Buckling analysis of thick cylindrical shells using micropolar theory

Abstract

Modeling complex materials with internal structure such as porous solids is challenging as in some cases the classical theory cannot provide precise responses. By considering the scale effects through additional kinematic descriptors and six constants for isotropic materials, the micropolar theory can accurately model complex materials like bone. This paper studies the buckling of a thick cylindrical shell using classical and non-classical theories. The cylinder’s material is considered bone and isotropic, and the critical load value for different geometries and boundary conditions has been obtained. Finally, the size-effect and importance of micropolar theory in micro dimensions are investigated. The micropolar equations are solved by a numerical solution using the 3D finite element method. The results show that decreasing the macroscopic length increases the stiffness of the cylinder more than that predicted by classical theory; In addition, by increasing the thickness of the cylinder and the importance of shear stresses, the micropolar theory predicts a more critical load than the classical one, and the result differences become more significant between micropolar and classical theories. Also, the characteristic length of the micropolar is investigated. The results show that the change of the critical load increased by moving toward the micro dimensions.