This book records the four NAFEMS Benchmark Challenges that were published in the Benchmark Magazine in 2015 together with their solutions and some additional supplementary information in the form of two appendices that were also publishedin the magazine.

The NAFEMS Benchmark Challenge initiative was instigated in the late summer of 2014 with the motivation being to provide an opportunity for increased interaction between NAFEMS and the readership of the Benchmark Magazine. The concept was to offer a challenge printed in one edition of Benchmark with the official solution or response being printed in the next edition of the magazine. In addition,a blog was added to the NAFEMS website to allow readers the opportunity to collaborate and to ask questions of NAFEMS. 

The challenges require the reader to think around the problem and carry out some detective work in seeking the solution. They are not trivial and whilst aimed at the young engineer, it is likely that more experienced engineering analysts will find something of value in them. The responses to the challenge were assessed and certificates provided for those responders who had made a good attempt at solving the challenge.

Whilst participation in these challenges was encouraged, and the full value of them might only be realised if the reader actually does participate, the official responses were designed to lead the reader through the challenge and should, therefore, be of interest even if the reader did not participate.

It should be recorded that the challenges and responses as presented in this book may vary slightly from those presented in the Benchmark magazine. In particular with more space available in this book some of the responses have been expanded to draw additional value out of the challenge. 

NAFEMS Professional Simulation Engineer (PSE) initiative has associated with it aset of Competencies and for those working towards qualification via this initiative,these challenges and their official solutions should form a useful reference; the solutions to these challenges observe the best principles of simulation governance and might be considered as examples which the young engineer can follow in his or her own analysis work.

Contents

1. Introduction ................................................................................................. 1
2. Benchmark Challenge Number 1 ............................................................... 3
3. Benchmark Challenge Number 2 ............................................................. 21
4. Benchmark Challenge Number 3 ............................................................. 41
5. Benchmark Challenge Number 4 ............................................................. 49
6. Concluding Remarks ................................................................................ 67
7. Appendix 1 - An Error in Timoshenko ..................................................... 69
8. Appendix 2 - Yield Line Analysis of Slabs .............................................. 79

Notes & Corrections

In 2019 the article "An Exact Solution of Truss Vibration Problems" was published in the Proceedings of the Estonian Academy of Sciences. The article references challenge NBC05 and uses the technique in the paper to determine the first seven natural frequencies. The first two frequencies in the publication verify the FE results produced in NBC05.

NBC08:

Figure 3 – The constitutive relations should, of course, include a Young’s Modulus multiplier.