Elasticity and stability of corrugated conical shells with diverse orthotropy

Abstract

Curved thin-walled structures have attracted significant attention within engineering communities thanks to their remarkable properties, including high load-bearing capacity, tailorable directional stiffness, adaptability, and lightweight characteristics. The geometric intricacies of these structures not only influence their mechanical behavior but also provide a vast design space for exploring new frontiers in structural development. This study investigated a unique form of curved thin-walled structure, namely the corrugated annular conical shell, which exhibits diverse degrees of cylindrical orthotropy across various corrugation patterns. An analytical model was formulated based on the minimum total potential energy principle and first-order shear deformable shell theory to predict the non-monotonous force-deflection relationships and non-uniform stress distributions in corrugated conical shells when axially loaded under compression. Within this novel framework, the local undulation shape, corrugation pitch, and amplitude emerged as influential determinants of the responses of corrugated shells, intrinsically intertwined with the polar and shear orthotropy ratios. The accuracy of our analytical model was verified by comparing its results to those obtained using the finite element method and experimental measurements. A machine learning method was employed to classify the stability behaviors of corrugated annular conical shells and derive comprehensive design maps for the first time. Corrugated annular conical shells hold enticing potential for applications as adaptive spring units or building blocks for more sophisticated architectural metamaterials.