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Benchmark Tests For Various Finite Element Assemblies

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 of 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