Quadrilateral scaled boundary spectral shell elements with assumed natural strains

Abstract

This paper presents new variable-order shell elements that require only the shell mid-surface to be discretized, contain no rotational degree of freedom and adopt the full three-dimensional constitutive relationship. In the formulation, a shell element is treated as a three-dimensional continuum undergoing small deformations and its middle surface is represented by a quadrilateral spectral element. Along the thickness direction, the shell geometry is described by scaling the middle surface and the displacements are expressed approximately by interpolating the displacements on the top, middle and bottom surfaces with quadratic Lagrange shape functions. The assumed natural strain method is applied to eliminate transverse shear locking, membrane locking and curvature thickness locking while the volumetric locking is alleviated by elevating the element order. Numerical examples demonstrate that the developed shell elements are superior in applicability, accuracy and efficiency.