Development of a Flat Shell Element in Hybrid-type Penalty Method

Abstract

In this study, to apply a hybrid-type penalty method (HPM) to problems such as the thermal cracking of glass and model order reduction (MOR) techniques, we develop a flat shell element. First, we derive a hybrid virtual work equation based on the governing equation of general three-dimensional elastic problems. Next, we will arrange the assumptions for reducing the order to a two-dimensional problem that is the basis of the flat shell element. Furthermore, the displacement field of the in-plane and out-of-plane deformations is expressed as a quadratic function, and by synthesizing them, the displacement field of the flat shell element is assumed. By substituting these relationships into the hybrid-type virtual work equation, the discretization equation of the flat shell element is derived. Finally, we evaluate the performance of the proposed flat shell element by using a simple numerical example.