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
Messages
32
Reaction score
0
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
 
Engineering news on Phys.org
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.
 
Last edited by a moderator:
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
 

Thread 'Query on Isentropic relationships (such as PV^gamma = constant)'

Hi all, I have a question. So from the derivation of the Isentropic process relationship PV^gamma = constant, there is a step dW = PdV, which can only be said for quasi-equilibrium (or reversible) processes. As such I believe PV^gamma = constant (and the family of equations) should not be applicable to just adiabatic processes? Ie, it should be applicable only for adiabatic + reversible = isentropic processes? However, I've seen couple of online notes/books, and...
View full post »

Thread 'Dry sump pump issue'

I have an engine that uses a dry sump oiling system. The oil collection pan has three AN fittings to use for scavenging. Two of the fittings are approximately on the same level, the third is about 1/2 to 3/4 inch higher than the other two. The system ran for years with no problem using a three stage pump (one pressure and two scavenge stages). The two scavenge stages were connected at times to any two of the three AN fittings on the tank. Recently I tried an upgrade to a four stage pump...
View full post »

Similar threads

Why Are My Bending Moment Signs Incorrect in the Direct Stiffness Method?
Replies
3
Views
3K
Engineering Total Lateral Stiffness from Stiffness Matrix
Replies
0
Views
1K
Derivation of First Storey Shear Rigidity for a Rigid Frame
Replies
2
Views
1K
Engineering Why Are My Bending Moment Signs Incorrect Using the Direct Stiffness Method?
Replies
9
Views
3K
(Structural Analysis) Moment Distribution Method: Help?
Replies
1
Views
10K
Engineering Stiffness of a Concrete Core in a Multi-Storey Building
Replies
2
Views
2K
Hi I'm Jayvhie, Mechanical Engineer from PH
Replies
1
Views
440
I FEM Method in 2D with Triangular Elements
Replies
12
Views
4K
Stiffness Matrix Method: Symmetry vs Introducing a new node / joint
Replies
1
Views
2K
Stiffness Matrix for Linear Tetrahedral Element
Replies
5
Views
6K

Hot Threads

Recent Insights

Back
Top