Olek Zienkiewicz is internationally recognised as one of the leading developers of the Finite Element Method which is a computer-based technique that has, since the 1960s, revolutionised design and analysis procedures in civil, mechanical, aerospace and other branches of engineering.

Initially, the formulation of the method followed a traditional structural engineering approach but as the underlying mathematical basis became understood its application to other disciplines became possible.

The methodology remains a flourishing research topic and its application has considerable potential in new scientific areas, including biomedical engineering and the life sciences.

### Olek Zienkiewicz 18th May 1921 – 2nd January 2009 Elected FRS 1978

### EARLY BACKGROUND

Olek Zienkiewicz was born on 18th May 1921, in Caterham, England, of a Polish father and English mother. He was the seventh son of a seventh son, which in folklore endowed him with magical and clairvoyant powers - and may, or may not, have been responsible for his remarkable career. His early life was greatly influenced by the turbulence of European history over the first half of the twentieth century. Towards the end of the First World War, Czar Nicholas of Russia was first overthrown by revolutionaries who formed a government under Alexander Kerensky, which was in turn overthrown by the Bolsheviks. In 1917 Zienkiewicz’s father, Casimir, held the post of Consul in Birmingham for the Kerensky government which only lasted for a short period. The practice of law is tied to the legal system of one’s government so that employment in his profession in England was effectively closed to him. Therefore, in 1922 the Zienkiewicz family returned to Poland, first to Warsaw and then to Lodz, before moving once more in 1926 to Katowice where his father held the post of district judge up to the outbreak of World War II.

Recognising his obvious academic talents his parents sent him to a boarding school near Poznan and his schooling went well for two years until he suffered a sporting injury which became serious due to a staphylococcus infection of his hip bone. Known as osteomyelitis, the disease required lengthy hospital stays and operations which left him with a limp. The latter, it should be noted, never impeded him in a vigorous outdoor life that encompassed sailing, scuba diving, hiking and a general love of the outdoors and of nature. Extended hospitalisation did not deter the young Zienkiewicz from scholarly excellence and he completed his high school studies in June 1939. He planned to compete for admission to the Warsaw Polytechnic in September and moved to Warsaw in preparation for the examination.

Fate, of course, intervened in the form of the outbreak of the Second World War on 1st September 1939. Warsaw was soon under siege and the days that followed were among the most eventful of his entire life, which he spent building barricades, overturning trams and digging trenches. After several days, the order came to evacuate and Olek made hasty preparations to leave, taking a new camera, drawing instruments, a pair of socks – and nothing else except the clothes he was wearing. He had arranged to meet his mother and sister at a certain bridge and found that his sister was even less prepared for the times that lay ahead, having only a pair of high-heeled shoes and two packets of cigarettes. Many exciting days were to follow, including wandering through the countryside for ten days, a return to Warsaw and, eventually, a reuniting of the family in Katowice.

After several weeks the family managed to obtain a visa to Italy, which had not yet entered the war, and then subsequently on to Angiers in France, where Casimir Zienkiewicz worked for the Polish government in exile. This stay proved to be short-lived, however, with the fall of France occurring in June 1940. The family was able to keep one step ahead of the invaders and reached the west coast of France at St. John de Luz, near Bayonne, where they sailed to England on the Polish ship Batory on the very day, 22nd June, 1940, when the armistice between France and Germany was signed.

Once in England Olek began to think of a university education. The British Council had available to Poles a special scholarship for study at Imperial College, where he opted for a course in Civil Engineering, as the university did not have a degree scheme in Naval Architecture which was his preferred choice. Placed first in his studies at the end of the first year, he was given two scholarships for the remaining time at Imperial College. He graduated in 1943, one of two first-class honours recipients, the other being D. W. Holder who subsequently became a noted aerodynamicist at the National Physical Laboratory, Teddington, and later Professor of Engineering Science at Oxford, and was also elected a Fellow of the Royal Society.

Upon graduation, Zienkiewicz discussed the possibility of research work with A. J. S. Pippard who offered a scholarship to work jointly with him and R. V. Southwell on a dam analysis project. Southwell and Pippard were two of the principal figures in the development of structural mechanics in the 1930s and 1940s. Southwell’s relaxation method bridged the gap between the classical methods developed over the century prior to 1930 and the large-scale computational methods of today, which emerged in the late 1950s.

