# Analytic description and explicit parametrization of the equilibrium shapes of elastic rings and tubes under uniform hydrostatic pressure

@article{Djondjorov2010AnalyticDA, title={Analytic description and explicit parametrization of the equilibrium shapes of elastic rings and tubes under uniform hydrostatic pressure}, author={Peter A. Djondjorov and Vassil M. Vassilev and Iva{\"i}lo M. Mladenov}, journal={arXiv: Mathematical Physics}, year={2010} }

## 40 Citations

### Analytic Description of the Equilibrium Shapes of Elastic Rings Under Uniform Hydrostatic Pressure

- Engineering, Physics
- 2011

The parametric equations of the plane curves determining the equilibrium shapes that a uniform inextensible elastic ring could take subject to a uniform hydrostatic pressure are presented in an…

### Deformation of a Circular Elastic Tube between Two Parallel Bars: Quasi-Analytical Geometrical Ring Models

- Engineering
- 2015

Several engineering problems are confronted with elastic tubes. In the current work, homothetic quasi-analytical geometrical ring models, ellipse, stadium, and peanut, are formulated allowing a…

### The \theta-formulation of the 2D elastica -- Buckling and boundary layer theory

- Engineering
- 2023

The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This…

### Universal Wrinkling of Supported Elastic Rings.

- EngineeringPhysical review letters
- 2022

An exactly solvable family of models describing the wrinkling of substrate-supported inextensible elastic rings under compression is identified. The resulting wrinkle profiles are shown to be related…

### Analytical solution of the cantilevered elastica subjected to a normal uniformly distributed follower load

- Engineering
- 2020

### A perturbation approach on buckling and postbuckling of circular rings under nonuniform loads

- Engineering
- 2018

### Equilibrium shapes of cylindrical rotating liquid drops

- Mathematics, Physics
- 2014

We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the vertical axis. We restrict ourselves here to surfaces which are…

### Equilibrium shapes of cylindrical rotating liquid drops

- Mathematics, PhysicsBulletin of the Brazilian Mathematical Society, New Series
- 2015

We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the vertical axis. We restrict ourselves here to surfaces which are…

### Self-contact of a flexible loop under uniform hydrostatic pressure

- PhysicsEuropean Journal of Mechanics - A/Solids
- 2020

### Postbuckling up to Collapse of Polar Orthotropic Linearly Elastic Rings Subjected to External Pressure

- Engineering
- 2016

Post-buckling and collapse phenomenon of a thick closed ring subjected to external pressure on its outer surface is analyzed in this research. Ring is made of a linearly elastic polar orthotropic…

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