Structural Engineering -12x12 stiffness matrix analysis

In summary, Elbarto is trying to find the equations for the 12x12 stiffness matrix for each member in a 3D global system. If anyone has any information on this, they would be greatly appreciated.
  • #1
elbarto
33
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
 
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  • #2
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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  • #3
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
 
  • #4
Oh. So you're using some kind of beam element. I'll see if I can dig them up in my FEA book.
 
  • #5
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
 

1. What is a stiffness matrix in structural engineering?

A stiffness matrix is a mathematical representation of the stiffness of a structural system. It is used to analyze and predict the behavior of a structure under different loading conditions. The stiffness matrix takes into account the material properties, geometry, and constraints of a structure to determine its stiffness.

2. Why is a 12x12 stiffness matrix used in structural engineering?

The 12x12 stiffness matrix is used in structural engineering because it allows for a more detailed analysis of a structure. It takes into account all six degrees of freedom (translation and rotation in three directions) at each node, making it suitable for complex structural systems.

3. How is a 12x12 stiffness matrix calculated?

A 12x12 stiffness matrix is calculated by considering the stiffness of each element in a structure and assembling them together based on their connectivity. The stiffness of each element is determined by its material properties, geometry, and boundary conditions. The resulting stiffness matrix is then solved using numerical methods to determine the displacements and forces in the structure.

4. What are the advantages of using a 12x12 stiffness matrix analysis?

The use of a 12x12 stiffness matrix allows for a more accurate and detailed analysis of a structure. It can capture the effects of geometric and material nonlinearity, as well as the interactions between different elements. This allows for a better understanding of the behavior and performance of a structure, leading to more efficient and cost-effective designs.

5. Are there any limitations to using a 12x12 stiffness matrix analysis?

While a 12x12 stiffness matrix analysis is a powerful tool in structural engineering, it does have its limitations. It is a time-consuming and computationally intensive process, making it more suitable for smaller and simpler structures. Additionally, it relies on accurate input data and assumptions, which can affect the accuracy of the results.

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