± jp ± pi
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3 Q1. AE 321 5) Compatibility equations a) What do the compatibility equations tell us?
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