In diesem Buch für Ingenieure und Studenten erfahren Sie Grundlegendes zur Finite-Elemente-Methode praxisnah anhand von überschaubaren Beispielen, die mit RFEM berechnet wurden.
Verifikationsbeispiele
Buch über FEM und RFEM
Catenoid
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.
Euler Buckling
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.
Plastic Material Oscillations
This verification example is based on Verification Example 0122. A single-mass system without damping is subjected to an axial loading force. An ideal elastic-plastic material with characteristics is assumed. Determine the time course of the end-point deflection, velocity and acceleration.
Beam in Axial Compression According to ADM
Determine the allowable axial compressive strength of a pinned 8 ft long beam of various cross-sections made of Alloy 6061-T6 and laterally restrained to prevent buckling about its weak axis in accord with the Aluminium Design Manual.
Beam in Flexure According to ADM
Verify that a beam of different cross-sections made of Alloy 6061-T6 is adequate for the required load, in accord with the Aluminium Design Manual.
Eight-Member Symmetric Shallow Truss Snap-Through
A symmetrical shallow structure is made of eight equal truss members, which are embedded into hinge supports. The structure is loaded by the concentrated force and alternatively by the imposed nodal deformation over the critical limit point when the snap-through occurs. Imposed nodal deformation is used in RFEM 5 and RSTAB 8 to obtain full equilibrium path of the snap-through. The self-weight is neglected in this example. Determine the relationship between the actual loading force and the deflection considering large deformation analysis. Evaluate the load factor at given deflections.
Cable Equilibrium Force
A cable is loaded by means of the uniform load. This causes the deformed shape in the form of the circular segment. Determine the equilibrium force of the cable to obtain the given sag of the cable. 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
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.
Four-Member Truss Snap-Through
A structure is made of four truss members, which are embedded into hinge supports. The structure is loaded by a concentrated force and alternatively by imposed nodal deformation over the critical limit point, when snap-through occurs. Imposed nodal deformation is used in RFEM 5 and RSTAB 8 to obtain full equilibrium path of the snap-through. The self-weight is neglected in this example. Determine the relationship between the actual loading force and the deflection considering large deformation analysis. Evaluate the load factor at given deflections.
Bourdon Effect
A pipe with the tubular cross-section is loaded by means of internal pressure. The internal pressure causes axial deformation of the pipe, what is called Bourdon effect. Determine the axial deformation of the pipe endpoint.
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Knowledge Base
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