|
|
||
|
|
|
|
See:
http://www.eoas.info/biogs/P000909b.htm
http://www.jstor.org/discover/10.2307/769968?uid=3739560&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=47699028759677
From:
http://www.science.org.au/fellows/memoirs/wittrick.html
Academic and Professional qualifications:
M.A. (Master of Arts, University of Cambridge, 1947)
Ph.D. (Doctor of Philosophy, University of Sydney, 1950)
Sc.D. (Doctor of Science, University of Cambridge, 1969)
F.R.Ae.S. (Fellow of the Royal Aeronautical Society)
M.I.C.E. (Member of the Institution of Civil Engineers)
Fellowships
F.A.A. (Fellow of the Australian Academy of Science; elected 1958)
F.R.S. (Fellow of the Royal Society; elected 1980)
F.Eng. (Fellow of the Fellowship of Engineering; elected 1981)
Honorary Degrees
May 1984 Honorary Doctor of Science (Engineering), Chalmers University of Technology, Göteborg, Sweden
July 1985 Honorary Doctor of Science, University of Wales
University of Sydney (1945-1964)
At the end of World War II the chair of aeronautical engineering at the University of Sydney was occupied by A.V. Stephens, a Cambridge man whose research interest lay in the field of aerodynamics. The department was a small one and, as it was the only one in Australia, Stephens was anxious to attract someone able to develop a strong teaching and research effort in aircraft structures. He therefore sought the advice of Professor J.F. Baker (later Lord Baker of Windrush), originally an aeronautical engineer, who in 1943 had become head of the Engineering Department at Cambridge and had gathered around him a most enthusiastic group to work on steel structures. Wittrick had spent a short period teaching and assisting in research in that department and with his excellent academic record and some experience at the Royal Aircraft Establishment, Farnborough, was highly recommended by Baker. At the age of twenty-three, he became one of the youngest senior lecturers ever appointed to the University of Sydney.
Getting to Sydney in those days with not without its difficulties. Wittrick had married in June 1945, and while he was granted a passage quickly, his wife Joyce had to wait until a later date. The irony of the situation was that the ship in which Bill sailed had some empty berths. Joyce joined her husband some months later after a long tedious journey around the Cape. Both being endowed with Yorkshire determination, they did not allow such frustrations to interfere with the task of making a good life in Australia.
The small department at Sydney had its compensations for Wittrick. The teaching load was not particularly onerous and since his interest in aircraft structures was mainly theoretical, he was able to engage in research very soon after his arrival. At that time, considerable attention was being given to swept-back wings for high-speed aeroplanes and particularly to the delta wing, for which the leading edge is highly swept but the trailing one is more or less unswept so that the taper and 'average' sweep are large. This was a complex problem on which a great deal of work was being done though few papers had been published. For swept and tapered wings with ribs parallel to the root, Wittrick produced solutions for their behaviour under load. He demonstrated the coupling between flexure and twist, and the effect of root restraint which could be significant for large angles of sweep. A detailed account of this work is to be found in his thesis entitled 'Torsion and Bending of Swept and Tapered Wings with Ribs Parallel to the Root', submitted for the degree of Ph.D. The appendix contains detailed numerical applications of the theory to a highly tapered unswept four-boom tube of rectangular section, with a completely restrained root section, under varying bending moment and torque. No mean task when the only aid then available was the mechanical hand-operated calculating machine!
It is interesting to note that when Wittrick was awarded the Ph.D. degree in 1950, he became the first recipient in the University of Sydney. The thesis is now lodged under restricted access in the Rare Books section of the University Library. Associated with it are a number of publications, the first of which was said to be the first paper on this topic published anywhere in the world.
With hindsight, we can see that Wittrick's adoption of the well-established assumption of rigid line-of-flight ribs was not appropriate for swept wings, because it markedly exaggerated the coupling between torsion and flexure. However, this served a useful purpose, because it highlighted a novel structural phenomenon and acted as both a trigger and a spur to those who then recognised the need for a more exact analysis.
In the early 1950s Wittrick returned to his interest in buckling, prompted by problems arising in the design of swept wings concerning the elastic stability of irregularly shaped panels (such as parallelograms and triangles) subjected to edge loads. He also produced an elegant solution for the buckling of orthotropic and isotropic rectangular plates under various biaxial loading and boundary conditions. A number of other papers on similar topics were also published. Indeed, in 1954 his papers formed a substantial part of the literature on these problems.
