1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Elastic solid

  1. Sep 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that the constitutive equation for an elastic solid can be expressed in the form:

    Tij=[tex]\frac{1}{2}[/tex][tex]\frac{\rho}{\rho0}[/tex][tex]\frac{\partial(xi)}{\partial(XR)}[/tex][tex]\frac{\partial(xj)}{\partial(XS)}[/tex]([tex]\frac{\partial(W)}{\partial(\gammaRS)}[/tex]+[tex]\frac{\partial(W)}{\partial(\gammaSR)}[/tex])

    2. Relevant equations

    A constitutive equation for finite elastic solid is:
    Tij=[tex]\frac{\rho}{\rho0}[/tex][tex]\frac{\partial(xi)}{\partial(XR)}[/tex][tex]\frac{\partial(xj)}{\partial(XS)}[/tex]([tex]\frac{\partial(W)}{\partial(CRS)}[/tex]+[tex]\frac{\partial(W)}{\partial(CSR)}[/tex])

    where [tex]\gamma[/tex]=[tex]\frac{1}{2}[/tex](C-I) (I is the identity matrix)

    3. The attempt at a solution

    so therefore i have to show that [tex]\frac{\partial(W)}{\partial(CRS)}[/tex]+[tex]\frac{\partial(W)}{\partial(CSR)}[/tex]=[tex]\frac{1}{2}[/tex]([tex]\frac{\partial(W)}{\partial(\gammaRS)}[/tex]+[tex]\frac{\partial(W)}{\partial(\gammaSR)}[/tex])
    using the fact that [tex]\gamma[/tex]=[tex]\frac{1}{2}[/tex](C-I),
    [tex]\frac{\partial(W)}{\partial(CRS)}[/tex]+[tex]\frac{\partial(W)}{\partial(CSR)}[/tex]=[tex]\frac{1}{2}[/tex]([tex]\frac{\partial(W)}{\partial(\gammaRS)+(1/2)I}[/tex]+[tex]\frac{\partial(W)}{\partial(\gammaSR)+(1/2)I}[/tex])

    so what do i do with the (1/2)I, did i make a mistake?
     
  2. jcsd
  3. Sep 8, 2009 #2
    oh no, the latex didnt come out right...and it took me ages!!! i hope it looks understandable.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Elastic solid
  1. Total Solid angle (Replies: 4)

  2. Writing solids (Replies: 2)

  3. Volume of solid (Replies: 11)

Loading...