Three-Dimensional Elasticity Solutions for Isotropic and Generally Anisotropic Bodies

摘要

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 prismatic 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 P_j is defined by successive partial differentiations with respect to z. For isotropic materials, a recursive algorithm can be used for generating the solution to P_(j+1) from that for P_j 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.