Thermal stresses in orthotropic Cosserat elastic cylinders

摘要

This paper is concerned with the equilibrium theory of orthotropic Cosserat continua. We study the thermoelastic deformation of a beam which is subjected to a prescribed thermal field. The work is motivated by the recent interest in the using of the orthotropic Cosserat elastic solid as a model for bones and various engineering materials with microstructure. The temperature variation is a assumed to be independent of the axial coordinate. First, we investigate the case of a homogeneous solid. Then we study the deformation of a beam which is composed by two materials welded together along the surface of separation. The solution could be used to investigate the behavior of bone implants. We present some results concerning the plane strain problem of orthotropic beams and reduce the three-dimensional problem to the study of some plane problems. The results are used to investigate the deformation of a circular beam subjected to a uniform thermal field.