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Far from the hole, Sigma-r is a function of theta only. At theta = 0, Sigma-r ~ Sigma-o. This makes sense since r is aligned with x when theta = 0. At theta = 90 deg., Sigma-r ~ 0 which also makes sense since r is now aligned with y. We'll check these trends in the ANSYS results.

sigma_theta

Now we will examine how sigma_theta varies in the plate. We will approach this very similarly to how we approached the examination of sigma_r:

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at r = a

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at r>>a

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Now we will examine the stress far from the hole at theta = 0 and theta = pi/2

Sigma-theta

Let's next consider the expected trends for Sigma-theta, the rcircumferential stress, in the vicinity of the hole and far from the hole. The analytical solution for Sigma-theta in an infinite plate is:

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At r = a, this reduces to

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At theta = 90 deg., Sigma-theta = 3*Sigma-o for an infinite plate.

For r>>a,

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At theta = 0 and theta = 90 deg., we get

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Far from the hole, Sigma-theta is a function of theta only but it's variation is the opposite of Sigma-r. AS one goes around the hole from theta = 0 to theta = 90 deg., Sigma-theta increases from 0 to Sigma-o. More trends to check in the ANSYS results.Image Removed

Tau_r_theta

Finally, we will examine how the shear stress in the r_theta direction varies in the plate. The equation for the shear stress in the plate is:

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