During this period Wittrick found time to examine a number of intriguing problems in the wider field of engineering. One example was his work on the stability of a heated bimetallic disc, which constituted one of the few exact solutions of the stability of a non-linear elastic system to be published up to that time. The behaviour of the disc also relates to the thermo-elastic stability of skin panels of supersonic aircraft and missiles. Another example was his study of the theory of crossed flexural pivots, which had been widely used in scientific instruments, particularly balances, because of their inherent lack of friction. When subjected to load they exhibited certain phenomena associated with their stability that were often undesirable. Wittrick's papers on this topic gave a comprehensive analysis of their behaviour and led to the design of new and improved flexural pivots in which the undesirable features were to a large extent eliminated.
By 1953, having devoted some years to research on swept-back wings in an environment somewhat remote from other centres of aeronautical research, Wittrick decided that it was time to acquaint himself more fully with overseas ideas on these problems. He therefore arranged to spend about six months at the California Institute of Technology working with a group interested in the structural behaviour of swept-back wings. He was awarded a Fullbright/Smith-Mundt grant and appointed a Research Fellow at CIT where he was invited to conduct weekly seminars on the results of his own research. Also, in collaboration with Professor Y.C. Fung, he made a study of a (structural) boundary-layer phenomenon that occurs, for example, at the free edges of thin cantilever plates in the large-deflexion regime. This edge effect involves localised out-of-plane displacements that result in middle-surface forces which, because of the curvature of the plate, have components acting normal to the plate. Over a narrow region, typically of order (plate thickness/plate curvature)1/2, these forces cause the moment per unit length in a direction normal to the boundary to increase from zero to a value that effectively enables the interior regions of the plate to deform linearly into a developable surface. When this research was undertaken, Fung and Wittrick were unaware of the inextensional theory of plates(1) that gave a general technique for determining the generators of such developable surfaces. These separate researches were, however, complementary because the one provided details of the localised mechanisms required for the other. Interest in these researches stemmed from their application to very thin solid wings and fins on missiles.
On his return to Sydney, Wittrick was promoted to Reader. One of the referees was a senior member of CIT who made the comment: 'Dr. Wittrick is the type of scholar and research worker that we would have liked to keep at CIT as a member of our permanent staff. This is not only the feeling of those in the Aeronautics Department, but also of the staff members in our Applied Mathematics, Mechanical Engineering and Applied Mathematics groups'.
In 1956, Wittrick succeeded Stephens as Lawrence Hargrave Professor of Aeronautical Engineering at Sydney, and was inevitably drawn more into the affairs of the Faculty where his clear thinking and grasp of essentials were greatly appreciated. Over the years, he had built up a reputation among staff and students not only as a scholar and research worker brimming over with ideas, but also as someone who had developed an excellent relationship with his small band of students both as a teacher and a friend. He had little time for academic politics and even less for ponderous administrative procedures and interminable committees. Nevertheless, he was prepared to give time to devising a scheme for processing examination results that, for students with good aggregates, allowed certain compensations for shortcomings in a few subjects. This did much to quicken the progress of these students without in any way reducing standards. He also found time to take part in sport. As one of his colleagues of that time, G.A.O. Davies (now head of the Department of Aeronautics at Imperial College of Science and Technology) has remarked, 'Bill Wittrick had this [respect] in full measure in all fields, including the sporting one. Postgraduates found that guile is a powerful weapon on the squash court and a pretty potent one in the hands of a slow spinner on a turning wicket too'. It was therefore particularly appropriate that for some years Wittrick served as Senate representative on the Sports Union Committee.
After the Comet aircraft disaster in 1953, Wittrick turned his attention to problems of minimising stress concentrations around the windows in aircraft fuselages. 'Neutral hole' theory(2) showed that it was theoretically possible to design a reinforced hole such that there were no stress concentrations in the surrounding plate. For the 2:1 stress field in a pressurised fuselage, the neutral hole is a square-root of 2:1 'vertical' ellipse - a not unreasonable shape - but the total weight of the required edge reinforcement is about 2.5 times the weight of the 'removed' plate. There is therefore a design trade-off between weight and stress concentration. The neutral reinforcement also exhibits a localised peak near the ends of the major axis, whereas the designer would prefer a uniform reinforcement. There was therefore a need to determine the stress concentrations due to elliptical and other holes with various degrees of uniform edge reinforcement. To tackle this formidable range of problems, Wittrick turned to analytical methods put forward by the Russian school of elasticians that had become known through translations by J.R.M. Radok of two of Muskhelishvili's books. In this way he was able to predict the stress concentrations around reinforced holes of 'rounded square' and 'rounded triangular' shape, in addition to the important 'neutral' elliptical shape that has been used in various civil aircraft windows. For part of this work Wittrick was awarded the Orville Wright Prize of the Royal Aeronautical Society.
