Interdependent Interpolation Element- Timoshenko Beam

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^e x_{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...2%2C0%7D%7D%5D

Attached Thumbnails