Modeling a simple elasticity problem
Variational approach for the finite element method

Consider an elastic cord of unit length, fixed at its ends, which at rest occupies a position coinciding with the axis Ox. This string is subjected to a force of density per unit length $f\left(x\right)$ whose direction is perpendicular to the Ox axis. Under the effect of this force, the string undergoes a displacement $u\left(x\right)$ , perpendicular to the Ox axis. In the following, we'll assume that this displacement is small. The problem boils down to determining $u\left(x\right)$...