A Review Of Benchmark Problems For Geometric Non-Linear Behaviour Of 3D Beams And Shells

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N.C. Knowles

First Published - June 1990
Softback, 104 Pages

This document reports the work performed under the NAFEMS contract NEL/F/521 entitled “Review of Benchmark Problems for 3-D Beams and Shells with Geometric Non-linearity”. The object of the work is to produce a compendium of problems which are suitable to be worked up as benchmarks for 3-dimensional beam and shell finite element assemblies. Recommendations are also made for a necessary and sufficient set of such benchmarks. The work is focussed on 3-dimensional geometric non-linearity of beams and shells, but 2-demensional behaviour and the effects of time independent material non-linearity (i.e. plasticity) are not excluded. Creep effects however are not pursued. This would require a separate study.

Although the role of benchmarks in the finite element community is becoming well established, some explanation of “suitability” and hence the criteria used for assessing candidate problems is necessary. This is provided in Section 2.

Section 3 then describes the organisation of the work. This follows very closely then spirit and intent of an earlier contract dealing with material non-linearity(*) and he was arranged in 3 stages namely:

• Stage 1 Search for suitable problems
• Stage 2 Collation, classification and critical review
• Stage 3 Identification and reporting of a sufficient set of problems

In Section 4 the classification of potential problems into three groups, namely Beams, Shells and Branched Shells is explained. All the problems have been assigned a ranking from 1 to 4, according to that degree to which they satisfy the selection criteria, and this is also explained in Section 4.

Section 5 discusses the various physical attributes of the non-linear behaviour of beam and shell assemblies and hence the extent of the required benchmarks. Each problem is summaries on a single sheet in Appendix 2. The aim here is to present only the key physical features of each test sufficient to allow the reader to decide on its relevance. Fully detailed references are contained in Section 7.

Contents

INTRODUCTION

SCOPE OF WORK

General Purpose of Benchmark Tests
Area of Application: Scope of Nonlinearity
Criteria for Selection

SEARCH FOR BENCHMARK PROBLEMS

Methods of Search
Results of Search

CLASSIFICATION, RANKING AND PRESENTATION OF THE PROBLEMS

Classification
Ranking
Presentation of the Potential Benchmarks

ATTRIBUTES OF POTENTIAL BENCHMARKS

Beams
Shells

RECOMMENDED PROBLEMS AND FURTHER WORK

Recommended Benchmarks
Further Work

REFERENCES

ACKNOWLEDGEMENTS

APPENDICES

Appendix 1 : Index and Attributes
Appendix 2 : Potential Benchmarks
Appendix 3 ; Recommended Subset