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corotational concept
Wed, 2014-07-16 07:12 - mjalilych1
hello Dear friends
I have one question about corotational concept. is it possible to obtain tangent
stiffness matrix by TL approach and updating degrees of freedom(including displacement and
rotation by corotational. please aware me of related papers.
best regrads
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Hi
Hi
First what do you mean by corotational? do you mean corotational rate?
TL(Total lagrangian) formulation and Update lagrangian formulation gives the same results but they are two approach, it does not matter what constitutive model you deal with, at the end you will have the same results.
TL deal with kinematic and kinetic variables in refrence configuration and UL deal with kinematic and kinetic variables in current configuration.
thanks for your response.
thanks for your response.
I study geometrically nonlinear euler bernoulli beam. beam remains elastic. I obtain tangent stiffness matrix in TL approach. but there are tangant terms in tangent stiffness matrix. I want to use a local frame attaching to element(similar to corotational concept) and then continue problem.
best regards
Actualy I'm not an expert in
Actualy I'm not an expert in beam theory but I can give some idea for clarification
In Corotational concept a local frame is attache to element or integration point. The local tangent stiffness matrix in this case is different from the global stiffness matrix. for example for a rotated rod the local stiffness matrix is a diagonal matrix, since the rod axial force is just dependent on deformation of axial displacement (not tangential or transverse displacement), but the global stiffness matrix has both diagonal and non-diagonal terms, the global stiffness matrix is resulted by rotating the local stiffness matrix.
since in TL formulation you drive all derivatives(gradient operators) base on material refrence coardinates, your coardinates can not be rotated. you should deal with refrence coardinates.
but if you still want to use a local frame attached to the element, it is ok, you can have discret deformation gradients by the chain rule and this formula:
[B]=round(.)/round(X)= round(.)/round(zeta)*round(zeta)/round(X)
where zeta is your local coardinate parameter....
Rotation, Stiffness Matrices and Corotarional Rates
Dear Aslan,
The stiffness matrix for a bar element is not diagonal in local cooridinate system. More importantly the discussion of rotation from local coordinate system to global coordinate system is completely different from the discussion of corotational rates. A corotational rate for example with respect to spin tensor is written like this:
å = d(a)/dt - wa + aw
which is objective under rigid body rotation.
Mohsen
Dear Mohsen
Dear Mohsen
His question is not about objective rates jaumman(corotational) or other rates... I had the same mistake first, his question is about the kinematic description of a geometrically nonlinear problem. as you know there are three description for geometrical nonlinearity:
1-UL(update lagrangian)
2-TL(total lagrangian)
3-CR(corotational)
corotational description usually deal with large rotation and small strains ... we don't need just rate formulation to describe material behavior ... energy( hyper-elastic for example) formulation can be used too in corotational description...
you are right the bar element stiffness matrix is not diagonal, i made mistake ... thank you for correcting me
however I find this useful ...
Corotational total Lagrangian formulation for three-dimensional beamelement
KUO M. HSIAO
Read More: http://arc.aiaa.org/doi/abs/10.2514/3.10987?journalCode=aiaaj
Corotational
Dear Aslan,
Thanks for your descriptions.
Mohsen
Corrotational Rates
The discussion on corrotational rates is a vast and controversial topic. You have to be more specific about your question. However about references on corrotational rates and their applications in plasticity you can have a look at Dafalias works, for example the following one:
Dafalias YF. Plastic spin: necessity or redundancy? International Journal of Plasticity 1998; 14:909-931.
You can see many corrotational rates in his work and discussion on tangent operators as well.
Mohsen
thanks all Dear friend for
thanks all Dear friend for colloboration.