iMechanica - Comments for "bending behaviour of a cantilever beam modeled by shell elements"
https://imechanica.org/node/9914
Comments for "bending behaviour of a cantilever beam modeled by shell elements"enSeveral things you need to
https://imechanica.org/comment/16673#comment-16673
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<p><em>In reply to <a href="https://imechanica.org/node/9914">bending behaviour of a cantilever beam modeled by shell elements</a></em></p>
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Several things you need to do to verify whether you figured out the real reason:
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1. Verify whether you used linear element or nonlinear element in your finite element simulation. It really does not matter how large the deflection looks, if you used linear element in your FEA, and your beam is slender, you should be able to get a decent match.
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2. Verify whether you FEA results changes with refinement of your mesh. Take the converged results as the true solution.
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3. If you used nonlinear FEA, you can compare it nonlinear solution for large deflection beam. For a cantilever under tip transverse load, you can find the analytical formulas for the nonliner solution in Timoshenko's book. Gere, J. M., Timoshenko, S. P., 1990. Mechanics of Materials, 3rd Edition. PWS-Kent, Boston, Massachusetts. Chapter 7, deflection of beams.
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</ul>Fri, 29 Apr 2011 20:41:43 +0000Wenbin Yucomment 16673 at https://imechanica.orgDear Wenbin Yu,thanx a
https://imechanica.org/comment/16654#comment-16654
<a id="comment-16654"></a>
<p><em>In reply to <a href="https://imechanica.org/node/9914">bending behaviour of a cantilever beam modeled by shell elements</a></em></p>
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Dear Wenbin Yu,
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thanx a lot for your comment. You are right, but the width and thickness of the beam are small comparing to its length..
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But I think I have now understood why I get some 25% error in comparison to the Bernoulli beam theory. It seems that Bernoulli-Euler beam analytical solution is only valid for small displacements,while in my FE simulation,the beam goes under rather large displacement although it remains in the elastic region (deflection at the end of the beam is 5% of the length of the beam),so there would be an error w.r.t analytical solution!
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I hope my understanding is right!
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Thanks again for your clarification and comment!
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Setareh
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</ul>Thu, 28 Apr 2011 15:39:46 +0000setarehcomment 16654 at https://imechanica.orgDear Wenbin Yu,thanx a
https://imechanica.org/comment/16653#comment-16653
<a id="comment-16653"></a>
<p><em>In reply to <a href="https://imechanica.org/node/9914">bending behaviour of a cantilever beam modeled by shell elements</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Dear Wenbin Yu,
</p>
<p>
thanx a lot for your comment. You are right, but the width and thickness of the beam are small comparing to its length..
</p>
<p>
But I think I have now understood why I get some 25% error in comparison to the Bernoulli beam theory. It seems that Bernoulli-Euler beam analytical solution is only valid for small displacements,while in my FE simulation,the beam goes under rather large displacement although it remains in the elastic region (deflection at the end of the beam is 5% of the length of the beam),so there would be an error w.r.t analytical solution!
</p>
<p>
I hope my understanding is right!
</p>
<p>
Thanks again for your clarification and comment!
</p>
<p>
Setareh
</p>
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</ul>Thu, 28 Apr 2011 15:39:27 +0000setarehcomment 16653 at https://imechanica.orgLet me assume you are doing
https://imechanica.org/comment/16616#comment-16616
<a id="comment-16616"></a>
<p><em>In reply to <a href="https://imechanica.org/node/9914">bending behaviour of a cantilever beam modeled by shell elements</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Let me assume you are doing a linear analysis. If both the width and the thickness are smaller enough comparing to the length, you should get comparable results between a beam theory and a plate/shell theory for the behavior you are looking at. If the thickness is much smaller than both the width and the length and the width is comparable to the length. You beam theory will fail as you cannot model it as a beam anymore.
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If you want to dive into more technical details, your analytical beam formulas require unixal stress assumption: all the stress components in the cross-sectional plane vanish, including the normal stress along the thickness. These assumptions are realistic only if both the width and the thickness are much smaller than the length. Your plate/shell assumes normal stress along the thickness direction equal to zero. However, your normal stress along with width can be nonzero. This is valid if the thickness if much smaller than the width and length.
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</ul>Thu, 21 Apr 2011 12:30:00 +0000Wenbin Yucomment 16616 at https://imechanica.orgI am still waiting for any
https://imechanica.org/comment/16613#comment-16613
<a id="comment-16613"></a>
<p><em>In reply to <a href="https://imechanica.org/node/9914">bending behaviour of a cantilever beam modeled by shell elements</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
I am still waiting for any input.....
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thanx a lot:)
</p>
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</ul>Thu, 21 Apr 2011 08:57:06 +0000setarehcomment 16613 at https://imechanica.org