Another figure which had an early influence on Olek was W. G. Bickley, Professor of Mathematics at Imperial College, who was keenly interested in algebra in a matrix format which would become a cornerstone of future computational procedures. At the commencement of Olek’s graduate studies, he provided personal tutoring in the mathematics that was needed for the dam analysis project. This was a gesture that he never forgot and may explain, in part, Olek’s willingness to spend so much time with young researchers throughout his career.

After the award of his Ph.D. in 1945, Olek moved directly into engineering practice. With his appetite for dams having been whetted by his postgraduate work, he became attracted to the design and construction of these massive structures. He approached the consultancy firm of Sir William Halcrow and was offered a post leading a survey party on a dam project in Scotland. After salary negotiation culminating in the offer of £250 per annum, he was asked if he could drive a car. ‘Naturally’ came the reply and he promptly went out and took the test, in those days, for a provisional license. To the time of his death he did not take a test for a regular driving license. Olek spent four years with Halcrow, first with the survey task and then on the design and construction of the Glen Affric Hydroelectric System in northern Scotland.

In 1949 various opportunities for a change of direction came to Olek’s attention and one which appealed to him, and he accepted, was a lectureship in the Department of Engineering at Edinburgh. The department, headed by Ronald Arnold, was well known, especially in the field of applied dynamics. For advice on research avenues, he went to Charles Jaeger, a noted authority in fluid mechanics, who suggested several topics in the field of hydraulics. Soon he was contributing research papers in a variety of topics, such as open channel waves, water hammer and lubrication phenomena. This was a period of ease in his academic career, steadily developing his teaching skills and honing his research techniques.

To add to this idyllic scene, he met a young graduate student from Canada, Helen Fleming who was working towards an M.Sc. degree in chemistry. They were soon engaged and were married in 1952. Their first son, Andrew, arrived in 1953 and son David was born a year later.

Towards the end of 1956, offers materialised for posts elsewhere. He eventually decided on accepting a position as Associate Professor of Civil Engineering at Northwestern University, USA, facilitated by Pippard who had spent some time there as a visitor. During his four years at Northwestern, he developed lifelong friends such as John Dunders and Seng Lip Lee. Also, during this period their daughter Krystyna was born in 1958. Sadly, his father passed away in this same year at age 86.

In 1961, he began a new adventure that led to the activities for which he became world-renowned. The Chair of Professor of Civil Engineering became vacant at Swansea, due to the departure of B. G. Neal to Imperial College, and Olek was successful in the ensuing competition. Although the salary was substantially less than he was receiving at Northwestern, he relished the attraction of a professorship in the UK system at that time, wherein it was possible to influence the work and professional development of many others. Moreover, it was a time of unprecedented expansion of higher education in the United Kingdom.

Shortly after Olek’s arrival at Swansea a young Chinese student walked into his office and sought advice regarding study for a Ph.D. degree. The student possessed only Chinese credentials and Olek accepted him on the basis of an extensive interview conducted on the spot. The student, Y. K. Cheung, was to work under Olek’s guidance on the first finite element research at Swansea and to collaborate on the first edition of the now-classic treatise, The Finite Element Method. From 1961 to the present, the Department of Civil Engineering at Swansea has achieved a reputation as one of the world’s foremost centres of finite element research.

### BIBLIOGRAPHY

The following publications are those referred to directly in the text. A full bibliography is available as electronic supplementary material at http://rsbm.royalsocietypublishing.org

1. Zienkiewicz, O. C. (1947) The stress distribution in gravity dams. J. Inst. Civ. Eng., 27, 244-271.

2. Zienkiewicz, O. C. (1957) Temperature distribution within lubricated films between parallel bearing surfaces and its effect on the pressure developed. Proc. Conf. on Lubrication and Wear, Inst. Mech. Eng., London, 1-3 October, 1-7.

3. Charnes, A., Lemke, C. E. and Zienkiewicz, O. C. (1959) Virtual work, linear programming and elastic limit analysis. Proc. Roy. Soc. A., 251, 110-116.

4. Zienkiewicz, O. C. and Gerstner, R. W. (1961) The method of interface stress adjustments and its uses in the solution of some plane elasticity problems. Int. J. Mech. Sci., 2, 267-276.

5. Zienkiewicz, O. C. (1980) The finite element story. Internal Report No. C/R.317.80, Inst. For Num. Meth. In Eng., University of Wales Swansea.

