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The Standard NAFEMS Benchmarks

In 1986 NAFEMS attempted to produce the first set of independent "standard" tests which could be applied to any Finite Element System. The tests were intended for the use of code developers, users and others who were interested in the performance of specific codes. they were designated to be a little more searching  than those publicised or quoted by the software developers, since these were naturally intended to demonstrate the favourable performance of a system rather than the deficiencies.

these tests were critical they were not "pathological", i.e they were not designed such that any competent commercial system would be unable to provide satisfactory results. Targets were normally single point values of stress for static structural problems, temperature for thermal problems and frequency  for free vibration problems. Wherever possible targets were obtained from analytical solutions but numerical solutions, from more than one system, have also been used.

It was appreciated at the tome of selection that it was not desirable that the "standard" set should be subject to frequent  changes and every effort was made to ensure that their specification was clear and unambiguous and that they could  be run on any competent system without reference to other sources. (However the appropriate back-up references were supplied for the benefit of those who wanted additional information). Nevertheless, one of the benchmarks (test T3 for transient thermal analysis) proved unsatisfactory. The reasons for this were explained in the "Benchmark" article by Alan Welsh. ("Benchmark", January 1989, p23).

A substantial number of benchmarks have been studied with a view to producing a larger set. Those reviewed have included dynamic and non-linear tests in addition to further linear problems. At this stage it has been decided to provide a revised version of the transient, thermal problem, (T3), to add further linear static further tests, (designed to cover additional features), and to  include some free vibration tests selected from those detailed in the report resulting from the contract to devise Free Vibration Benchmarks (NAFEMS document FVB dated November 1987). No Non-Linear tests  been included at present.

The format of the original set has been retained and the specification has been kept as brief as possible consistent with content and clarity and avoidance of ambiguity.

Readers are invited to comment on the Benchmarks, and constructive criticism will be welcomed. It would be particularly helpful to have suggestions for further tests, if tests for "testable " features prove to be lacking. Readers are also invited to submit the Benchmark results for systems with whicj they are concerned. several such sets have been submitted and appeared in "Benchmark" from time to time. This will continue to be a feature of the magazine.

Revision 2 has corrections to LE8, LE10, LE11 and T3. The correction to LE10 is important since both the magnitude and location of the target stress have been amended.

Revision 3 includes corrections to LE4, LE7, LE9 and LE10.


  • Elliptic Membrane - Analysis type: Linear elastic

  • Cylindrical Shell patch test - Analysis type: Linear elastic

  • Hemisphere-point loads - Analysis type: Linear elastic

  • Axisymetric hyperbolic shell, edge loading  - Analysis type: Linear elastic

  • Z-section cantilever - Analysis type: Linear elastic

  • Skew Plate Normal Pressure - Analysis type: Linear elastic plate bending

  • Asymmetric cylinder/sphere-pressure - Analysis type: Linear elastic asymmetric

  • Asymmetric Shell Pressure - Analysis type: Linear elastic axisymetric

  • Asymmetric branched shell-pressure - Analysis type: Linear elastic asymmetric

  • Thick plate pressure - Analysis type: Linear elastic solid

  • Solid cylinder/Taper/Sphere-Temperature - Analysis type: Linear elastic solid

  • One Dimensional Heat Transfer with Radiation - Analysis type: Heat conduction

  • Membrane with Hot-Spot - Analysis type: Linear thermo-elastic

  • One Dimensional Transient Heat Transfer - Analysis type: Transient Heat Conduction

  • Two dimensional heat Transfer with convection - Analysis type: Heat Conduction

  • Pin-ended Double Cross: in-plane vibration

  • Cantilever with off-centre point masses

  • Deep Simply-Sorted Beam

  • Free Thin Square Plate

  • Clamped Thin Rhombic Plate

  • Cantilevered Thin Square Plate

  • Clamped Thick Rhombic Plate

  • Cantilevered Tapered Membrane

  • Free Cylinder: Axisymmetric vibration

  • Thick Hollow Sphere: Uniform radial Vibration

  • Simply-supported 'solid' square plate

  • Cantilevered thin square plate

Document Details

Date 1st January 1990


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