# Verification Examples

## Helicoid

VE 0208

10 February 2019

A membrane is stretched by means of isotropic prestress between two radii of two concentric cylinders not lying in a plane parallel to the vertical axis. Find the final minimal shape of the membrane - the so-called helicoid, and determine the surface area of the resulting membrane. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in analytical solution, also self-weight is neglected in this example.

## Catenoid

VE 0207

14 November 2018

A cylindrical membrane is stretched by means of isotropic prestress. Find the final minimal shape of the membrane - catenoid. Determine the maximum radial deflection of the membrane. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in analytical solution, also self-weight is neglected in this example.

## Balloon – Prestressed Membrane

VE 0206

8 October 2018

A spherical balloon membrane is filled with gas with atmospheric pressure and defined volume (these values are used for FE model definition only). Determine the overpressure inside the balloon due to the given isotropic membrane prestress. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in analytical solution, self-weight is also neglected in this example.

## Buckling of a Circular Ring

VE 0094

10 July 2018

A thin circular ring of rectangular cross-section is exposed to an external pressure. Determine the critical load and corresponding load factor for in-plane buckling.

## Thin-Walled Conical Vessel with Hydrostatic Pressure

VE 0085

19 February 2018

A thin-walled conical vessel is filled with water. Thus, it is loaded by the hydrostatic pressure. While neglecting self-weight, determine the stresses in surface line and circumferential direction. The analytical solution is based on the theory of thin-walled vessels. This theory was introduced in Verification Example 0084.

## Scordelis-Lo Roof

VE 0083

4 December 2017

A shell roof structure under pressure load is modelled, where the straight edges are free, while at the curved edges the y- and z‑translations are constrained. Neglecting self‑weight, compute the maximal (absolute) vertical deflection, and compare the results with COMSOL Multiphysics 4.3.

## Thin-Walled Spherical Vessel

VE 0084

4 December 2017

A thin-walled spherical vessel is loaded by inner pressure. While neglecting self‑weight, determine the von Mises stressand the radial deflection of the vessel.

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