An extension of Almansi's problem for orthotropic elastic beams

First we construct the boundary value problem in the context of the elastostatics of elastic orthotropic beams, which are loaded on the ends and on the lateral surface. Then we determine the solution of this problem with the help of some functions of stress. In this way we find an extension of Prandtl's method and, in the same time, an natural extension of the known Almansi's problem from the classical plane problem of torsion.

Automated summary

First, we establish the boundary value problem for elastic orthotropic beams in the context of elastostatics, where the beams are loaded at the ends and on the lateral surface. Then, we solve this problem by using stress functions, which leads to an extension of Prandtl's method and naturally extends the known Almansi's problem from the classical plane problem of torsion.