Exercice 1

Build up your own python program to solve a beam with an arbritary number of elements and arbritary loading. Do it either in a text file (.py) or in a new jupyther notebook. You can use object-oriented programming, as suggested below.

In particular, test your program on a clamped-clamped beam submitted ot a uniform transverse load $\underline f(s)=-p\underline e_2$. It can be shown (see the class of Structural Mechanics) that the analytical solution for the transverse displacement is $$ v(s) = \dfrac{p s^2}{24EI}(L-s)^2 $$ Compare the numerical solution against this analytical solution when using $n=5$, $n=10$, $n=20$, $n=100$ elements

You find below an example to start a Frame class. The example include geometry and visualization features. You should add the methods (i.e. the functions of the class) to assemble K, F, impose bcs and solve the system.

Once done, test the solution for a cantilever beam under its own weigth. Compare againt the analytical solution

Exercice 2

Extend the Frame class by including the case of beam segments with several orientations. Look also at the reference in the Syllabus. Test on examples