Large elastic deformations in thin cantilever rods due to concentrated loadings

In this paper the problem of large elastic deformations in cantilever thin rods subjected to concentrated loads is considered. Taking into account the incompressibility assumption of the center line and the equations relating the internal moments with the curvatures and torsion of the rod before and after the deformation, the non-linear equilibrium system, composed of six coupled differential equations of first order, is transformed to a new system of higher order. The cases of geometries of initially curved rods and their cross-sections were investigated, for which the higher order system of equations may be decoupled and solved in a closed form. Several applications of thin curved cantilever rods were made and the potentialities of the method were shown with these examples.