structures

The red crane

The red crane by Weimen He

One of my favourite institutions to visit is the Bodleian’s Weston Library in Oxford.  I have written before about their rotating exhibition in the Treasury of unique books and manuscripts from their collection [see my post entitled ‘Pope and Austen‘ on September 9th, 2015].  A recent visit did not disappoint and included one of John Le Carré’s manuscripts showing his extensive editing as well as early texts written on birch bark.  However, it was in the shop that something really caught my eye.  The fusion of art and engineering in a postcard depicting a painting called ‘The red crane’, by artist in residence, Dr Weimen He, capturing the moments in time during the refurbishment of the library.  This level of fusion is rare in my experience and perhaps the ethos that created it is one of the reasons the Weston Library is such a pleasure to visit.

The Roman architect, Vitruvius identified the three principles of good structural design to be ‘firmitas, utilitas, venustas’ or durability, utility and beauty.  Too often utility, including value for money, trumps beauty and shortens horizons for durability; so that little is contributed to our culture and nothing worthwhile will be left for future generations.

BTW there is a very large bookshop next door to the Weston Library and I couldn’t resist buying ‘The Story of a Brief Marriage‘ by Anuk Arudpragasam.  It’s a beautiful novel of consciousness about love and war.

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Getting smarter

A350 XWB passes Maximum Wing Bending test [from: http://www.airbus.com/galleries/photo-gallery%5D

Garbage in, garbage out (GIGO) is a perennial problem in computational simulations of engineering structures.  If the description of the geometry of the structure, the material behaviour, the loading conditions or the boundary conditions are incorrect (garbage in), then the simulation generates predictions that are wrong (garbage out), or least an unreliable representation of reality.  It is not easy to describe precisely the geometry, material, loading and environment of a complex structure, such as an aircraft or a powerstation; because, the complete description is either unavailable or too complicated.  Hence, modellers make assumptions about the unknown information and, or to simplify the description.  This means the predictions from the simulation have to be tested against reality in order to establish confidence in them – a process known as model validation [see my post entitled ‘Model validation‘ on September 18th, 2012].

It is good practice to design experiments specifically to generate data for model validation but it is expensive, especially when your structure is a huge passenger aircraft.  So naturally, you would like to extract as much information from each experiment as possible and to perform as few experiments as possible, whilst both ensuring predictions are reliable and providing confidence in them.  In other words, you have to be very smart about designing and conducting the experiments as well as performing the validation process.

Together with researchers at Empa in Zurich, the Industrial Systems Institute of the Athena Research Centre in Athens and Dantec Dynamics in Ulm, I am embarking on a new EU Horizon 2020 project to try and make us smarter about experiments and validation.  The project, known as MOTIVATE [Matrix Optimization for Testing by Interaction of Virtual and Test Environments (Grant Nr. 754660)], is funded through the Clean Sky 2 Joint Undertaking with Airbus acting as our topic manager to guide us towards an outcome that will be applicable in industry.  We held our kick-off meeting in Liverpool last week, which is why it is uppermost in my mind at the moment.  We have 36-months to get smarter on an industrial scale and demonstrate it in a full-scale test on an aircraft structure.  So, some sleepness nights ahead…

Bibliography:

ASME V&V 10-2006, Guide for verification & validation in computational solid mechanics, American Society of Mech. Engineers, New York, 2006.

European Committee for Standardisation (CEN), Validation of computational solid mechanics models, CEN Workshop Agreement, CWA 16799:2014 E.

Hack E & Lampeas G (Guest Editors) & Patterson EA (Editor), Special issue on advances in validation of computational mechanics models, J. Strain Analysis, 51 (1), 2016.

http://www.engineeringvalidation.org/

Listening with your eyes shut

I am in the London Underground onboard a train on my way to a conference on ‘New Approaches to Higher Education’ organised by the Institution of Engineering and Technology and the Engineering Professors’ Council.  The lady opposite has her eyes closed but she is not asleep because she opens them periodically as we come into stations to check whether it’s her stop.  I wonder if she is trying to reproduce John Hull’s experience of the depth of sounds as a blind person [see my post entitled ‘Rain brings out the contours in everything‘ on February 22, 2017].  For the second time in recent weeks, I close my eyes and try it for myself.  It is surprising how in a crowded train, I can’t hear anyone, just the noise made by the train.  It’s like a wobble board that’s joined by a whole percussion section of an orchestra when we go around a bend or over points.  The first time I closed my eyes was at a concert at the Philharmonic Hall in Liverpool.  My view of the orchestra was obstructed by the person in front of me so, rather than stare at the back of their head, I closed my eyes and allowed the music to dominate my mind.  Switching off the stream of images seemed to release more of my brain cells to register the depth and richness of Bach’s Harpsichord Concerto No. 5.  I was classified as tone deaf at school when I was kicked out of the choir and I learned no musical instruments, so the additional texture and dimensionality in the music was a revelation to me.

Back to the London Underground – many of my fellow passengers were plugged into their phones or tablets via their ears and eyes.  I wondered if any were following the MOOC on Understanding Super Structures that we launched recently.  Unlikely I know, but it’s a bit different, because it is mainly audio clips and not videos.  We’re trying to tap into some of the time many people spend with earbuds plugged into their ears but also make the MOOC more accessible in countries where internet access is mainly via mobile phones.  My recent experiences of listening with my eyes closed, make me realize that perhaps we should ask people to close their eyes when listening to our audio clips so that they can fully appreciate them.  If they are sitting on the train then that’s fine but not recommended if you are walking across campus or in town!

