Conversion local stiffness matrix to global
Conversion local stiffness matrix to global
(OP)
hi,
Regarding the triangular plate(thick) element, the book(FEM Analysis by Mircea RADES) that I'm reading refers to:
"Note that nodal coordinates are usually given in global axes. Calculation of the element stiffness matrix referred to local axes requires the local coordinates of nodes 2 and 3. These can be obtained from their global coordinates using the corresponding transformation matrix.
In order to assemble the global stiffness matrix, the element matrices have
to be first transformed from local to global axes through a matrix triple product which is one of the more time-consuming procedures in finite element analysis. "
It's obvious that conversion of coordinates from global to local one are performed in order to simplify the integration of derivatives and integrands. But to comprise the global matrix(assembly), local stiffness matrix should be converted to global ones.
What I've in hand is the 9x9 local stiffness matrix obtained for each element(triangle), global +local coordinates and connectivity data.
So the problem boils down to how to convert those local matrices to global ones, by the datas that I've in hand?
Your comments will be appreciated,
Regarding the triangular plate(thick) element, the book(FEM Analysis by Mircea RADES) that I'm reading refers to:
"Note that nodal coordinates are usually given in global axes. Calculation of the element stiffness matrix referred to local axes requires the local coordinates of nodes 2 and 3. These can be obtained from their global coordinates using the corresponding transformation matrix.
In order to assemble the global stiffness matrix, the element matrices have
to be first transformed from local to global axes through a matrix triple product which is one of the more time-consuming procedures in finite element analysis. "
It's obvious that conversion of coordinates from global to local one are performed in order to simplify the integration of derivatives and integrands. But to comprise the global matrix(assembly), local stiffness matrix should be converted to global ones.
What I've in hand is the 9x9 local stiffness matrix obtained for each element(triangle), global +local coordinates and connectivity data.
So the problem boils down to how to convert those local matrices to global ones, by the datas that I've in hand?
Your comments will be appreciated,






RE: Conversion local stiffness matrix to global
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RE: Conversion local stiffness matrix to global
Hello.
ing. FERRARI Alberto - www.ferrarialberto.it
RE: Conversion local stiffness matrix to global
At a glance, it focuses on frame structures but the logic should be the same for piece-wise structures (triangular/quad meshing) as well? I noticed something under the "Coordinate Transformation" title, what you refer to as transformation matrix in your article is actually rotation matrix. While I'll have translation+rotation = transformation matrix in my case.
I think that give me the clue, if I compose the rotation matrix (9x9)along the diagonal with accurate inner products and add up the translation matrix, then it should work. Pseudo code is like below :
[GLOBAL ELEMENT MATRIX]= [Translate]1x9+[rotation]9x9X[LOCAL MATRIX]X[-rotation]9x9-[Translate]1x9
Where [Translate]1x9 will have form of [DeltaX1 DEltaY2 0 ......... DeltaY8 0 ]T
Could you comfirm it ? (Pay attention to the minuses , I'm not sure they are visible enough)
I still feel bit of uneasy, that is the correct way of manipulating the local matrix like that.Didn't we violate the symmetry of matrix?
Regards,
RE: Conversion local stiffness matrix to global
Translation matrix should be 9x9 diagonally furnished, as well.
It's a proof that's enough for today :)
RE: Conversion local stiffness matrix to global
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Conversion local stiffness matrix to global
But what a pity that it doesn't cover shell/plate elements in depth other than in-plane problems, plate bending elements has been covered only in 4.7 Section with simple rectangular elements. Where my achievement is to find the solution to the plate/shell elements.