An anisotropic heterogeneous beam with overspecified boundary conditions

In this paper a heterogeneous anisotropic cylindrical beam with a rigidly fixed base is considered as an alternative to the relaxed Saint-Venant's problem.The rigidly fixed base results in a problem with overspecified boundary conditions for which a proof of existence is given.The results of this paper indicate that the relaxed Saint-Venant's problem, for loads independent of the axial coordinate, ignores the dependence of the stress field on the axial coordinate.Dependence of the stress field on the axial coordinate could result in warping of transverse cross sections and nonzero in-plane stresses, which is significant for understanding the behavior of natural structures such as wood and mammalian bone.