6. Bazeley, G. P., Cheung, Y. K., Irons, B. M. and Zienkiewicz, O. C. (1965) Triangular elements in plate bending: Conforming and non-conforming solutions. Proc. Conf. on Matrix Methods in Structural Mechanics, (eds. J. S. Przemieniecki, R.M. Bader, W.F., Bozich, J.R. Johnson, and W.J. Mykytow) , Oct. 26-28, 547-576, Report No. AFFDL-TR-66-80, Wright-Patterson AFB, Ohio.

7. Oden, J. T. (2009) Private communication.

8. Zienkiewicz, O. C., Qu, S., Taylor, R. L. and Nakazawa, S. (1986) The patch test for mixed formulation. Int. J. Num. Meth. Engng., 23, 1873-1883.

9. Zienkiewicz, O. C., Taylor, R. L., Papadopoulos, P. and Oñate, E. (1990) Plate bending elements with discrete constraints: A new triangular element. Computers and Structures, 35, 505-522.

10. Oñate, E, Zienkiewicz, O. C., Suarez, B. and Taylor, R. L. (1992) A general methodology for deriving shear constrained Reissner-Mindlin plate elements. Int. J. Num. Meth. Engng., 33, 345-367.

11. Zienkiewicz, O. C. and Cheung, Y. K. (1965) Finite elements in the solution of field problems. The Engineer, September 24, 220, 507-510.

12. Zienkiewicz, O. C. and Parekh, C. J. (1970) Transient field problems:2-dimensional and 3-dimensional analysis by isoparametric finite elements. Int. J. Num. Meth. Engng., 2, 61-81.

13. Zienkiewicz, O. C., Lyness, J. F. and Owen, D. R. J. (1977) Three dimensional magnetic field determination using a scalar potential – a finite element solution. I.E.E.E. Transactions of Magnetics, MAG-13, No. 5, 1649-1656.

14. Zienkiewicz, O. C. (1965) (a) Two dimensional stress analysis and plate flexure by finite differences. Ch. 2, 20-40. (b) Finite element procedure in the solution of plate and shell problems. Ch. 8, 120-144. From Stress Analysis (O. C. Zienkiewicz and G. S. Holister, eds.), John Wiley and Sons.

15. Ergatoudis, I., Irons, B. M. and Zienkiewicz, O. C. (1968) Curved isoparametric quadrilateral elements for finite element analysis. Int. J. Solids Struct., 4, 31-42.

16. Hughes, T. J. R. (2009) Private communication.

17. Ahmad, S., Irons, B. M. and Zienkiewicz, O. C. (1968) Curved thick shell and membrane elements with particular reference to axi-symmetric problems. Proc. Second Conf. on Matrix Methods in Structural Mechanics (eds. R.M. Bader, L. Berke, W.J. Mykytow, J. S. Przemieniecki and M. H. Shirk), October, 1968, 539-572, Report No. AFFDL-TR-68-150, Wright-Patterson AFB, Ohio.

18. Ahmad, S., Irons, B. M. and Zienkiewicz, O. C. (1970) Analysis of thick shell and thin shell structures by curved finite elements. Int. J. Num. Meth. Engng., 2, 419-451.

19. Zienkiewicz, O. C., Taylor, R. L. and Too, J. M. (1971) Reduced integration technique in general analysis of plates and shells. Int. J. Num. Meth. Engng., 3, 275-290.

20. Taylor, R. L. (2009) Private communication.

21. Pugh, E. D. L., Hinton, E. and Zienkiewicz, O. C. (1978) A study of quadrilateral plate bending elements with ‘reduced integration’. Int. J. Num. Meth. Engng., 12, 1059-1079.

22. Zienkiewicz, O. C. and Watson, M. (1966) Some creep effects in stress analysis with particular reference to concrete pressure vessels. J. Nuclear Engng. and Design, 4, 406-412.

23. Zienkiewicz, O. C., Watson, M. and King, I. P. (1968) A numerical method of visco-elastic stress analysis. Int. J. Mech. Sci., 10, 807-827.

24. Zienkiewicz, O. C., Valliappan, S. and King, I. P. (1969) Elasto-plastic solution of engineering problems; initial stress, finite element approach. Int. J. Num. Meth. Engng., 1, 75-100.

25. Zienkiewicz, O. C. and Nayak, G. C. (1973) A general approach to problems of plasticity and large deformation. The Mathematics of Finite Elements and Application, 1-37, (J. Whiteman, ed.), Academic Press.

