Category Archives: structures

35 years later and still working on a PhD thesis

It is about 35 years since I graduated with my PhD.  It was not ground-breaking although, together with my supervisor, I did publish about half a dozen technical papers based on it and some of those papers are still being cited, including one this month which surprises me.  I performed experiments and computer modelling on the load and stress distribution in threaded fasteners, or nuts and bolts.  There were no digital cameras and no computer tomography; so, the experiments involved making and sectioning models of nuts and bolts in transparent plastic using three-dimensional photoelasticity [see ‘Art and Experimental Mechanics‘ on July 17th, 2012].  I took hundreds of photographs of the sections and scanned the negatives in a microdensitometer.  The computer modelling was equally slow and laborious because there were no graphical user interfaces (GUI); instead, I had to type strings of numbers into a terminal, wait overnight while the calculations were performed, and then study reams of numbers printed out on long rolls of paper.  The tedium of the experimental work inspired me to work on utilising digital technology to revolutionise the field of experimental mechanics over the following 15 to 20 years.  In the past 15 to 20 years, I have moved back towards computer modelling and focused on transforming the way in which measurement data are used to improve the fidelity of computer models and to establish confidence in their predictions [see ‘Establishing fidelity and credibility in tests and simulations‘ on July 25th, 2018].  Since completing my PhD, I have supervised 32 students to successful completion of their PhDs.  You might think that was a straightforward process of an initial three years for the first one to complete their research and write their thesis, followed by one graduating every year.  But that is not how it worked out, instead I have had fallow years as well as productive years.  At the moment, I am in a productive period, having graduated two PhD students per year since 2017 – that’s a lot of reading and I have spent much of the last two weekends reviewing a thesis which is why PhD theses are the topic of this post!

Footnote: the most cited paper from my thesis is ‘Kenny B, Patterson EA. Load and stress distribution in screw threads. Experimental Mechanics. 1985 Sep 1;25(3):208-13‘ and this month it was cited by ‘Zhang D, Wang G, Huang F, Zhang K. Load-transferring mechanism and calculation theory along engaged threads of high-strength bolts under axial tension. Journal of Constructional Steel Research. 2020 Sep 1;172:106153‘.

Slow start to an exciting new project on thermoacoustic response of AM metals

We held the kick-off meeting for a new research project this week.  It’s a three-way collaboration involving three professors based in Portugal, the UK and USA [Chris Sutcliffe, John Lambros at UIUC and me]; so, our kick-off meeting should have involved at least two of us travelling to the laboratory of the third collaborator and spending some time brainstorming about the challenges that we have agreed to tackle over the next three years.  Instead we had a call via Skype and a rather procedural meeting in which we covered all of the issues without really engendering any excitement or sparking any new ideas.  It would appear that we need the stimulus of new environments to maximise our creativity and that we use body language as well as facial expressions to help us reach a friendly consensus on which  crazy ideas are worth pursuing and which should be quietly forgotten.

Our new research project has a long title: ‘Thermoacoustic response of Additively Manufactured metals: A multi-scale study from grain to component scales‘.  In simple terms, we are going to look at whether residual stresses could be designed to be beneficial to the performance of structural parts used in demanding environments such as those found in reusable spacecraft, hypersonic flight vehicles and breeder blankets in fusion reactors.  Residual stresses are often induced during the manufacture of parts and are usually detrimental to the performance of the part.  Our hypothesis is that in additive manufacturing, or 3D printing, we have sufficient control of the manufacture of the part that we can introduce ‘designer stresses’ which will improve the part’s performance in demanding environments.  The research is funded jointly by the National Science Foundation (NSF) in the USA and the Engineering and Physical Sciences Research Council (EPSRC) in the UK and is supported by The MTC and Renishaw plc; you can find out more at Grants on the Web. The research will be building on our recent research on ‘Potential dynamic buckling in hypersonic vehicle skin‘ [posted July 1st, 2020] and earlier work, see ‘Hot stuff‘ on September 13th, 2012.  While the demanding environment is not new to us, we will be using 3D printed parts for the first time instead of components made by conventional (subtractive) machining and taking them to higher temperatures.

