Three-Dimensional Elasticity Solutions for Isotropic and Generally Anisotropic Bodies
Classical methods of two-dimensional elasticity can be extended to give an exact solution of the three-dimensional problem for the beam — i.e. a general solution for the pris- matic bar loaded on its lateral surfaces, subject only to the restriction that the tractions can be expanded as power series in the axial coordinate z. A series of sub-problems Pj is defined by successive partial differentiations with respect to z. For isotropic materials, a recursive al- gorithm can be used for generating the solution to Pj+1 from that for Pj in the context of the Papkovich-Neuber solution. For the generally anisotropic material, a similar strategy is proposed, based on partial integrations of Stroh’s formulation of the two-dimensional problem.
Patrick Sean Keogh
J.R. Barber, "Three-Dimensional Elasticity Solutions for Isotropic and Generally Anisotropic Bodies", Applied Mechanics and Materials, Vols. 5-6, pp. 541-550, 2006