An event that was of great interest to Wittrick was the establishment of a computer facility at the University of Sydney in 1956. This was probably the first viable digital computer in the Southern Hemisphere and was appropriately called Silliac since it was a development of the Illiac pioneered by the University of Illinois. Wittrick's early work on swept-wing structures and on stress concentrations around holes in shells, and his first excursions into plate bending, were more than enough to convince him of the research advantages of this new tool. Again his colleague Davies has given a graphic account of Bill's enthusiasm: 'The machine was as large as a double decker bus and its thousands of valves rapidly overtaxed the air-conditioning system, so that it was rarely 100% reliable. Bill could be seen, with the few academics willing to embrace such a monster, loading, compiling, bootstrapping and diagnosing faults on the machine itself - including corrective measures such as hitting the valves with a rubber hammer'. But for all its shortcomings, Silliac was not decommissioned until 1968.
On appointment to the chair, Wittrick began to take a more active part in the national research programme in aeronautics. He became a member of the Australian Aeronautical Research Committee, charged with the task of advising the Minister for Supply who had under his control the aircraft factories and Aeronautical Research Laboratories in Melbourne. In 1961 Wittrick was invited by the Minister to become chairman of this committee. It was therefore entirely appropriate that in 1962 he should be appointed one of the three Australian representatives on the Commonwealth Aeronautical Advisory Council responsible for co-ordinating aeronautical research throughout the Commonwealth.
Wittrick again went on sabbatical leave in 1960. Part of the time was spent as a visiting professor at the College of Aeronautics at Cranfield, and the rest making visits to universities and industrial organisations, first in the USA under the sponsorship of the Carnegie Corporation, then in Canada and certain European countries. He returned from this experience convinced that there were still many problems of plate buckling in need of examination. This is reflected in his subsequent papers such as those dealing with the effect of tapering thickness, elastic restraints and some further non-linear shell-boundary-layer effects.
In 1964 Bill Wittrick was still a comparatively young man of forty-two. He had been nearly twenty years in the same department and was obviously ready for some new challenge. To his colleagues he frankly expressed the view that it would be a good thing for himself and the vitality of his department if he were to move on. He had made outstanding contributions to the fund of Australian research that had been recognised by special awards and notably by his election to Fellowship of the Australian Academy of Science in 1958. He had played a full and active part in all aspects of university life and was currently Dean of the Faculty of Engineering. His acceptance of the chair of structural engineering at the University of Birmingham was a matter of great regret. Yet Bill, Joyce, Jane and Ann - as the family were affectionately known - left Australia with the sincere good wishes of friends, colleagues and students alike.
Birmingham University (1964-1982)
After going to Birmingham University in October 1964, the main thrust of Wittrick's research was to provide aerospace designers with the means of calculating, accurately and efficiently, the buckling loads or natural frequencies of vibration, together with the associated modes, of thin prismatic structures, the individual walls of which are subjected to uniform biaxial compression and shear and may have either isotropic (metal) or anisotropic (composite) elastic properties.
The work started in a fairly small way from an idea Wittrick had in 1965 for extending the Engineering Sciences Data Unit - Structures Data Sheets on the local (i.e. short wavelength) buckling of stiffened isotropic panels to cope with loading cases in which the individual flats carry shear in addition to longitudinal compression. The wavelength was supposed to be sufficiently small compared with the panel length for end effects to be ignored, so that the panel could be considered to be effectively of infinite length. It was assumed that the longitudinal line junctions between adjoining flats remained straight during buckling, but that rotations occurred about them. The fact that the nodal lines in the flats are curved in the presence of shear loading, resulting in (spatial) phase differences between the sinusoidally varying rotations about the various junctions, was allowed for by introducing complex vectors of rotations and the concept of complex 'stability functions'. The stiffness matrices turned out to be complex Hermitian. This work was done in conjunction with a Ph.D. student, P.L.V. Curzon, and resulted in four joint papers published in 1968 and 1969.
