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THE general theorems given in Sections 4 and 6 include, from the fundamental point of view, all that is required for the analysis of redundant structures. However, to facilitate practical calculations it is helpful to develop more explicit methods and formulae. To find these is the purpose of this Section.

This paper develops general purpose programmes for an electronic digital computer for use when the Argyris Matrix Method of Structural Analysis is employed. Programmes for both the force and displacement methods are given and they apply for arbitrarily large structures. The procedure to be followed in the particular case of the structural analysis of a delta wing is outlined and the advantages of using magnetic tape storage are considered.

THE important series under the title ‘Energy Theorems and Structural Analysis’ which we published during the winter of 1954–5 will have made our readers familiar with the work of PROFESSOR J. H. ARGYRIS. More recently we have published a series by MR P. M. HUNT of Ferranti Ltd. on the programming of the Argyris method for the Ferranti Pegasus electronic digital computer. We believe that, taken together, these methods will be found to be of wide application to the problems facing the structural analysis departments of the aircraft firms, and that they will take their place as important design tools. Indeed, it is not unlikely that, as in so many cases before, other industries will find it to their advantage to adopt these techniques, pioneered on behalf of the aircraft industry, in so far as they may be found to be applicable.

A DSIR Sponsored Research Programme on the Development and Application of the Matrix Force Method and the Digital Computer. This work presents a rational method for the structural analysis of stressed skin fuselages for application in conjunction with the digital computer. The theory is a development of the matrix force method which permits a close integration of the analysis and the programming for a computer operating with a matrix interpretive scheme. The structural geometry covered by the analysis is sufficiently arbitrary to include most cases encountered in practice, and allows for non‐conical taper, double‐cell cross‐sections and doubly connected rings. An attempt has been made to produce a highly standardized procedure requiring as input information only the simplest geometrical and elastic data. An essential feature is the use of the elimination and modification technique subsequent to the main analysis of the regularized structure in which all cutouts have been filled in. Current Summary A critical historical appraisal of previous work in the Western World on fuselage analysis is given in the present issue together with an outline of the ideas underlying the new theory.

This paper presents a preliminary analysis of the effects of kinetic healing at supersonic speeds on the torsional and flexural stiffnesses of thin solid wings. The main investigation is based on the small deflexion theory, but the scope of the analysis for torsion is extended to cover the effects of large deformations.

WE define as an open tube a thin‐walled structure, the cross‐section of which does not include any closed circuit. This property is common, for example, to the curved channel, the interspar wing cut‐out and the panel stiffened with Z‐sections, illustrated in FIG. 1 (a, b, c). But the interspar cut‐out with nose cell (FIG. 1d) is not an open tube in the present definition. All structures discussed in this paper are assumed to be cylindrical and to have a constant cross‐section. It is relatively simple to extend the results to conical taper and longitudinally varying thickness, but this would be beyond the scope and space of the present analysis (see, however, ref. 5).

FAILURE of panels under static compression, or for that matter under any loads, involves a vast array of problems ranging from properties of material to initial instability and post‐buckling phenomena as occurring in various types of panels. It is not intended here to do justice to all these aspects of the subject but to select a single—but at the same time very important—topic, develop its analysis as fully as possible, and present the results in a readily applicable form. The structure investigated is the single skin stiffened panel under compression and the mode of failure considered, denoted by flexural cum torsional failure, involves predominantly flexure and torsion of the stringer with a wavelength of greater order of magnitude than stringer height and pitch. By torsional deformation of the stringer we understand a rotation of its undistorted cross‐section about a longitudinal axis R in the plane of the plate, the position of which will be selected later on (see FIG. 1b). The panel may, of course, also fail in a local mode of stringer and plate with a short wave‐length of the order of magnitude of stringer height and pitch, but the analysis of this case is not included here (see, however, Argyris and Dunne). Note that a local mode of deformation of a stringer formed by straight walls is commonly defined as a distortion of the cross‐section in which the longitudinal edges where two adjacent walls meet remain straight (see FIG. 1c).

IN this issue we publish the last section of the present part of DR J. H. ARGYRIS'S ‘Energy Theorems and Structural Analysis’. It may not be out of place to give some indication of the reasons for publishing a work of this length in the form of a series of articles, particularly as some of our readers whose first interest is not in the theory of structures may feel that a disproportionate amount of space has been devoted to it. Serial publication does mean that the results of such work as DR ARGYRIS has been doing appear at the earliest possible moment. Although the development of the theories has been going on for some time, the manuscript of each published section has only been assembled in its final form, and the illustrations drawn, about a month to six weeks before the appearance of the issue in which it has been published. This has meant that all concerned have had to work to a tight schedule, not least the author and his small team, and it has left little time for the solution of the complex problems of type‐setting with which our printers have had to deal. As a result of all this, we hope, the methods of structural analysis proposed will be available to the industry earlier than if publication had been delayed until the manuscript was complete, and the whole could be presented in book form. The series has aroused great interest, and we believe that it will have a considerable influence on the structural analysis of the next generation of aircraft.

This paper describes a scheme which enables an electronic digital computer to deal directly with matrices and matrix instructions. It enables the transformation between the specification of matrix calculations on paper and the actual operations within the computer to be carried out in easy and concise terms. Using this scheme the paper develops the appropriate programmes of instructions to be given to the computer for the calculations involved when applying the Argyris matrix method for the analysis of stresses and displacements in arbitrary clastic structures. In order to introduce the reader to the technique a programme for a simple structure is given in Part I. General purpose programmes applicable to more complex structures are given in Parts II and III.

THE paper by Dr J. H. ARGYRIS which we publish in this issue is of unusual interest and importance. In conjunction with Mr P. C. DUNNE the author has been responsible for great development in the science of stressing of aircraft structures. Their theories were expounded in detail in the Journal of the Royal Aeronautical Society in 1947 and 1949 and they were responsible for much of the work on the early stressed‐skin data sheets issued by the Society.