- #1
acg8934
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Homework Statement
Given a body in a state of plane stress with no body forces where
[tex]\sigma[/tex]x=x2y
[tex]\sigma[/tex]y=(y3-3y)/3
Find [tex]\tau[/tex]xy
Homework Equations
For plane stress
[tex]\partial[/tex][tex]\sigma[/tex]x/[tex]\partial[/tex]x + [tex]\partial[/tex][tex]\tau[/tex]xy/[tex]\partial[/tex]y + X = 0
[tex]\partial[/tex][tex]\sigma[/tex]y/[tex]\partial[/tex]y + [tex]\partial[/tex][tex]\tau[/tex]xy/[tex]\partial[/tex]x + Y = 0
No body forces: X=0 Y=0
Simplified:
[tex]\partial[/tex][tex]\sigma[/tex]x/[tex]\partial[/tex]x = -[tex]\partial[/tex][tex]\tau[/tex]xy/[tex]\partial[/tex]y
[tex]\partial[/tex][tex]\sigma[/tex]y/[tex]\partial[/tex]y = -[tex]\partial[/tex][tex]\tau[/tex]xy/[tex]\partial[/tex]x
The Attempt at a Solution
[tex]\partial[/tex][tex]\sigma[/tex]x/[tex]\partial[/tex]x = 2xy
[tex]\partial[/tex][tex]\sigma[/tex]y/[tex]\partial[/tex]y = y2-1
Putting this into above equations gives:
[tex]\partial[/tex][tex]\tau[/tex]xy/[tex]\partial[/tex]y = -2xy
[tex]\partial[/tex][tex]\tau[/tex]xy/[tex]\partial[/tex]x = -y2+1
[tex]\int[/tex][tex]\partial[/tex][tex]\tau[/tex]xy = [tex]\int[/tex]-2xy[tex]\partial[/tex]y
[tex]\tau[/tex]xy = -y2x
[tex]\int[/tex][tex]\partial[/tex][tex]\tau[/tex]xy = [tex]\int[/tex]-y2+1[tex]\partial[/tex]x
[tex]\tau[/tex]xy = -y2x + x
These should both be equal, but I'm not sure what I'm doing wrong. I think its my integration.
Please help.