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The NAFEMS Benchmark Challenge - 01

October 13th, 2014 - Updated December 22nd with Hints!

by Angus Ramsay, Ramsay Maunder Associates

Nafems Benchmark Challenge

30 years ago NAFEMS started life as the National Agency for Finite Element Methods and Standards. One of the organisation’s initial aims was to design a series of benchmarks that could be used to determine the accuracy of an analysis code. Guidelines on what makes a suitable benchmark can be found in many of our early publications. One of the guiding principles behind the benchmarks that readers may not be aware of is that:

“The benchmark should have some educational merit”

A.A. Becker, Background to Material Non-Linear Benchmarks.

Education and best practice are still at the heart of NAFEMS' activities and it is with this spirit and a hint of fun that we would like to introduce the Benchmark Challenge Problem series and Angus Ramsay, who will be acting as Independent Technical Editor. Angus will be posting a series of challenge problems that will be hosted here on the NAFEMS blog pages. You can view the first in the series below -We recommend that readers check the blog regularly, as Angus will be posting hints and tips relating to the challenge problem.

NAFEMS invites readers to send their responses to or using the comment feature at the bottom of the challenge pages. The reader providing the highest number of correct answers to the series of problems will be entered into a draw to win an iPad mini in October 2015.

Good luck!

Download the challenge PDF here:


And download some 'hints and tips' here:


Remember, Angus will be discussing the challenge in the comments section below, you can ask any questions/discuss the challenge at any time, and send your responses to

New Hints  - December 22nd, 2014

The current benchmark challenge has asked readers to obtain solutions to the square plate with linear tractions using models comprising a single four-noded element and a single eight-noded element and provide the values for the von Mises stress at the centre of the plate with appropriate commentary.

Expressions were provided for calculating consistent nodal forces and using these leads to the nodal forces shown in figure 1. 

Figure 2: Consistent Nodal Forces for the Two Models 

As indicated in Figure 2 the consistent nodal forces are either 1/6 or 1/3 Newtons and it is seen that for a model edge they sum to the correct value of 1/2N. The left-hand column of the first figure shows the consistent nodal force contributions from each edge whilst the second column shows the net nodal forces when these edge contributions have been summed at each node. For both four and eight-noded elements, the net nodal forces at the corner nodes are zero. Thus, for the four-noded element, the model has zero loading which will clearly lead to no response! For the eight-noded element, on the other hand, the mid-side nodes do receive non-zero contributions from the boundary tractions and the model should, therefore, produce a response. So the next step is to go and actually analyse the eight-noded model……….

Download all the Benchmark Challenges and their solutions in the Education and Training Working group section of the NAFEMS website.