Wittrick quickly realised that the approach could be generalised to include all possible forms of buckling in a unified way, provided that the prevailing conditions were such that all modes were sinusoidal or nearly so. That is the case if the stresses in the flats are invariant in the longitudinal direction, and either the ratio of half-wavelength to the panel length is small enough for end effects to be unimportant or (in the absence of shear loading) the ends of the panel are 'diaphragm supported'. In general the longitudinal line junctions no longer remain straight during buckling and each one has four (complex) degrees of freedom associated with it, consisting of three translations plus one rotation. In order to cater for the destabilising effect of the membrane loading in the flats on in-plane deformations (which is necessary, for example, in the case of a web of a stiffener in an overall mode, or a flange of a stiffener in a torsional mode), it was necessary to base the equations of equilibrium of the theory of elasticity on the geometry of a deformed element. The analytical basis is provided in 'A unified approach to the initial buckling of stiffened panels in compression', Aeronautical Quarterly, 19 (1968), 265-283, for calculating the buckling loads of panels under uniform longitudinal compression. This was extended in 'General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures', Int. J. Mech. Sci., 10 (1958), 949-966, to include more complicated load systems, with each flat subjected to biaxial compression and shear. Moreover, by permitting all forces and displacements to vary sinusoidally with time, the analysis also opened up the possibility of calculating either the critical buckling loads (corresponding to zero frequency) or the natural frequencies and modes of a loaded panel, within a single computer program.
The one big problem remaining, before the by now large body of theory could be incorporated into a general-purpose computer program for use by designers, was how to extract the eigenvalues, i.e. the critical loads or natural frequencies. Because the stiffness matrices are derived from exact solutions of the partial differential equations, the elements of the overall stiffness matrix (the singularity of which provides the criterion for calculating the eigenvalues) are transcendental functions of the eigenvalues and not linear ones as in a conventional (approximate) finite-element solution. The only known method of solution at that time was by trial and error, based upon the value of the determinant. For many reasons this is both unreliable and inefficient. First, it is all too easy to miss eigenvalues in the event of coincident or nearly coincident ones; secondly, it is impossible to know a priori how small to make the load (or frequency) increment in the trial and error process; thirdly, the determinant may change sign via infinity as well as via zero; fourthly, such infinities in exceptional cases coincide with each other and with zeros; and finally such methods are extremely difficult to incorporate into a general-purpose program.
It took several years to overcome this problem but, in the end, F.W. Williams and Wittrick developed an extension of the Sturm sequence procedure. In both buckling and vibration problems it enables the number of eigenvalues lying between zero and any chosen value to be calculated with ease and provides a safe, reliable and efficient algorithm for general-purpose programs. The algorithm was first published in the context of vibration of skeletal frames and then of any linearly elastic structure but was also extended to apply to the buckling problem. It should be noted that in the latter problem, unlike the vibration one, both positive and negative eigenvalues can occur in general. The algorithm also provides a straightforward exact means of assembling the structure from substructures which may themselves be assembled from smaller substructures and so on to any depth, thereby enabling the maximum possible advantage to be taken of any repetition as is usual in stiffened panels (e.g. identical and equally-spaced stiffeners). The algorithm has found many applications and was developed further to cover vibration of spinning bodies.
Finally the whole analysis was further extended to include anisotropy of the individual flats, such as occurs in composite structures. It was assumed that there is no interaction between bending and membrane forces and deformations (i.e. symmetric lay-ups) and that the membrane properties are orthotropic (i.e. equal numbers of plies in the +0 and -0 directions). The bending properties were taken to be fully anisotropic, including interaction between bending and twist.
The later stages of development of all this theory, and its incorporation into the general-purpose computer program called VIPASA (Vibration and Instability of Plate Assemblies with Shear and Anisotropy), was carried out under a research contract supervised by Dr. F.W. Williams (later Professor of Civil Engineering, UWIST, Cardiff). The program was commissioned during 1972 and handed over to the Royal Aircraft Establishment and the aerospace industry.
Following a joint paper about this work that was presented at an IUTAM Symposium at Harvard in 1974, the program was extensively tested by NASA and subsequently made available to all the major aerospace organisations in the USA and Britain. It has been used on numerous design projects and was immediately chosen by NASA for checking the design of the Space Shuttle. In the latter role it correctly predicted a type of buckling failure that had been missed in the design stages and was only found during test.
Wittrick's plate and eigenvalue work led more or less directly to many other papers. However, his interests were much broader than this and led to significant contributions in other areas.
Wittrick's work on the stability of plates opened up the possibility of a better understanding and the solution of a number of structural problems in civil engineering. These have been examined by research workers in various countries. In Australia, use has been made of Wittrick's analyses by N.W. Murray (professor of civil engineering at Monash University) to obtain theoretical results for comparison with some careful experimental studies of the influence of initial imperfections on the buckling loads of steel plates. The treatment described by Wittrick is an exact solution and was later followed up by an alternative semi-analytical finite-strip method. The latter has been extended by G.J. Hancock (associate professor of civil engineering at the University of Sydney) to interpret the behaviour of steel I-beams fabricated from steel plate when subject to local, distortional and lateral buckling.
Page 84 / 220