The thumbnail shows measured modal shapes for a subtractively-manufactured plate subject to the three temperature regimes: room temperature (left), transverse heating of the centre of the plate (middle) and longitudinal heating on one edge (right) from Silva, A.S., Sebastian, C.M., Lambros, J. and Patterson, E.A., 2019. High temperature modal analysis of a non-uniformly heated rectangular plate: Experiments and simulations. J. Sound & Vibration, 443, pp.397-410.


Graphite for Very High Temperature Reactors (VHTR)

One of the implications of the second law of thermodynamics is that the thermal efficiency of power stations increases with their operating temperature.  Thus, there is a drive to increase the operating temperature in the next generation of nuclear power stations, known as Generation IV reactors.  In one type of Generation IV reactors, known as the Very High Temperature Reactor (VHTR), graphite is designed to be both the moderator for neutrons and a structural element of the reactor.  Although the probability of damage in an accident is extremely low, it is important to consider the consequences of damage causing the core of the reactor to be exposed to air.  In these circumstances, with the core temperature at about 1600°C, the graphite would be exposed to severe oxidation by the air that could change its material properties and ability to function as a moderator and structural element.  Therefore, in recent research, my research group has been working with colleagues at the UK National Nuclear Laboratory (NNL) and at the National Tsing Hua University (NTHU) in Taiwan to conduct experiments on nuclear graphite over a range of temperatures.  Our recently published article shows that all grades of nuclear graphite show increased rates of oxidation for temperatures above 1200°C.  We found that large filler particles using a pitch-based graphite rather than a petroleum-based graphite gave higher oxidation resistance at these elevated temperatures.  This data is likely to be important in the design and operations of the next generation of nuclear power stations.

The work described above was supported by the NTHU-University of Liverpool Dual PhD Programme [see ‘Citizens of the world‘ on November 27th, 2019] and NNL.  This is the fifth, and for the moment last, in a series of posts on recent work published by my research group.  The others are: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020; ‘Thinking out of the box leads to digital image correlation through space‘ on June 24th, 2020; and, ‘Potential dynamic buckling in hypersonic vehicle skin‘ on July 1st, 2020.

The image is figure 5: SEM micrographs of the surface of petroleum-based IG-110 graphite samples oxidized at various temperatures from Lo IH, Tzelepi A, Patterson EA, Yeh TK. A study of the relationship between microstructure and oxidation effects in nuclear graphite at very high temperatures.  J. Nuclear Materials. 501:361-70, 2018.


Lo I-H, Yeh T-K, Patterson EA & Tzelepi A, Comparison of oxidation behaviour of nuclear graphite grades at very high temperatures, J. Nuclear Materials, 532:152054, 2020.

Potential dynamic buckling in hypersonic vehicle skin

The skin of an aircraft is supported on the inside by a network, or mesh, of ribs and stringers running approximately at right angles to one another; so that the skin is effectively a series of rectangular plates supported around their edges.   In hypersonic flight, above five times the speed of sound, these rectangular plates are subject to vibration and to high temperatures that vary spatially and with time.  The combined vibratory and thermal loading causes the plates to buckle out of plane which has two possible detrimental consequences: first, it causes the formation of fatigue cracks leading to catastrophic failure; and, second, it might influence the formation of the boundary layer in the flow over the skin of the aircraft and affect the aerodynamics of the aircraft.  In my laboratory, we have built a test-rig that allows us to subject rectangular plates to random mechanical vibrations up to 1000Hz and, at the same time, to temperature distributions upto 1000K that vary in time and space.  Earlier this year, we published an article in which we showed, by experiment, that an edge-reinforced rectangular plate behaved as a dynamic system in response to thermal loading.  In other words, when a constant temperature distribution is applied, the shape of the plate varies with time until an equilibrium state is achieved.  In addition, we found that the post-buckled shape of the plate is not proportional to the energy supplied but dependent on the in-plane temperature distribution.  Probably, both of these observed behaviours are a result of differential thermal expansion of the plate and its reinforcements.

The image shows point-wise temperature and displacement measurements (centre) at the centre and edge of a reinforced plate (top) subject to a localised strip of heating over time as shown by the temperature distributions (bottom).

This is the fourth in a series of posts on recent work published by my research group.  The others are: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020; and, ‘Thinking out of the box leads to digital image correlation through space‘ on June 24th, 2020.


Santos Silva AC, Lambros J, Garner DM & Patterson EA, Dynamic response of a thermally stressed plate with reinforced edges, Experimental Mechanics, 60:81-92, 2020.