The paper aims to study, using the finite element method, the elastic behavior of a cylinder made by a material with micropolar structure, containing (as the results of the processing or introduced intentionally) voids. To study such a type of problem, a theoretical model of a continuous solid body with voids in the material is presented, after which, in order to determine the effect that these voids have, a model with finite elements is made, using Lagrange’s equations. This model can be applied to any type of elastic solid with voids. In the paper study the elastic response of a hollow cylinder made by a material with voids. Finally, comparative results are obtained to show the influence of voids on the elastic behavior of the body in some classic cases. These results are compared with the values obtained in the literature by experimental methods. It is found that a small percentage of voids can lead to significant variations on the mechanical properties.

本文旨在使用有限元方法研究由具有微极结构的材料制成的圆柱体的弹性行为，该材料包含（作为加工结果或有意引入的）空隙。为了研究此类问题，提出了材料中具有空隙的连续固体的理论模型，然后，为了确定这些空隙的影响，使用拉格朗日方程建立了有限元模型。该模型可应用于任何类型的具有空隙的弹性实体。在本文中，研究了由具有空隙的材料制成的空心圆柱体的弹性响应。最后，通过比较结果来展示一些经典案例中空隙对车身弹性行为的影响。将这些结果与通过实验方法在文献中获得的值进行比较。发现小百分比的空隙会导致机械性能的显着变化。