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Benchmark Tests For Various Finite Element Assemblies

This report on proposed benchmarks for static finite element tests supercedes a previous interim report. It is self-contained and includes, where helpful, theory of references to analytics material in appendices. A set of basic system performance tests have been developed which use a simple geometry. These are followed by a set fo membrane assemblies designed to test element behaviour under various mechanical  and thermal loadings and this theme is continued  for plate bending elements. Several three dimensional shell benchmarks are defined and finally folded plate beam is examined. All benchmarks have target figures evaluated to at least 1% accuracy and in all cases the typical performance of a finite element system is quoted.



  • Introduction
  • Presentation of the Benchmarks
  • Benchmark Data Sheets
  • Standard Properties

Benchmarks Set 1 - Basic System Tests

  • Introduction
  • Tapered Quadrilateral Membrane Plate
  • Tapered Quadrilateral Bending Plate
  • Tapered Axisymmetric Thick Shell
  • General Discussion of Set 1 Benchmarks

Benchmarks Set 2 - Planar Membrane Elements 

  • Introduction
  • Circular ring under Uniform External Pressure
  • Circular Ring Under Concentrated Load at 45 Degrees Normal to the Outside Edge
  • Circular Ring with a Quadratically Varying Radial Temperature Distribution
  • Shear Diffusion Problem
  • Membrane Stress Concentration  Benchmark
  • General Discussion of Set 2 Benchmarks

Benchmarks Set 3 - Plate bending Elements 

  • Introduction
  • Plate Bending Benchmarks
  • General Discussion of Set 3 Benchmarks

Benchmarks Set 4 - General Shell Elements 

  • Introduction
  • Quarter Hemisphere under Uniform Internal Pressure
  • Quarter Hemisphere under Concentrated Loads
  • General Discussion of Set 4 Benchmarks

Benchmarks Set 5 - Folded Plate Structures

  • Introduction
  • Z-Section thin Walled Cantilever Beam under hear and End Torque
  • General Discussion of Set 5 Benchmarks

Appendix 1 - Elliptical Plate Membrane Solution
Appendix 2 - Elliptical Plate Under Bending
Appendix 3 - Thermal  Loading of a Circular Plate


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A. Kamoulakos, D. Hitchins & G.A.O Davies

First Published - 1986

Softback Report - 113 pages