Anisotropic behaviors of helically corrugated cylindrical shells: Homogenized in-plane stiffness

Abstract

Abstract Thin-walled corrugated structures have been widely used in engineering applications for centuries, because corrugation enables engineers to tailor directional dependent properties despite the structures being made of isotropic materials. However, the vast majority of research has paid attention to corrugated plates and relatively scarce studies are on corrugated shells. This paper, therefore, aims to investigate elastic behaviors of thin cylindrical shells that possess sinusoidal corrugating patterns in the helical direction. Elastic responses of undulated shells under three types of deformation, namely, axial elongation, axial torsion, and radial expansion are thoroughly investigated by using the finite-element method (FEM) via ABAQUS™. The effective stiffness of the corrugated cylinders is determined by a homogenization technique in a representative unit cell element. A variety of FEM models are created according to four groups of dimensionless parameters, i.e. radius-to-thickness ratio, radius-to-corrugating depth ratio, helical angle and the number of waveform (thread) in a cylinder cross section. The results show that the degree of anisotropy induced by the corrugated shells is different from that of a fiber-reinforced composite material, significantly sensitive to their configurations, and can be extraordinarily higher than the perfect round shell made of the same parent material. Unorthodox coupling quantities of torsional-axial, torsional-radial, and axial-radial coupling deformations are encountered at some specific geometries. Anisotropy design space in the form of spherical maps is given as a guideline to effectively design or select a proper helically corrugated cylindrical shell with the desired stiffness properties.