Semi-exact solutions for large deflections of cantilever beams of non-linear elastic behavior

Here the problem was more challenging: the combined action of a force applied at the tip and a uniformly distributed load. The nonlinearity was expressed as a relationship of the Ludwick type between the stress $\sigma$ and the strain $\varepsilon$. That is, $\sigma\propto \varepsilon^{1/n}$, with $n$ being material-dependent ($=1$ for the previously studied linear materials).

Surprisingly, I could find some few cases where a semi-analytical solution was possible, holding for materials like acetal plastic and glass fibre.