An improved treatment of mixed interpolation functions in eight-node assumed natural strain shell element for vibration analysis

摘要

In this article, we investigate the vibration analysis of plates and shells, using an eight-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The natural frequencies of plates and shells are presented, and the forced vibration analysis of plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve the eight-node shell element for free and forced vibration analysis, a new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner-Mindlin theory, which directly addresses the transverse shear deformation without a shear correction factor, is adopted for the development of a new eight-node assumed strain shell element with rotary inertia effect. In order to validate the finite element numerical solutions, the reference solutions of plates based on the first-order shear deformation theory are presented. Results of the present theory show good agreement with the reference solutions. In addition, the effect of damping is investigated on the forced vibration analysis of plates and shells.