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.