FEM:A simple stiffness matrix problem

[arifgokcen]

Homework Statement

Homework Equations

1-Stiffness matrix?
2-When i am doing the deformation,should i consider stress stiffenning or just solve the problem as is

The Attempt at a Solution

I tried to form the necessary stiffness matrix but couldn't understand how should i approach the problem.I place two axial springs and one torsional spring at 1st end.However in the question "G" is not given so i shouldn't use torsional spring(as my prof. said.He just explained this part that i shouldn't use torsional spring).

then i formed a new 4x4 matrix for the first element and third element.
This matrix has 3 axial columns and 1 bending column with 2nd column being a bending column.

and for 2nd element i formed a 6x6 matrix with u_2,u_3,v_2,v_3,w_2,w_3

I know its trivial but still having problems.Very new to the topic so please elaborate

Thanks

 

[SteamKing]

I recommend the book, 'Applied Finite Element Analysis', 2. ed., by Larry Segerlind.

Here is a link to a pdf copy:

ftp://161.53.116.242/Predavanja_vjez...0Segerlind.pdf

This book will show you step-by-step how to set up a stiffness matrix and solve it. Given the nature of your problem, a 6x6 element is not required. A 4x4 element should be sufficient.

Given the loading and construction of the frame, I cannot see that any torsional moments are present. Remember, torsion is twisting of a beam about its longitudinal axis. Your frame has only axial loads and bending loads.

 

[arifgokcen]

What about the second part of my question.

Should i consider stress stiffenning.

I have downloaded book and problem 19-4 looks very similar as you said it shows 4x4 so i will try to solve that part again.

Thank you for you help

 

[SteamKing]

I'm not sure what you mean by 'stress stiffening', but unless you are specifically requested to do so, I would not.

There are certain simplifying assumptions implied in the stiffness method which keeps the analysis linear. If these assumptions are not applied, then instead of finding a direct solution to the stiffness equations, the problem becomes non-linear, and iterative methods of solution are required.

 

[rezeew]

As a scientist, my response to this content would be to provide guidance and clarification on how to approach the problem. Firstly, it is important to understand the concept of stiffness matrix and how it relates to the problem at hand. The stiffness matrix is a mathematical tool used to describe the stiffness of a structure or system. It is a square matrix that relates the applied forces to the resulting displacements in the structure.

In this problem, you have been given three springs at the first end, but the value of "G" is not given. This means that you cannot use the torsional spring in your stiffness matrix, as it requires the value of "G". Therefore, you should only consider the two axial springs in your stiffness matrix.

Next, it is important to understand the concept of stress stiffening. Stress stiffening is the increase in stiffness of a structure due to the presence of internal stresses. This can occur in structures that are subjected to large deformations. In this problem, it is not specified whether stress stiffening should be considered. Therefore, it is safe to assume that you should solve the problem without considering stress stiffening.

Based on this information, you can proceed to form your stiffness matrix for the first and third elements. It should be a 4x4 matrix with 3 axial columns and 1 bending column. For the second element, you will need a 6x6 matrix with 2 axial columns, 2 shear columns, and 2 bending columns. The variables u, v, and w represent the displacements in the x, y, and z directions respectively.

In summary, my advice would be to carefully consider the given information and apply the concepts of stiffness matrix and stress stiffening to solve the problem. If you are still having difficulties, it would be beneficial to seek clarification from your professor or consult additional resources. Good luck with your homework!