I am trying to establish what interpolation functions he used to obtain the 8 approximation functions (eqn 5.3.25a) shown in the attached excerpt from the book.

He states that a cubic approximation can be used for and aninterpendentquadratic approximation for thus I write

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).

inverse[{{1,x,x^2,x^3},{1,x,x^2,0},{1,y,y^2,y^3},{1,y,y^2, 0}}] - Wolfram|Alpha

Note: This has been submitted to PF 3 weeks ago with no response

Interdependent Interpolation Element- Timoshenko Beam

Regards

bugatti