(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://imageshack.us/photo/my-images/513/selection027.png"

http://imageshack.us/photo/my-images/513/selection027.png

2. Relevant equations

[itex]E_{ij}=\frac{1}{2} \left( \frac{\partial{u_i}}{\partial{X_j}} \frac{\partial{u_j}}{\partial{X_i}} - \delta_{ij}\right) [/itex]

[itex]\epsilon_{ij}=\frac{1}{2}\left(\frac{\partial{u_i}}{\partial{X_j}}+\frac{\partial{u_j}}{\partial{X_i}}\right)[/itex]

3. The attempt at a solution

I'm not exactly sure where to begin. I understand how to find [itex]E_{ij}[/itex] and [itex]\epsilon_{ij}[/itex] given the displacement field, but I am not sure how to construct the field. So far, I came up with:

[itex]u=0.001x_1+0.003x_2+0.002x_3[/itex]

[itex]v=0.002x_2+0.001x_3-0.001x_4[/itex]

But I'm not sure that's right at all, or if I'm supposed to be looking at each individual point, e.g.:

[itex]u_1=0.001x_1[/itex]

[itex]v_1=0[/itex]

[itex]u_2=0.003x_2[/itex]

[itex]v_2=0.002y_2[/itex]

[itex]u_3=0.002x_3[/itex]

[itex]v_3=0.001y_3[/itex]

[itex]u_4=0[/itex]

[itex]v_4=-0.001y_4[/itex]

Am I even remotely close with either idea?

Thanks!

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# Homework Help: Continuum Mechanics: Eij and eif given coordinates and displacements

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