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Linear Spring System - FEM

  1. Oct 28, 2012 #1
    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.
    Diagram.jpg

    2. Relevant equations
    eqtns.jpg


    3. What confuses me

    From the equilibrium condition [itex]f_1+f_2=0[/itex] I could have easily written [itex]f_2=-f_1[/itex] 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 [itex]f_2=-f_1[/itex] but then write [itex]\delta=u_1-u_2[/itex] 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
  2. jcsd
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