On the Almansi-Michell Problems for an Inhomogeneous, Anisotropic Cylinder

Abstract

AbstractA semi-analytical finite element (SAFE) method is presented for constructing solutions for an arbitrarily loaded cylinder, whose cross-section is general in terms of its shape and the number of distinct, perfectly bonded elastic, rectilinear anisotropic materials. The surface traction and body force loads need to be expressed in a power series of the axial coordinate. Linear three-dimensional theory is used. For a homogeneous isotropic cylinder, it is known as the Almansi-Michell problem, and the SAFE analysis herein is an extension to inhomogeneous, anisotropic bodies. By SAFE, the cross-section is discretized. The displacement field is expressed by interpolation functions over the cross-section and by analytical functions axially. The method herein is an extension of the authors' previous method cylinder with a general cross-section. Herein, the SAFE solution procedure is given and numerical examples will be presented.