On a consistent rod theory for a linearized anisotropic elastic material II. Verification and parametric study

Abstract

We have derived a rod theory by an asymptotic reduction method for a straight and circular rod composed of linearized anisotropic material in part I of this series. In the current work, we first verify the derived rod theory through five benchmark Saint-Venant’s problems. Then, under a specific loading condition (line force at the lateral surface with two clamped ends), we apply the rod theory to conduct a parametric study of the effects of elastic moduli on the deformation of a rod composed of four types of anisotropic materials including cubic, transversely isotropic, orthotropic, and monoclinic materials. Analytical solutions for the displacement, axial twist angle, stress, and principal stress have been obtained and a systematic investigation of the effects of elastic moduli on these quantities is conducted, which is the main feature of this paper. It is found that these elastic moduli arise in a certain form and in a certain order in the solutions, which gives information about how to appropriately choose moduli to adjust the deformation. Among the four anisotropic materials, it turns out that the monoclinic material presents the most remarkable mechanical behavior owing to the existence of a coupling coefficient: it yields coupled leading-order rod equations, non-trivial axial twist angle, non-negligible transverse shear deformation, and a more adjustable principal stress along the axis.