Structural Engineering -12x12 stiffness matrix analysis

AI Thread Summary
The discussion focuses on the need for a 12x12 stiffness matrix for elastic analysis of 3D frame structures using MATLAB. The original poster is using the direct stiffness method but lacks specific equations for the matrix that accounts for bending moments. A participant suggests resources, including a presentation on 3D truss stiffness matrices and mentions that their FEA textbooks contain relevant information. The original poster confirms they are working with a full 3D frame element, requiring consideration of all 12 degrees of freedom. The conversation highlights the challenge of finding precise equations and the willingness to share findings within the forum.
elbarto
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Hi,
I am trying to write a MATLAB script to do an elastic analysis of 3D frame sturctures. The method I am using is the direct stiffness method, but I cannot find the equations for the 12x12 stiffness matrix for each member in the global system.

If anyone has any information on 3D matrix analysis I would greatly appreciate the help. So far none of the texts I have found have explicitly given these formula.

I have the 6x6 matracies for 2D analysis if anyone is interested.

Thank You

Elbarto
 
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I am assuming that you are using something along the lines of a truss element, but in a 3D structure, i.e. members can carry no bending moments.

Take a look here :
http://www.google.com/url?sa=t&source=web&ct=res&cd=6&url=http%3A%2F%2Fwww.engineer.tamuk.edu%2Fdepartments%2Fieen%2Ffaculty%2FDrLPeel%2FCourses%2FMeen5330%2Fstudent_presentations%2FFEA_F06.ppt&ei=bkvrSKziMdywmQf0mcHaCg&usg=AFQjCNFyXckTs9v56tKt3qI9Yc-c1jALjQ&sig2=k9yvGnIMuqDkYuKnyPc9kg

Towards the back of the presentation it talks about the 3D truss stiffness matrix. Both of my FEA books also discuss this as well. See if you can get a hold of a copy from your library or a fellow student.
 
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Thank you for your reply. That is almost exactly what I am chasing, tho I need the 12x12 stiffness matraix equations because I am considering bending so I will have the 6 additional degree of freedom to account for due to the rotation of each node.

If I find the equations I will post them here. Are you allowed to photo copy pages from textbooks and post them here or is that against forum rules?

Thanks, Elbarto
 
Oh. So you're using some kind of beam element. I'll see if I can dig them up in my FEA book.
 
Yes I am doing a full 3D frame element so I have to consider all 12 DOF's for each member. I had a look in my library today and think I managed to find the local member stiffness equations which will probably work ok if I play around with them a bit but I would appreciate it if you could check your textbook out.

Thanks alot
Regards Elbarto
 

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