Alan Arnold Griffith

Everest of fracture surface [By Kaspar Kallip (CC BY-SA 4.0), via Wikimedia Commons]

Some of you maybe aware that I hold the AA Griffith Chair of Structural Materials and Mechanics at the University of Liverpool.  I feel that some comment on this blog about Griffith’s seminal work is long overdue and so I am correcting that this week.  I wrote this piece for a step in week 4 of a five-week MOOC on Understanding Super Structures which will start on May 22nd, 2017.

Alan Arnold Griffith was a pioneer in fracture mechanics who studied mechanical engineering at the University of Liverpool at the beginning of the last century.  He earned a Bachelor’s degree, a Master’s degree and a PhD before moving to work for the Royal Aircraft Establishment, Farnborough in 1915.

He is famous for his study of failure in materials.  He observed that there were microscopic cracks or flaws in materials that concentrated the stress.  And he postulated that these cracks were the source of failure in a material.  He used strain energy concepts to analyse the circumstances in which a crack or flaw would propagate and cause failure of a component.  In order to break open a material, we need to separate adjacent atoms from one another, and break the bonds between them.  This requires a steady supply of energy to do the work required to separate one pair of atoms after another and break their bonds.  It’s a bit like unpicking a seam to let out your trousers when you’ve put on some weight.  You have to unpick each stitch and if you stop working the seam stays half undone.  In a material with a stress raiser or concentration, then the concentration is quite good at delivering stress and strain to the local area to separate atoms and break bonds.  This is fine when external work is being applied to the material so that there is a constant supply of new energy that can be used to break bonds.  But what about, if the supply of external energy dries up, then can the crack continue to grow?  Griffith concluded that in certain circumstances it could continue to grow.

He arrived at this conclusion by postulating that the energy required to propagate the crack was the work of fracture per unit length of crack, that’s the work needed to separate two atoms and break their bond.  Since atoms are usually distributed uniformly in a material, this energy requirement increases linearly with the length of the crack.  However, as the crack grows the material in its wake can no longer sustain any load because the free surface formed by the crack cannot react against a load to satisfy Newton’s Law.  The material in the wake of the crack relaxes, and gives up strain energy [see my post entitled ‘Slow down time to think (about strain energy)‘ on March 8th, 2017], which can be used to break more bonds at the crack tip.  Griffith postulated that the material in the wake of the crack tip would look like the wake from a ship, in other words it would be triangular, and so the strain energy released would proportional to area of the wake, which in turn would be related to the crack length squared.

So, for a short crack, the energy requirement to extend the crack exceeds the strain energy released in its wake and the crack will be stable and stationary; but there is a critical crack length, at which the energy release is greater than the energy requirements, and the crack will grow spontaneously and rapidly leading to very sudden failure.

While I have followed James Gordon’s lucid explanation of Griffith’s theory and used a two-dimensional approach, Griffith actually did it in three-dimensions, using some challenging mathematics, and arrived at an expression for the critical length of crack. However, the conclusion is the same, that the critical length is related to the ratio of the work required for new surfaces and the stored strain energy released as the crack advances.  Griffith demonstrated his theory for glass and then others quickly demonstrated that it could be applied to a range of materials.

For instance, rubber can absorb a lot of strain energy and has a low work of fracture, so the critical crack length for spontaneous failure is very low, which is why balloons go pop when you stick a pin in them.  Nowadays, tyre blowouts are relatively rare because the rubber in a tyre is reinforced with steel cords that increase the work required to create new surfaces – it’s harder to separate the rubber because it’s held together by the cords.

By the way, James Gordon’s explanation of Griffith’s theory of fracture, which I mentioned, can be found in his seminal book: ‘Structures, or Why Things Don’t Fall Down’ published by Penguin Books Ltd in 1978.  The original work was published in the Proceedings of the Royal Society as ‘The Phenomena of Rupture and Flow in Solids’ by AA Griffith, February 26, 1920.

Attribute triplets

It’s curious how we latch on to three-word lists, or attribute triplets.  There’s the famous one attributed to Julius Caesar in a letter to the Roman Senate about one of his military victories: ‘Veni. Vidi. Vici.’ – I came. I saw. I conquered.  In my forthcoming MOOC on Understanding Super Structures, I cite the Roman architect and engineer, Vitruvius who recommended that structures should have ‘Firmatas. Utilitas. Venustas.’ – Durability. Utility. Beauty.   Perhaps these were the original soundbites.  In modern times, the concept has been taken down-market by realtors (estate agents) who talk about ‘Location. Location. Location.’  And, by my leadership coach at the Center for Creative Leadership, who told us that the three laws of leadership were ‘Communication. Communication. Communication.’  This seems to represent trading content for impact . So, I was surprised to see, on the frontpage of our weekend newspaper in large type, the following:  ‘Knowledge. Integrity. Discretion.’  I thought perhaps they were describing the attributes of a college tutor or a life mentor.  However, they were part of an advertisement for a realtor, who was claiming ‘to have unrivalled knowledge [and to] provide a trusted and personal service’.  Sounds like a college tutor again!  Maybe as college professors, we should promote ourselves as having ‘Knowledge. Skills. Understanding.’  Of course, we don’t offer these attributes to our students, only the opportunity to learn how to acquire them – a subtlety that’s missed by a substantial number of our students.