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).