Tag Archives: mechanics

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.

Thinking out of the box leads to digital image correlation through space

This is the third in a short series of posts on recent engineering research published by my research group.  Actually, two have already been published: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; and ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020 and then I got distracted.  This third one arose from the same project as the time-damage maps which was sponsored by the United States Air Force.  The time-damage maps allow us to explore the evolution of failure in complex materials; however, we already know that damage tends to initiate from imperfections or flaws in the microstructure in the material.  New continuous fibre reinforced composite (CFRC) materials based on ceramics are very sensitive to defects or anomalies in their microstructure, such as misalignment of fibres.  However, they are capable of withstanding temperatures in excess of 1500 degrees Centigrade, which offers the opportunity to use them in jet engines or nuclear power plants to help generate energy more efficiently.  Therefore, it is worthwhile investigating effective methods of inspecting their microstructure which we can do either destructively by repetitively polishing away the surface of a sample and viewing it in a microscope, or non-destructively using x-ray tomography.  In both cases, the result is hundreds of ‘images’ containing millions of data values from which it is challenging to extract useful information.  In our work, we have used a little lateral thinking, to show how digital image correlation, usually used to track deformation of structures using multiple images collected over time [see ‘256 shades of grey‘ on January 22nd, 2014] , can be used to track fibres through the multiple images of the layers of the microstructure.  The result is the sort of ‘stick’ diagram in the image showing the orientation of fibres through the sample.  We have demonstrated that our new algorithm was more reliable and 30 times faster than its nearest rival.

The image shows, at the top, a typical stack of images from the microscope of a ceramic matrix composite; and, at the bottom, a plot of 3d profiles of the fibres tracked using the DIC-based method with the fibres orientated nominally at ±45° from the sectioning (x-y) plane shown in red and green colours.


Amjad K, Christian WJR, Dvurecenska K, Chapman MG, Uchic MD, Przybyla CP & Patterson EA, Computationally efficient method of tracking fibres in composite materials using digital image correlation, Composites Part A, 129:105683, 2020.


Condition-monitoring using infrared imaging

If you have travelled in Asia then you will probably have experienced having your health monitored by infrared cameras as you disembarked from your flight.  It has been common practice in many Asian countries since long before the COVID-19 pandemic and perhaps will become more usual elsewhere as a means of easily identifying people with symptoms of a fever that raises their body temperature.  Since, research has shown that infrared thermometers are slightly more responsive as well as quicker and easier to use than other types of skin surface thermometers [1].  In my research group, we have been using infrared cameras for many years to monitor the condition of engineering structures by evaluating the distribution of load or stress in them [see ‘Counting photons to measure stress‘ on November 18th, 2015 and  ‘Insidious damage‘ on December 2nd, 2015].  In the DIMES project, we have implemented a low-cost sensor system that integrates infrared and visible images with information about applied loads from point sensors, which allows the identification of initiation and tracking of damage in aircraft structures [2].  I reported in December 2019 [see ‘When seeing nothing is a success‘] that we were installing prototype systems in a test-bench at Empa.  Although the restrictions imposed by the pandemic have halted our tests, we were lucky to obtain data from our sensors during the propagation of damage in the section of wing at Empa before lockdown.  This is a landmark in our project and now we are preparing to install our system in test structures at Airbus once the pandemic restrictions are relaxed sufficiently.  Of course, we will also be able to use our system to monitor the health of the personnel involved in the test (see the top image of one of my research team) as well as the health of the structure being tested – the hardware is the same, it’s just the data processing that is different.

The image is a composite showing images from a visible camera (left) and processed data from infrared camera overlaid on the same visible image (right) from inside a wing box during a test at Empa with a crack extending from left to right with its tip surrounded by the red area in the right image.  Each nut in the image is about 20 mm in diameter and a constant amplitude load at 1.25 Hz was being applied causing a wing tip displacement of 80 mm +/- 15 mm.

The University of Liverpool is the coordinator of the DIMES project and the other partners are Empa, Dantec Dynamics GmbH and Strain Solutions Ltd.

The DIMES project has received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 820951.


The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.


[1] Burnham, R.S., McKinley, R.S. and Vincent, D.D., 2006. Three types of skin-surface thermometers: a comparison of reliability, validity, and responsiveness. American journal of physical medicine & rehabilitation, 85(7), pp.553-558.

[2] Middleton, C.A., Gaio, A., Greene, R.J. and Patterson, E.A., 2019. Towards automated tracking of initiation and propagation of cracks in aluminium alloy coupons using thermoelastic stress analysis. Journal of Nondestructive Evaluation, 38(1), p.18.

Homework practical exercises in structural mechanics

Last week I wrote about the practical exercises that I have been setting as homework in my first year undergraduate course on thermodynamics.  The instruction sheets that I published had been used by thousands of learners on my MOOC, Energy! The Thermodynamics of Everyday Life; and slightly modified versions had been used by more than a thousand students at the University of Liverpool.  A few years ago, I produced another MOOC called ‘Understanding Superstructures’ which also contained three practical exercises for online learners to perform in their kitchens.  I have not used them as part of a blended undergraduate course but nevertheless they have been completed by hundreds of participants in the MOOC.  I have decided to share them for colleagues to use in support of first year courses on the Mechanics of Solids or the Mechanics of Structures.  There is strong food flavour and no additional equipment is needed. Please feel free to use them to support your teaching.

Instruction sheets for thermodynamics practical exercises as homework:

Structural collapse | Crushing and toppling of towers

Stress concentrations | Newspaper tension tests

Residual stresses | Bending carrots