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Compressing cylinder

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Dear All


I am doing simulations on compression of 3D solid cylinder (where all the surfaces are free to move) by applying uniform stresses on the top and bottom surfaces. When I check the strain components (say e_xx ) by taking 2D cross section along the axis of the cylinder, I found out that it is identical in all cross section near and far away from the top and bottom surfaces where the stress is applied.


Based of Saint Venant principle I expected this to happen for very long cylinder but not for very short one. Is there something I missed?



Thanks,
H.

1 Reply Last Post 17.11.2015, 10:49 GMT-5
Jeff Hiller COMSOL Employee

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Posted: 9 years ago 17.11.2015, 10:49 GMT-5
Hello,
For an isotropic cylinder aligned with the x axis, and uniformly loaded on its end faces, with no constraints on the boundaries (other than to remove rigid body motions, of course), the analytical solution to the linear problem is:
for the stress tensor:

and for the strain tensor:

Hence, these tensors do not vary in space.
You're thinking of the case where the faces are constrained. In that case, the solution is non-trivial.
Best,
Jeff
Hello, For an isotropic cylinder aligned with the x axis, and uniformly loaded on its end faces, with no constraints on the boundaries (other than to remove rigid body motions, of course), the analytical solution to the linear problem is: for the stress tensor: [math]\sigma = \frac{T}{A} e_x \otimes e_x[/math] and for the strain tensor: [math]\epsilon = \frac{T}{EA} e_x \otimes e_x -\frac{\nu T}{EA} (e_y \otimes e_y + e_z \otimes e_z)[/math] Hence, these tensors do not vary in space. You're thinking of the case where the faces are constrained. In that case, the solution is non-trivial. Best, Jeff

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