26. Nayak, G. C. and Zienkiewicz, O. C. (1972) Note on the alpha-constant stiffness method for the analysis of non-linear problems. Int. J. Num. Meth. Engng.,4, 579-582.

27. Nayak, G. C. and Zienkiewicz, O. C. (1972) Convenient form of stress invariants for plasticity. Proc. A.S.C.E., J. of Struct. Div., 98, ST4, 949-953.

28. Nayak, G. C. and Zienkiewicz, O. C. (1972) Elasto-plastic stress analysis: Generalisation for various constitutive relations including strain softening. Int. J. Num. Meth. Engng., 5, 113-135.

29. Zienkiewicz, O. C. and Cormeau, I. C. (1974) Visco-plasticity; plasticity and creep in elastic solids A unified numerical solution approach. Int. J. Num. Meth. Engng., 8, 821-845.

30. Zienkiewicz, O. C. and Godbole, P. N. (1974) Flow of plastic and visco-plastic solids with special reference to extrusion and forming processes. Int. J. Num. Meth. Engng., 8, 3-16.

31. Zienkiewicz, O. C., Humpheson, C. and Lewis, R. W. (1975) Associated and non-associated visco-plasticity and plasticity in soil mechanics. Geotechnique, 25, 671-689.

32. Kanchi, M. B., Zienkiewicz, O. C. and Owen, D. R. J. (1979) The visco-plastic approach to problems of plasticity and creep involving geometric nonlinear effects. Int. J. Num. Meth. Engng., 12,169-181.

33. Zienkiewicz, O. C., Nayak, G. C. and Owen, D. R. J. (1972) Composite and ‘overlay’ models in numerical analysis of elasto-plastic continua. Foundations of Plasticity. (A Sawczuk, ed.), 107-122, Noordhoff Press.

34. Pande, G. N., Owen, D. R. J. and Zienkiewicz, O. C. (1977) Overlay models in time dependent non-linear material analysis. Comp. & Struct. 7, 435-443.

35. Zienkiewicz, O. C. (1975) Why finite elements? Ch.1 in Finite Elements in Fluids (R. H. Gallagher, J. T. Oden and O. C. Zienkiewicz, eds.), Vol. 1, 1-23, John Wiley & Sons.

36. Heinrich, J. C., Huyakorn, P., Mitchell, A. R. and Zienkiewicz, O. C. (1977) An ‘upwind’ finite element scheme for two-dimensional convective transport equation. Int. J. Num. Meth. Engng., 11, 131-143.

37. Zienkiewicz, O. C., Lőhner, R., Morgan, K. and Nakazawa, S. (1984) Finite elements in fluid mechanics – A decade of progress. Finite Elements in Fluids (R. H. Gallagher et al., eds.), 5, Ch. 1, 1-26.

38. Godbole, P. N. and Zienkiewicz, O. C. (1974) Finite element analysis of steady flow of non-Newtonian fluids. Finite Element Methods in Engineering (A. P. Kabaila and V. P. Pulmano, eds.), University of New South Wales, 785-798.

39. Zienkiewicz, O. C. and Cheung, Y. K. (1964) The finite element method for analysis of elastic isotropic and orthotropic slabs. Proc. Inst. Civ. Eng., 28, 471-488.

40. Zienkiewicz, O. C. and Lewis, R. W. (1973) An analysis of various time-stepping schemes for initial value problems. Earthquake Eng. & Struct. Dyn., 1, 407-408.

41. Bettencourt, J. M., Zienkiewicz, O. C. and Cantin, G. (1982) Consistent use of finite elements in time and the performance of various recurrence schemes for the heat diffusion equation. Int. J. Num. Meth. Engng., 17, 931-938.

42. Zienkiewicz, O. C., Wood, W. L. and Taylor, R. L. (1980) An alternative, single step, algorithm for dynamic problems. Earthquake Engng. Struct. Dyn., 8,31-40.

43. Zienkiewicz, O. C. and Naylor, D. J. (1971) The adaptation of critical state soil mechanics for use in finite elements. In Stress–strain behaviour of soils: Proceedings of the Roscoe Memorial Symposium, Cambridge, 29–31 March 1971 (ed. R. H. G. Parry), pp. 537–547. G. T. Foulis & Co., Henley-on-Thames

44. Zienkiewicz, O. C. and Pande, G. N. (1977) Some useful forms of isotropic yield surfaces for soil and rock mechanics. Ch. 5, 179-190. Finite Elements in Geomechanics, (G. Gudehus, ed.), John Wiley and Sons.

