FEM stiffness matrix for simple frame exploiting symmetry

In summary, the Finite Element Method (FEM) stiffness matrix is a square matrix used in structural analysis to represent the stiffness of a structure. It is calculated by combining the stiffness values of individual elements, taking into account material properties, geometry, and boundary conditions. Exploiting symmetry in the matrix can reduce computational effort without affecting accuracy, but it is important to ensure the structure is truly symmetric. The FEM stiffness matrix can also be used for non-symmetric structures, but requires higher computational effort and accurate definition of element properties and boundary conditions.
  • #1
JohnnyR
3
0
Hello. I need help with the following problem:
Unavngivet.jpg
Unavngivet1.jpg

I don't know where to start. I know that the frame can be split up into one symmetric part and one symmetric+assymetric part but i forgot the theory and rules on translation and axis etc.
I hope someone can help as I have to hand in the assignment soon and my grade depends on it.

Best regards
Johnny
 
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  • #2
Sorry about your memory loss, but the policy at PF is that you must show some effort at a solution before you can receive help.
 

1. What is the Finite Element Method (FEM) stiffness matrix?

The FEM stiffness matrix is a square matrix that represents the stiffness of a structure in the Finite Element Method. It is used to solve structural analysis problems by dividing a structure into smaller elements and calculating their stiffness, which is then combined to form the overall stiffness matrix for the entire structure.

2. How is the FEM stiffness matrix calculated for a simple frame?

The FEM stiffness matrix for a simple frame is calculated by using the stiffness equations for each element of the frame. These equations take into account the material properties, geometry, and boundary conditions of the frame. The stiffness values for each element are then combined to form the overall stiffness matrix for the frame.

3. What is the significance of exploiting symmetry in the FEM stiffness matrix for a simple frame?

Exploiting symmetry in the FEM stiffness matrix for a simple frame can significantly reduce the computational effort required. This is because symmetric structures have repeating elements, and the stiffness values for these elements can be calculated once and then copied to the corresponding elements, rather than calculating them separately for each element.

4. How does exploiting symmetry affect the accuracy of the FEM stiffness matrix for a simple frame?

Exploiting symmetry does not affect the accuracy of the FEM stiffness matrix for a simple frame. This is because the stiffness values for the symmetric elements are identical, so there is no loss of accuracy in copying them. However, it is important to ensure that the structure is truly symmetric, as any inaccuracies in the symmetry may affect the accuracy of the stiffness matrix.

5. Can the FEM stiffness matrix be used for structures that are not symmetric?

Yes, the FEM stiffness matrix can be used for structures that are not symmetric. However, the computational effort required will be higher as the stiffness values for each element will need to be calculated separately. In such cases, it is important to ensure that the structure is properly discretized and that the element properties and boundary conditions are accurately defined to obtain an accurate stiffness matrix.

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