The Resisting Mechanism during the Large Normal Deflection of Thin Shells Subjected to Follower Forces

Abstract

The load resistance mechanism of thin shells, such as the submerged shell structures in underwater marine constructions, are in principle of a nonconservative nature since the associated loads are the hydrostatic pressure and drag forces of the follower type.The general governing equations of equilibrium for thin shells are available from the literature in various details. In this research we consider shells defined in a monoclinically convected coordinate system subjected to follower loads and undergoing large deformations. The feasibility and significance of the theoretical formulations have already been substantiated through various numerical simulation results.In the simultaneous equations governing the equilibrium of shells, the presence of terms related to the shell curvature and other consequential terms such as the Christoffel symbols, clearly make them a substantially different class from the plate theory. This distinction, which may otherwise be denoted as the 'Form Effect' in more common terminology, renders the shell theory a lot more complicated and one that needs in-depth analytical effort to unravel the full significance of all the possible implications.The present paper elaborates on the mechanism of large deformation by studying the share of different stiffness factors on the total load resistance equilibrium picture of shells from the very shallow to the deep curvature range going through the subsequently increasing loading stages. This study concentrates mainly on the equilibrium in the normal direction. The resisting mechanism due to the extensional and the bending stiffness parts are considered as the two main entities and their subdivisions and other separable factors are studied in unison to draw out an overall picture. The partial cylindrical and spherical shells are considered and the results bring out the clear distinction between resistance mechanism of the two shells, especially in the deep curvature region.These results in their total details are believed to be helpful in understanding the deformation mechanism and formulate some design philosophy for shells and thereby serve as a guideline for appropriate formulations of the governing equations in particular cases.