Existence of equilibrium states of hollow elastic cylinders submerged in a fluid

Abstract

ABSTRACT. This paper is concerned with the existence of equilibrium states of thin-walled elastic, cylindrical shell fully or partially submerged in a fluid. This problem obviously serves as a model for many problems with engineering importance. Previous studies on the deformation of the shell have assumed that the pressure due to the fluid is uniform. This paper takes into consideration the non-uniformity of the pressure by taking into account the effect of gravity. The presence of a pressure gradient brings additional parameters to the problem which in turn lead to the consideration of several boundary value problems.KEY WORDS AND PHRASES. Existence of equilibrium states, hollow elastic cylinders, nonlinear eigenvalue problem, non-linear integro-differential equation, minimization of functional with several constraints, Browder Theorem, linearly independent operators. 1980

Existence of equilibrium states of hollow hollomon cylinders submerged in a fluid

“…By considering "planar" deformations of the cylinders we have generalized the results obtained for an inextensible elastic model in [8]. …”

“…It turns out that they must satisfy the inequality 2 τ π Γ < which has a simple geometric interpretation. We let (0,1), and define for , the following three functionals: We can verify (see [8] for details) the following properties:…”

“…By treating the problem as independent of the variable along the axis of the cylinder we arrive at a similar system of nonlinear ordinary differential equations governing the equilibrium to that of an inextensible Hollomon elasto-plastica for a circular ring presented in [9]. Our work generalizes that of [7], [8] and [10], where linear elastic cylinders are considered.…”

“…These are obtained by generalizing the formulations given in [8] for linear (elastica ) elastic cylinders to the case when the cylinder is made of Hollomon plastic material. In Section 3, we use the Implicit Function Theorem to give a proof of the existence of positive bifurcation solutions of small norms merging off the trivial solution for the case when the pressure is uniform.…”