An enriched virtual element method for 2D‐3C generalized membrane shell model on surface

Abstract

AbstractDealing with complex shell surfaces using the finite element method, we are often limited to simple geometric meshes such as triangles and quadrangles and have to refine the meshes to meet the calculation accuracy requirements, significantly increasing the calculation cost. The virtual element method (VEM), a new numerical method with high mesh flexibility, has been widely applied to many physical and mechanical problems. To the best of our knowledge, this method has yet to be studied for membrane shell models so far. In this paper, for the first time, we provide an enriched conforming VEM discrete scheme for the two‐dimensional three‐component (2D‐3C) generalized membrane shell (GMS) model proposed by Ciarlet et al. Furthermore, we prove the VEM discrete solution's existence and uniqueness for the GMS. Numerical experiments demonstrate that this discrete scheme is convergent and stable and can accurately represent the membrane stress state of conical, cylindrical, hyperbolical, and spherical shells clamped along a portion of their lateral faces. At the same time, we show the diversity of the grid subdivision. Thus, we develop the VEM for the GMS model successfully. In the future, we will continue to study the VEM for other shell models.