45. Zienkiewicz, O. C., Chang, C. T., Hinton, E. and Leung, A. H. (1980) Liquifaction and permanent deformation under dynamic conditions: Numerical solution on constitutive relations. Proc. Int. Symp. on Soils under Cyclic and Transient Loading. (eds: G. N. Pande and O.C. Zienkiewicz), Swansea. January 1980, 71-103, John Wiley & Sons, Chichester.

46. Zienkiewicz, O. C. and Bettess, P. (1975) Infinite elements in the study of fluid-structure interaction problems. Computing Methods in Applied Sciences, Lecture Notes in Physics, Volume 58, pp. 133-172, Springer-Verlag, Berlin.

47. Zienkiewicz, O. C., Kelly, D. W. and Bettess, P. (1977) The Sommerfeld (radiation) condition on infinite domains and its modelling in numerical procedures. Lecture Notes in Mathematics, Volume 703, pp. 169-203, Springer-Verlag, Berlin.

48. Fraeijs de Veubeke, B. and Zienkiewicz, O. C. (1967) Strain energy bounds in finite element analysis by slab analogy. J. Strain Analysis, 2, 265-271.

49. Zienkiewicz, O. C., Kelly, D. W. and Bettess, P. (1977) The coupling of the finite element method and boundary solution procedures. Int. J. Num. Meth. Engng, 11, 355-375.

50. Zienkiewicz, O. C., Kelly, D. W. and Bettess, P. (1980) Marriage a la mode – The best of both worlds (Finite elements and boundary integrals). Ch. 5, 81-107, Energy Methods in Finite Element Analysis (R. Glowinski, E. Y. Rodin and O. C. Zienkiewicz, eds.), John Wiley and Sons.

51. Kelly, D. W., de S. R. Gago, J. P, Zienkiewicz, O. C. and Babuska, I (1983) A-posteriori error analysis and adaptive processes in the finite element method. Part I – Error analysis, Int. J. Num. Meth. Engng., 19, 1593-1619, Part II – Adaptive mesh refinement, Int. J. Num. Meth. Engng., 19, 1621-1656.

52. Zhu, J. Z. and Zienkiewicz, O. C. (1988) Adaptive techniques in the finite element method, Communications in Applied Numerical Methods, 4, 197-204.

53. Ainsworth, M., Zhu, J. Z., Craig, A. and Zienkiewicz, O. C. (1989) Analysis of the Zienkiewicz-Zhu a-posteriori error estimator in the finite element method. Int. J. Num. Meth. Engng., 28, 2161-2174.

54. Zienkiewicz, O. C. and Zhu, J. Z. (1992) Superconvergent patch recovery and a-posteriori error estimation in the finite element method, Parts I and II. Int. J. Num. Meth. Engng., 33, 1331-1382.

55. Lőhner, R, Morgan, K. and Zienkiewicz, O. C. (1984) Domain splitting for an explicit hyperbolic solver. Comp. Meth. Appl. Mech. Eng., 45, 313-329.

56. Zienkiewicz, O. C., Lőhner, R., Morgan, K. and Peraire, J. (1986). High speed compressible flow and other advection dominated problems of fluid mechanics. Vol. 6, Ch. 2, 41-88, Finite Elements in Fluids (R. H. Gallagher et al. eds.), John Wiley and Sons

57. Zienkiewicz, O. C. and Codina, R. (1995) A general algorithm for compressible and incompressible flow. Part I – The Split Characteristic Based scheme. Int. J. Num. Meth. Fluids, 20, 869-885.

58. Zienkiewicz, O. C., Taylor, R. L., Zhu, J. Z. and Nithiarasu, P. (2005) The Finite Element Method – Three volume set, Butterworth-Heinemann.

59. Oñate, E (2009) Private communication.

60. Zienkiewicz, O. C. (1987) The first 25 years of the finite element method at Swansea. The University of Wales Review (J. H. Purnell, ed.), 5-19, No. 2, Autumn 1987.

61. Zienkiewicz, O. C. (1995) Origins, milestones and directions of the finite element method – A personal view. Archives of Computational Methods in Engineering, 2(1), 1-48.