Some Solutions of Stationary Problems Based on 3D Theory

Abstract

In the present chapter models of three-dimensional theory of elasticity are used in order to study the stationary deformation of hollow and solid anisotropic inhomogeneous cylinders of finite length. Solutions for the stress–strain state and natural vibrations of hollow inhomogeneous finite-length cylinders are presented, which were obtained by making use of spline-collocation and discrete-orthogonalization methods. The influence of geometrical and mechanical parameters, of the boundary conditions, of the loading character on the distributions of stress and displacement fields, and of the dynamical characteristics in such cylinders are analyzed. In some cases the results obtained by three-dimensional and shell theory are compared. When solving dynamical problems for orthotropic hollow cylinders with different boundary conditions at the ends the method of straight-line methods in combination with the discrete-orthogonalization method was applied as well. Computations for solid anisotropic cylinders of finite length with different boundary conditions were carried out by using the semi-analytical finite element method. In the case of free ends the results of the calculations for the natural frequencies were compared with those determined experimentally. The results of calculations of the mechanical behavior of anisotropic inhomogeneous circular cylinders demonstrate the efficiency of the discrete-continuous approaches proposed in this monograph for solving shell problems when using three-dimensional models of elasticity theory.