Some Basic Problems of the Mathematical Theory of Elasticity

Some Basic Problems of the Mathematical Theory of Elasticity

Some Basic Problems of the Mathematical Theory of Elasticity Fundamental Equations Plane Theory Of Elasticity Torsion And Bending by N. I. Muskhelishvili

Preface to Basic Problems of Mathematical Theory of Elasticity PDF

Although I do not think it possible or necessary to indicate all the changes and additions in the text of the earlier editions, I must draw the reader’s attention to the new arrangement of Chapters 14 – 16 (Chapter 17 is new).

Compared with the previous editions, the results contained in these chapters are not new, but the method by which they have been obtained has been replaced by a different one which seems to me to be more germane to the matter under consideration.

However, I should like to mention that the new method (which was influenced by the work of J. Plemelj on the theory of functions of a complex variable, published long before the first edition of my book, but unfortunately unknown to me at the time) leads to the same calculations as the former method.

For this reason and also because of the, say, greater complexity of the new method, I am not certain that I acted rightly in introducing this change.

Be that as it may, a comparison of the new and the old approach may prove usefuL In conclusion, I should like to add that as far as possible I have carefully quoted the authors of any results which I have used, just as I have done with regard to some of my own results, at times even of minor importance and adduced merely as examples.

I have followed this practice, not because I attach exaggerated importance to these results, but only to avoid puzzling the reader who might not be acquainted with the previous editions of my book and who might have encountered material taken from it without clear indication of its original source in some other publications (mostly non-Russian).

To simplify reference, the quoted works have been listed at the end of the book in alphabetical order. In references, the author is named and the number of his publication, according to this list, is given in square brackets.

The first edition was greatly assisted to its success by the preface of the late Academician Alexei Nikolaevich Krylov whose outstanding scientific and public merits are well known to all and for whom I shall always entertain feelings of profound gratitude and respect.

Krylov’s preface is reproduced below without any changes. I have not been able to fulfil in this edition the wish expressed by Krylov at the end of his preface concerning the development of numerical methods of solution.

While realizing the importance of his request, I felt that I would be unable to meet it sufficiently well. Nevertheless, Krylov’s wish has been fulfilled by other authors, referred to in the text of the book.

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