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Incorporation of Releases into stiffness matrix for Beam/frame element

Incorporation of Releases into stiffness matrix for Beam/frame element

Incorporation of Releases into stiffness matrix for Beam/frame element

(OP)
Dear All,

I'd like to know how one incorporates releases of frame/beam element(total 12x12 deegreee of freedom) into global stiffness. Actually the problem arises from the start with how to integrate releases into local stiffnes matrix of element, following the instructions from the books it is recommended to fill zeros of inner product of corresponind element where releases are defined, that is, if release is defined at the 3rd D.O.F. it is recommended to fill all 3rd rows and columns with zeros of local stifffness of beam frame element.

At that phase there are 2 question arising,
#1) do I have to condense the local matrix(whch has zeros in it) before global matrix assembly or can I use it directly wihtout any condensation. The risk of forming singular global matrix is not valid here because It will be not allowed to define releases which forms the lability.
#2) If condensation is required will I need to apply this before transformation matrix multiplication or after it ?

Your guidance will be appreciated,

RE: Incorporation of Releases into stiffness matrix for Beam/frame element

It has been awhile since I studied this topic. However, from what I recall, to locally release a DOF from a beam element, you must condense the stiffness matrix. If you multiply the transformation matrix after condensing, you will have a different number of DOF's. If you want to globally release a DOF, say for a pinned boundary condition, I believe you can simply change all of the values for that DOF in the global matrix to zero except for the diagonal which should be 1.

Please verify all of the above information as this is from my memory and plus you should never trust strangers on the internet.

RE: Incorporation of Releases into stiffness matrix for Beam/frame element

(OP)
Hi,

Strangers like you are always welcome :) Commenting on others is also good way and beneficial for the OP, it may give an essential sparkle or clue, sometimes I relly lost my way deep into formulas and to get out from that only the opinion from different aspect is needed.

Quote (BS2)

you must condense the stiffness matrix.
I assume that you mean local matrix of beam element, then I believe that reordering of rows and columns to form the condensed matrix must work in my case. Because released DOFs are supposed to be zeros and all others are forming the top-left term in Guyan reduction K11,reduced = K11 -K12*K22-1*K21 second term in RHS of equation will be zero.

Quote (BS2)

If you multiply the transformation matrix after condensing, you will have a different number of DOF's
IMHO It is normal to have different dofs after condensation, the key point will be how you integrate those into global stiffness. I use direct integration where you eliminate directly the zero values.

Regards,

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