Applied Elasticity [antikvár]

PREFACE In writing this book I have tried to see the subject from the point of view of the engineer rather from that of the mathematician. It is for that reason that the title Applied Elastidty has been chosen. Although there is not much in the book that could not be covered by the usual title Theory of Elastidty, yet this theory has been developed only so far as it seemed likely to lead to the solution of practical problems. Moreover, in the course of the work, only such problems as were deemed to have a practical interest have been chosen to illustrate the theory. One very important departure from the strict mathematical theory is to be found in the use of approximate methods of solution based on the principle of minimum energy. The application of this method requires nothing more difficult than somé simple integration, and the probable errors in the results attained are generally much smaller than the probable errors due to ignorance of the values of the elastic constants. The method is ideál for dealing with problems on stability, since, with very little effort, it usually gives buckling loads to within one per cent. The process can alsó be applied, with unexpected success, to the task of finding the periods of normál oscillations of elastic bodies. Mathematically these oscillation problems are identical with the stability problems before mentioned. Somé of the results of this book are here published, as far as I know, for the first time. Among these are Arts. 279 to 283 on the deflexion of a thin plate under normál pressure when the stretching of the middle surface is taken into account; Arts. 307, 308, 309, giving the approximate method of finding the buckling loads of deep beams; and Arts. 330, 331, 338, on the vibrations of a disk of variable thickness. I wish alsó to mention the successful application of the energy method to the problem of the buckling of thin tubes in Art. 324, in spite of the difficulty, to which the late Lord Rayleigh called attention, in getting an accurate expression for the energy in a bent plate.