Discussion. Dynamic Relaxation.

Abstract

Professor Otter gave a short history of the development of D R from computer tidal calculations based on Professor Hansen's method and subsequently given in detail in Rossiter and Lennon's paper.'l Mr A. S. Day, who had worked on the tidal problems had the idea that a similar formulation of the dynamic elastic equations would settle down to the static conditions of equilibrium and compatibility if a viscous damping term were included. At the same time he suggested that 'dynamic relaxation' would be a suitable name for the method.85. Early in 1962. the Authors' firm were requested by the CEGB to calculate the stresses in the Oldbury prestressed concrete reactor pressure vessel, and the method suggested by Day was developed and used both for the model and the prototype vessel with gratifying results. The calculation of temperatures and thermal stresses, and of the effects of the curved prestressing cables including friction as well as the gas pressure and gravity were all carried out successfully assuming elastic conditions. 86. Further work was undertaken for the proposed designs for the Wylfa pressure vessels and for the AEA advanced gas-cooled reactor vessel, and also for the concrete dam designs for the Arch Dams Committee of the Institution, and later for CERA. The latter work comprised both shell and continuum solutions.87. The main virtues of Hansen's method for the tidal problem were its use of interlaced nets, and separated equations for continuity and energy and the ease of introducing the various types of boundary conditions. The progress of the tidal iterations was easily visualized. All of these were also true of the D R method as used for elastic calculations.88. It was found later that a somewhat similar form of iteration had been suggested in 1950 by Fraenkel, but only for relatively simple forms of partial differential equation using the equations direct in their second order form and with non-interlacing nets. The second part of the Paper was more of an index of the papers in which mathematical justification of the method could be found, and Professor Otter was glad to know that there were mathematicians who were taking up the problem of making the basic mathematics of the method understood by engineers.Dr R. E. Hobbs described progress made in the analysis of arch dams by DR since the preparation of the Paper. Using tensor methods, a general program had been developed which could deal with any dam whose faces were surfaces of revolution. This program had been used to provide solutions to several profiles very quickly.90. Current research was concerned with the development of a program to deal with a completely general profile, and with the incorporation of valley flexibility into the analyses.