# Interdependent Interpolation Element- Timoshenko Beam

1. Dec 3, 2012

### bugatti79

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:

• ###### Interpolation Function.jpg
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Last edited: Dec 3, 2012