ABSTRACT
This chapter is devoted to the study of the deformation of nonhomogeneous and isotropic cylinders. Most of the works concerned with Saint-Venant’s problem are restricted to homogeneous cylinders. However, some investigations are devoted to Saint-Venant’s problem for nonhomogeneous cylinders where the elastic coefficients are independent of the axial coordinate, they being prescribed functions of the remaining coordinates. This theory is of interest from both the mathematical and technical points of view [3,75,88,130]. According to Toupin [329], the proof of Saint-Venant’s principle presented in Section 1.10 also remains valid for this kind of nonhomogeneous elastic bodies. The study of Saint-Venant’s problem for nonhomogeneous cylinders was initiated by Nowinski and Turski [256] and was developed in various later works [150,279,303,318]. An account of the historical developments of the theory of nonhomogeneous elastic bodies as well as references to various contributions may be found in Refs. 175, 209, 219, and 290. Many works concerned with Saint-Venant’s problem for nonhomogeneous cylinders are restricted to the case when the Poisson’s ratio is constant. A method to solve the problem, which avoids this restriction, was presented in Ref. 149.
