Linear Static Benchmarks - Volume 1

As part of a complete program to evaluate standards, robustness, and performance of finite element systems, a series of benchmarks has been developed for NAFEMS in the basic field of linear statics. All of these benchmarks share a common strategy in that they are relatively simple assemblies of elements and yet aim to test specific capabilities of systems in analysing various forms of basic structures subjected to various types of mechanical and thermal loads. Over a three-year period a  large number of tests have been developed and evaluated, their strengths and weaknesses exposed, and confidence in quoted targets established by separate analytical solutions whenever possible. All these aspects have been described in series of contractors' progress reports and a small group of six tests have been selected and published as one-page specifications in a NAFEMS report number FEBSTA Rev.1. Most of these tests have been run on a comprehensive number of commercial finite element systems and reported at the NAFEMS Conference in May 1987 or in Benchmark Magazine.

The intention is to add to the published list more statics benchmarks together with suitable tests for nonlinear structures and materials, dynamics and more ambitious thermal problems. A compendium of tests and codes' performances will consequently be compiled and continually amplified and updated as systems change, In the meantime, it was felt that the NAFEMS community would appreciate a self-contained summary of most of the satisfactory statics benchmarks in single-sheet format. That is the contents of this report.

In addition, we know there is an interest in the reasoning behind these tests, the details of the analytical solutions where appropriate and the expected performance of a typical finite-element solution. The role of these tests as an educational aid for practising engineers has come as a surprising bonus. 

Contents

Introduction

1. Tapered Membrane - End Load
2. Tapered Membrane - Inertia
3. Tapered Membrane - Edge Shear
4. Tapered Membrane - Gravity
5. Circular Membrane - Edge Pressure
6. Circular Membrane - Point Load
7. Circular Membrane - Parabolic  Temperature
8. Membrane Panel - Shear Diffusion
9. Elliptic Membrane - Edge Pressure

10. Tapered Plate - Edge Shear
11. Tapered Plate - Gravity
12. Elliptic Plate - Normal Pressure
13. Skew Plate - Normal Pressure

14. Tapered  Axisymmetric Solid - Pressure
15. Tapered Axisymmetric Solid - Gravity
16. Cylinder/Taper/Sphere Axisymmetric Solid - Temperature 

17. Hemispherical Thin Shell -  Pressure
18. Hemispherical Thin Shell -  Pinch Loads
19. Cylindrical Shell Regular Mesh - Edge Moment
20. Cylindrical Shell Regular Mesh - Pressure
21. Cylindrical Shell Distorted Mesh - Edge Moment
22. Cylindrical Shell Distorted Mesh - Pressure
23. Spherical Shell Regular Mesh - Inextensional  Bending
24. Catenoidal Shell - Pressure
25. Catenoidal Shell Regular  Mesh - Inextensional  Bending
26. Catenoidal Shell Distorted Mesh - Inextensional  Bending
27. Cylinder/Sphere  - Pressure
28. Circular parabaloid - Gravity

29. Z-section Cantilever Folded Plate - Torsion Bending
30. Z-section Cantilever Folded Plate - Beam Bending

31. Hyperbolic Axisymmetric Shell - Edge Load
32. Hyperbolic Axisymmetric Shell - Pressure
33. Hyperbolic Axisymmetric Shell - Harmonic Edge Load
34. Catenoidal Shell  - Pressure
35. Cylinder - Harmonic Edge Shear
36. Cylinder - Gravity (transverse)
37. Stiffened Cylinder - Pressure
38. Cylinder/Sphere Axisymmetric Variable Thickness - Pressure
39. Cylinder/Sphere Axisymmetric Constant Thickness - Pressure
40. Axisymmetric Shell - Pressure
41. Axisymmetric Branched Shell - Pressure

42. Solid Elliptic Thick Plate - Pressure
43. Solid Cylinder/Taper/Sphere - Temperature

About

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

First Published - January 1987

Softback, 98 Pages