On the deformation of almost cylindrical elastic beams

Background: The Saint-Venant problem for porous elastic cylinders is of interest both from the technical and mathematical point of view. The intended applications of solution are to mechanics of bone and to some engineering structures. Method: This work investigates the Saint-Venant problem for almost prismatic bars made of an isotropic porous material. We express the solution in terms of the solutions of two problems concerning the deformation of a right cylinder. Results and Conclusion: We use the method to study the extension of an almost prismatic conical frustum. It is found that the displacement vector is a polynomial of two degree in the cartesian coordinates. The volume fraction field depends linearly on the axial coordinate. The solution contains terms characterizing the influence of the material porosity and the dependence on the lateral surface