# Linear Spring System - FEM

1. Oct 28, 2012

### KleptoBear

This is not exactly a HW problem but a worked out problem that I am trying to understand. Below pictures are from Hutton's "Fundamentals of Finite Element Analysis"

1. The problem statement, all variables and given/known data

Derivation of system of equations for given figure.

2. Relevant equations

3. What confuses me

From the equilibrium condition $f_1+f_2=0$ I could have easily written $f_2=-f_1$ instead. This changes the signs of the diagonals. Yet, when I do this and solve a numerical example that is later done in the book on this same system, I get (expectedly!) same answers in magnitude but opposite in sign. Many books introduce FEM with similar examples and the five or six books that I have checked have the stiffness matrix exactly like above. Some do express the equilibrium condition as $f_2=-f_1$ but then write $\delta=u_1-u_2$ instead.
Is there a general convention that I am missing? I guess this may be a case of staring-at-what-you're-looking-for-but-not-seeing. Any help is appreciated. Thank you

Last edited: Oct 28, 2012