shpae functions FEM

dirk_mec1

1. The problem statement, all variables and given/known data


The displacement functions:




Derive the displacement functions 2-10 up to 2-13.

2. Relevant equations
Third cubic polynomial and elementary beam theory


3. The attempt at a solution
I don't understand how the displacement functions can be derived can somebody give me a hint?

dirk_mec1

Hmmm, the title should read displacement functions. The thing is I know that [itex] \xi [/itex] should run between 0 and 1 (because [itex] \xi = x/L) [/itex]. But why is the displacement: [tex]y(0) =
\theta_1 \cdot L [/tex] shouldn't there be a correction for the second angle? Moreover why is the displacement at the end zero e.g. why is y(1) =0?

By the way the picture ends like this:



ands starts like this: