... 2003 5:00 PM 36 Finite Element Analysis: Thermomechanics of Solids As proof, α j y j ⊗ βk zk = α j βk y j ⊗ zk = Ay j ⊗ Bz k = (A ⊗ B)(y j ⊗ z k ) (2.59) Now, the eigenvalues of A ⊗ In are × ... Page 16 Wednesday, February 19, 2003 4:55 PM 16 Finite Element Analysis: Thermomechanics of Solids Suppose now that v(t), θ, and φ are functions of time As in cylindrical coordinates, d ∂ v′ = ... 22 Finite Element Analysis: Thermomechanics of Solids Verify that T T (a) QQ = Q Q T −1 (b) Q = Q (c) For any × vector a Qa = a [The relation in (c) is general, and Qa represents a rotation of...