mechanics of fluids and solids1.Consider the vectors11//3V =1/8- {-ח-1//321/ /3(n)= V; ,and develop2.Consider the tensors10 3Aij = 3 -2 10 1 -2Bij =-1 0 13 112 -1 0and develop the following quantities :Tik = Aij Bjkc = Aij Bij3.Are these equations valid with respect to the index notations ?Tij1+ vE+ dij akka)ajj1- 2vb)Oj = dj TjTij =-p dij + 2"( Vij -ij Vit)c)d)dijk dmpq= djp dkq-ðjqðkpe)dipq dpqr dpq V pq= 0

Answered: 1. Consider the vectors 1//3 n= -1//3…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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mechanics of fluids and solids
1.
Consider the vectors
1
1//3
V =
1/8- {-ח
-1//3
2
1/ /3
(n)
= V; ,
and develop
2.
Consider the tensors
10 3
Aij = 3 -2 1
0 1 -2
Bij =-1 0 1
3 11
2 -1 0
and develop the following quantities :
Tik = Aij Bjk
c = Aij Bij
3.
Are these equations valid with respect to the index notations ?
Tij
1+ v
E
+ dij akk
a)
ajj
1- 2v
b)
Oj = dj Tj
Tij =-p dij + 2"( Vij -ij Vit)
c)
d)
dijk dmpq= djp dkq-ðjqðkp
e)
dipq dpqr dpq V pq= 0

Expert Solution

Step 1

As per Bartleby guidelines, for more than one questions asked, only first is to be answered. Please upload other separately.

Given two vectors,

$\vec{v} = \{\begin{matrix} 1 \\ - 2 \\ 2 \end{matrix}\} and \vec{n} = \{\begin{matrix} \frac{1}{\sqrt{3}} \\ - \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{matrix}\}$

To determine, $v^{(n)} = v_{i} n_{i}$

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