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Homework Help: Mechanics- stress tensor

  1. Apr 2, 2009 #1
    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: Apr 2, 2009
  2. jcsd
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