Page History

...

Far from the hole, Sigma-theta is a function of theta only but its variation is the opposite of Sigma-r (which is not surprising since r and theta are orthogonal coordinates; when r is aligned with x, theta is aligned with y and vice-versa). 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!

Tau

...

-r

...

-theta

Finally, we will examine how the shear stress in the r_theta direction varies in the plate. The equation The analytical solution for the shear stress Sigma-theta in the an infinite plate is:

at At r=a

This boundary condition can also be validated intuitively. Let's look at an element on the hole

Image Removed

As mentioned before, we know that any stress on a face must be zero; therefore the analytical solution at r = a is correct.

At r>>a

Image Removed

Now we will examine the values of Tau_r_theta when r>>a and at theta = 0 and theta = pi/2

Image Removed

and

Image Removed

By looking at a vanishingly small element at the hole , we see that Tau-r-theta at the hole is the shear stress at the hole. Since the hole is a free surface, this has to be zero.

Image Added

For r>>a,

Image Added

From this, we can deduce that Tau-r-theta = 0 both at theta = 0 and theta = 90 deg. Even more trends to check in ANSYSWe will reexamine all of these calculations so we may estimate the validity of the ANSYS simulation later in this tutorial.

sigma_xx

First, let's begin by finding the average stress, the nominal area stress, and the maximum stress with a concentration factor.

...