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Compressing cylinder
Posted 2015年11月17日 GMT-5 09:01 Geometry, Structural Mechanics 1 Reply
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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.
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 2015年11月17日 GMT-5 10:49
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Posted:
9 years ago
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
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