# Verifikationsbeispiele

#### Buch über FEM und RFEM

In diesem Buch für Ingenieure und Studenten erfahren Sie Grundlegendes zur Finite-Elemente-Methode praxisnah anhand von überschaubaren Beispielen, die mit RFEM berechnet wurden.

## Euler Buckling

VE 0096 14. November 2018

A strut with circular cross-section is supported according to four basic cases of Euler buckling and it is subjected to pressure force. Determine the critical load.

## Thin Rectangular Orthotropic Plate Under Uniform Load

VE 0091 10. Juli 2018

Thin rectangular orthotropic plate is simply supported and loaded by the uniformly distributed pressure. The directions of axis x and y coincide with the principal directions. While neglecting self-weight, determine the maximum deflection of the plate.

## Dynamic Force Distribution

VE 0121 10. Juli 2018

A single-mass system with dashpot is subjected to a constant loading force. Determine the spring force, the damping force and the inertial force at given test time. In this verification example, the Kelvin--Voigt dashpot, namely, a spring and a damper element in serial connection, is decomposed into its purely viscous and purely elastic parts, in order to better evaluate the reaction forces.

## Buckling of Beam with Various Cross-Sections

VE 0093 10. Juli 2018

A column is composed of a concrete part - rectangle 100/200 and of a steel part - profile I 200. It is subjected to pressure force. Determine the critical load and corresponding load factor. The theoretical solution is based on the buckling of a simple beam. In this case two regions have to be taken into account due to different moment of inertia and material properties.

## Single-Mass Oscillation with Dashpot

VE 0120 21. Februar 2018

A single mass system with dashpot is subjected to the constant loading force. Determine the deflection and the velocity of the dashpot endpoint in given test time.

VE 0087 20. Februar 2018

A curved beam consists of two beams with a rectangular cross-section. The horizontal beam is loaded by a distributed loading. While neglecting self-weight, determine the maximal stress on the top surface of the horizontal beam.

VE 0086 20. Februar 2018

A quarter-circle beam with a rectangular cross-section is loaded by means of an out-of-plane force. This force causes a bending moment, torsional moment and a transverse force. While neglecting self-weight, determine the total deflection of the curved beam.

## Thin-Walled Conical Vessel with Hydrostatic Pressure

VE 0085 19. Februar 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. Dezember 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. Dezember 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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