• Support PF! Buy your school textbooks, materials and every day products Here!

Mechanics- stress tensor

  • Thread starter gsh84
  • Start date
  • #1
3
0
The following information is given:

The Cartesian components of stress tensor are: [tex] \sigma_{ij}=m(\hat \lambda _{i}\hat \mu _{j}+\hat \lambda _{j}\hat \mu _{i})
, (i=1,2,3; \ j=1,2,3) [/tex].

[tex] \hat \lambda _{i} [/tex] and [tex] \hat \mu_{j} [/tex] are the Cartesian components of the unit vectors [tex] \hat \lambda [/tex] and [tex] \hat \mu [/tex] , who enclose an angle of [tex]2 \alpha [/tex].

m is a scalar with a stress dimension.

Now my question. What are the components([tex] \sigma_{11}, \sigma_{12}.. \sigma_{33}[/tex]) of the the stress tensor based based on this formulation?

According to the information you can say: [tex] \hat \lambda \cdot \hat \mu = \cos 2\alpha [/tex]

Is for [tex] \sigma_{11}[/tex] example: [tex] (\cos 2\alpha+\cos 2\alpha)p [/tex]?
And what would [tex] \sigma_{12}[/tex] be? 0?
 
Last edited:

Answers and Replies

Related Threads for: Mechanics- stress tensor

  • Last Post
Replies
1
Views
411
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
426
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
0
Views
4K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
3
Views
1K
Top