It should be recognised that when Olek and his colleagues began research into the finite element method at Swansea in 1961, the method was already a known technique. The mathematical foundations of the technique were laid in the early decades of the last century, with contributions by Ritz, Galerkin, Courant and others. Within the finite element community, the origins of the method are attributed to the contribution of Hrenikoff & McHenry (1941) who, using engineering intuition, approximated the response of a plate by an equivalent framework system and Courant (1943) who developed a more rigorous mathematical approach to the solution of a torsion problem by subdivision of the domain into triangular sub-regions. Progress from that time onward was slow, no doubt hampered by the lack of computing power, until the first recognisable finite element paper, by Turner, Clough, Martin & Topp appeared in 1956. By the end of that decade a substantial body of literature had been accumulated and the term ‘finite element’ was coined by R. W. Clough, University of California at Berkeley in 1960. It was against this background that Olek entered the finite element research arena. It should also be mentioned that it was at this time that J. H. Argyris FRS, Imperial College and later the University of Stuttgart, embarked on finite element research and their careers ran in parallel for the next four decades, both contributing prominently to the field. To use Zienkiewicz’s own words (5) to describe this scene:

*“My own introduction to finite elements dates back to 1958 when I first met Clough. With much of my earlier work being based on finite difference calculus (and relaxation methods – as an ex-member of the Southwell team in the 1940s), I naturally contested at first the merits of the new method which seemed to concentrate on the solution of problems which by then we were fully capable of solving. However, in one area of structural analysis the merit of subdivision seemed obvious. That was the field of shell analysis where the difficulties of formulating differential equations in curvilinear coordinates and subsequently applying finite difference approximations could be easily sidestepped by considering a shell to be composed of a series of simple, flat, triangular elements. It was in this area of activity that I made my first start (1962) – not yet realising that the search for a good triangular element to represent plate flexure was to be fraught with difficulties. This problem also motivated the research of Ray Clough and with a friendly competition we arrived at our goal some three years later presenting a series of triangular plate and shell elements at the Wright-Patterson Conference of 1965”*

The Wright-Patterson Conference held in Dayton, Ohio in 1965 was a landmark in finite element analysis and paper (6) describing the first triangular plate bending elements from the Swansea group contained a remarkable number of major new ideas. One was the use of area coordinates for integration over triangular regions. Another of the contributions in the paper was the notion of the patch test. The paper had described two finite elements, one of which was non-conforming. In a displacement finite element formulation, displacement continuity is assured across element boundaries, due to description of the element displacement field in terms of (common) interfacial nodal displacements, but the interface element tractions are generally discontinuous since the element stresses are derived from the, approximated, displacement field on an individual element basis. Elements of this type are termed as being non-conforming. Such elements were not new in finite element analysis, but no one had attempted to establish criteria for their convergence.

Bruce Irons, then working at Rolls Royce and co-author of the paper – and who was destined to become a colleague at Swansea, identified the conditions to be met in the choice of element approximation functions and, in the case that the condition of the inter-element conformity was not met, devised a simple test to be applied to a collection, or ‘patch’, of elements. The patch test has proven to be of fundamental importance in the finite element theory. It was also at this meeting that J. Tinsley Oden, a pioneer of the finite element method, made first contact with Olek (7):

*“I first met Olek at the Dayton finite element meetings in the mid 1960s, which is where some say the finite element method, being born in the mid 1950s, reached its adolescence. There were a number of original and important works that formed the foundations of the subject that were presented there by engineers and scientists working in this new and exciting field. Of course, Olek was already known to many there because of his first textbook on finite elements, co-authored with Y. K. Cheung. Olek’s intense interest and warmth was intriguing. We hit it off immediately and began a friendship that lasted until his passing some four decades later”*

Work on the notion of the patch test continued over the years. In collaboration with Robert L. Taylor, he extended the procedure to mixed element formulations, in which both displacement and stress terms are considered as primary variables (8) and which was subsequently used to ensure convergence of some new element forms for plates (9, 10).

It was during this period that the first industrial application of the finite element method, in Europe at least, took place in 1963 when Zienkiewicz and co-workers undertook the stress analysis of the Clywedog dam in mid-Wales. As can be seen from Figure 2, which illustrates the dam and the finite element discretisation employed, the mesh was extremely coarse by present day standards; which reflected the limited computational power available at that time. Nevertheless, the analysis provided valuable insight to the behaviour of the dam and its foundation.

A paper that appeared in 1965 and which was to have profound impact in later years was ‘Finite Elements in the Solution of Field Problems’ (11), co-authored with Y. K. Cheung. Up to this time the method had been restricted to structural mechanics problems, by expanding techniques for the analysis of frameworks into a method for the analysis of elastic continua. As such, the methodology relied heavily of the theorem of total potential energy. Zienkiewicz was able to perceive it as a more general tool for the analysis of all types of problems in mathematical physics that could be described in terms of a differential equation with given boundary and initial conditions. By employing weighted residual procedures, and in particular a Galerkin approach, computational solutions could be obtained for classes of problem where a potential function cannot be easily derived. In particular, he identified the procedure as a scheme for solving Laplace’s equation which governs the behaviour of ideal fluids and the torsion of prismatic sections. Olek and his colleagues soon amplified these ideas to deal with problems of heat transfer (12) and electromagnetics (13).