Twisting thin-walled orthotropic prismatic rod with elliptic hole on the lateral surface (Q2759464)

Elliptic hole in a box-like prismatic rod is assumed to be relatively small and located far from edges. The wall thickness is small compared to hole dimensions. First, the main stress state in a rod without a hole is found. For determination of the perturbed stresses arising in the vicinity of the hole, the wall near the hole is considered as a thin plate. Integration of equations of elasticity for orthotropic plate and a stress-free hole is done by the method of small parameter. As small parameters the wall thickness and the thickness coordinate are taken. Solution is subdivided into the two stages: (i) the problem of stretching-compression and (ii) the problem of bending. Expressions for the corresponding displacements are sought by the method of complex potentials. A numerical example is considered, plots of normal stresses are presented.