This paper performs a numerical analysis of the stress behavior of a hollow cylinder within the framework of micropolar elasticity, taking explicitly into account length-scale effects. The governing field equations are established in polar coordinates, where size dependence is captured through characteristic material length parameters and the formulation is given in terms of stress functions. The resulting boundary value problem is then solved by using the Generalized Differential Quadrature (GDQ) technique. The obtained numerical results clearly show a strong dependency of the stress response from the material length parameter. Indeed, increasing the latter from ????=0 the value corresponding to the classical elasticity model-to the considered micrometer scale value, the maximum values of radial and circumferential stresses decrease by about 46% and 45%, respectively, whereas the maximum value of couple stress mrθ decreases by about 30%. These findings are particularly relevant for micro-scale engineering applications such as MEMS devices and biomedical implants, where component dimensions approach the material's micro-structural scale and classical elasticity proves inadequate. Furthermore, the pronounced size effects observed at the inner radius where stress gradients are highest highlight the critical need for micropolar theory in accurate stress analysis of microscale cylindrical structures. This work provides a foundation for future research on functionally graded micropolar materials and establishes GDQ as an efficient computational tool for capturing intricate size-effects in advanced micro-structured components.
Ali et al. (2025) studied this question.