TEST BANK FOR Introduction to Nonlinear Finite Element Analysis By Nam Ho Kim Converted
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Exam (elaborations) TEST BANK FOR Introduction to Nonlinear Finite Element Analysis By Nam-Ho Kim (Solution Manual)
- Exam (elaborations) • 141 pages • 2021
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1.6. Exercises 
P1.1 Using Cartesian bases, show that (u Ä v) ⋅ (w Ä x) = (v ⋅ w)u Ä x where u, v, 
w, and x are rank 1 tensor. 
Solution: Using the Cartesian basis, ( )( ) ( )( ) i i j j k k l l u Ä v w Ä x = u e Ä v e ⋅ w e Ä x e . 
Since the dot product occurs between adjacent bases, we have 
( )( ) 
( )( ) 
( ) 
( ) 
( ) 
( )( ) 
i i j j k k l l 
i j k l j k i l 
i j k l jk i l 
i j j l i l 
j j i i l l 
u v w x 
u v w x 
u v w x 
u v w x 
v w u x 
d 
Ä ⋅ Ä 
= ⋅ Ä 
= Ä 
...
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