 Verification Examples

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.

Mathematical Pendulum

VE 0118

4 December 2017

The mathematical pendulum consists of a zero‑weight rope and a mass point at its end. The pendulum is initially deflected. Determine the angle of the rope at given test time.

Helical Spring

VE 0082

4 December 2017

Closely coiled helical spring is loaded by a compression force. The spring has a middle diameter D, the wire diameter d, and it consists of i turns. The total length of the spring is L. Determine the total deflection of the spring for the member model and one‑turn deflection for the solid model.

Cable with Concentrated Forces

VE 0080

4 December 2017

A cable in the initial position is loaded by two concentrated forces. The self‑weight is neglected. Determine the normal forces in the cable.

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.

Eccentricity Test

VE 0090

4 December 2017

Pinned beam with rectangular cross‑section is subjected to distributed loading and shifted vertically by eccentricity. Considering small deformation theory, neglecting self‑weight, and assuming that the beam is made of isotropic elastic material, determine the maximum deflection.

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.

Free Vibrations of String

VE 0112

27 October 2017

A thin string is tensioned by the initial strain and initially deflected. Determine the deflection of the test point at given test times.

Double Mass Oscillator

VE 0117

27 October 2017

A double-mass oscillator consists of two linear springs and masses, which are concentrated at the nodes. The self-weight of the springs is neglected. Determine the natural frequencies of the system.

Vibrations with Coulomb Friction

VE 0116

16 October 2017

A simple oscillator consists of mass m (considered only in x-direction) and linear spring of stiﬀness k. The mass is embedded on a surface with Coulomb friction and is loaded by constant-in-time axial and transversal forces.

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