Evaluation of shear and membrane locking in refined hierarchical shell finite elements for laminated structures

Guohong Li,Enrico Zappino,Alfonso Pagani,Erasmo Carrera,Gennady M Kulikov,Maria Cinefra,Alberto G De Miguel

doi:10.1186/s40323-019-0131-1

Abstract

Shear and membrane locking phenomena are fundamental issues of shell finite element models. A family of refined shell elements for laminated structures has been developed in the framework of Carrera Unified Formulation, including hierarchical elements based on higher-order Legendre polynomial expansions. These hierarchical elements were reported to be relatively less prone to locking phenomena, yet an exhaustive evaluation of them regarding the mitigation of shear and membrane locking on laminated shells is still essential. In the present article, numerically efficient integration schemes for hierarchical elements, including also reduced and selective integration procedures, are discussed and evaluated through single-element p-version finite element models. Both shear and membrane locking are assessed quantitatively through the estimation of strain energy components. The numerical results show that the fully integrated hierarchical shell elements can overcome the shear and membrane locking effectively when a sufficiently high polynomial degree is reached. Reduced and selective integration schemes can help with the mitigation of locking on lower-order hierarchical shell elements.

Highlights

Shell structures, especially composite laminated shells, have been widely used in modern engineering due to their high efficiency in holding loads
The results demonstrate that, it can be guaranteed that there is zero spurious mode for the reduced integrated hierarchical elements when p ≥ 3, and no spurious mode exists for selective integration when p ≥ 2
It is obvious that an element with only linear shape functions is not adequate for the modeling, the refinement of the shape functions starts from p = 2

Summary

Introduction

Especially composite laminated shells, have been widely used in modern engineering due to their high efficiency in holding loads. Refined shell theories have been implemented in the Finite Element (FE) method and can provide solutions with great accuracy [10,11]. Towards implementing numerically efficient simulation methods for multi-layered structures, hierarchical functions have been adopted in the construction of refined shell elements in the framework of CUF [12]. In Eng. Sci.(2019)6:8 mitigation of shear and membrane locking on refined multi-layered shell finite elements remains to be quantitatively assessed

Objectives

Results

Conclusion