On the deformation of micromorphic elastic beams

Abstract

This paper is concerned with the deformation of beams in the framework of the linear theory of micromorphic elastic solids. First, the plane strain of anisotropic and homogeneous elastic cylinders is investigated. Existence and uniqueness results are presented. Then, Saint-Venant’s problem for micromorphic beams is formulated. A method is established to reduce the extension, bending and torsion to the study of some plane problems. Finally, the deformation of beams loaded on the lateral surface is investigated. As a special case, the solution of the flexure problem is obtained. The method is used to study the deformation of a micromorphic rod subjected to a uniform pressure on the lateral surface.