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Interdependent Interpolation Element- Timoshenko Beam

  1. Dec 3, 2012 #1
    Folks,


    I am trying to establish what interpolation functions he used to obtain the 8 approximation functions. See attached excerpt from the book.

    He states that a cubic approximation can be used for ##w(x)## and an interpendent quadratic approximation for ##\Psi(x)## thus I write

    ##\Delta^e_1=w^e_1=c_1^e+c_2^ex_e+c_3^ex_e^2+c_4^ex_e^3 ##
    ##\Delta^e_2=S^e_1=c_1^e+c_2^ex_e+c_3^ex_e^2+0 ##

    ##\displaystyle\Delta^e_3=w^e_2=c_1^e+c_2^ex_{e+1}+c_3^ex_{e+1}^2+c_4^ex_{e+1}^3 ##
    ##\displaystyle\Delta^e_4=S^e_2=c_1^e+c_2^ex_{e+1}+c_3^ex_{e+1}^2+0 ##

    Putting into matrix form and inverting to find the c values wolfram comes up with the matrix being singular (note I am using dummy variables).

    http://www.wolframalpha.com/input/?i=inverse[{{1,x,x^2,x^3},{1,x,x^2,0},{1,y,y^2,y^3},{1,y,y^2,0}}]
     

    Attached Files:

    Last edited: Dec 3, 2012
  2. jcsd
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