Crack problems in the classical theory of elasticity

Book Reviews next and applied to discrete and concontrol problems. tinuous Both the Riccati equation and the maximum principle are developed through dynamic programming. Chapter VIII briefly describes some computational methods of optimization. In general, the author gives proper emphasis to most of the more important aspects of optimal control. (An exception to this is a preoccupation with Fibonacci sequences, which form a significant portion of the sections on sampled-data, dynamic programming and optimum search.) The derivations, while sometimes not rigorous from a mathematician’s viewpoint, are quite adequate for an engineer seeking an introduction to the subject, and the results are always presented in an accurate manner. In addition, when the author feels a subject has not been covered in sufficient depth, he does not hesitate to give reference to other publications, generally standard textbooks. On the other hand, the book is generally self-contained. Standard terminology is used throughout, and the text is amazingly free of typographical errors. There is no “new” or “advanced” material presented in the book, as that is not its purpose. The author intended to make the book easy to use for the uninitiated and he is extremely effective in accomplishing this goal. JOHN L. POKOSEI Department of Electrical Engineering University of New Hampshire Durham, New Hampshire CRACK PROBLEMS IN TIE CLASSICAL THEORY OF ELASTICITY, by I. N. Sneddon and M. Lowengrub. 221 pages, diagrams, 6 x 9 in. New York, John Wiley, 1969. Price, $14.95. Sneddon and Lowengrub present calculations, results and an extensive bibliography of much of the theoretical work concerned with crack problems solved by the mathematical theory of elasticity. Both authors have made significant contributions to the field and endeavor, in this work, to collect together all of the significant work pertaining to the solution of the Griffith crack problem and its three-

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dimensional analogue, the penny shaped crack. The material is arranged into three chapters. The first chapter is a short introductory exposition mainly of the basic equations forming the crack problem, together with some formulations for stresses and displacements in terms of potentials or complex functions. Only results are presented; for details of the calculations, the reader is encouraged to consult the original works. The second and third chapters present the formulation, the essential steps of the analysis, and the important mathematical results for a number of important two- and threedimensional crack problems. A reasonable amount of graphical presentation of results is presented and the solutions are well documented so that readers may refer to original papers for the solution details. The intent of the authors is essentially to present under one cover, the important problems, formulations and solutions dealing with the elastic stress and deformation distribution in the vicinity of a crack. The authors have succeeded admirably in their task and the monograph conta,ins a wealth of information. The presentation of the material is as clear as one can make it given the fact that a great deal of relatively sophisticated mathematics occurs between the presented results. Just enough outlining of the solution technique is presented for each problem so that the reader can feel confident in the results obtained. A bibliography of over 250 references is included from both Eastern and Western literature including works completed in 1969. The text will be a worthwhile addition to the library of those researchers interested in this line of endeavor or to anyone interested in solutions of complex mixed boundary value problems in the theory of elasticity. Also, the book could be of value to those not acquainted with the solution of ‘crack problems in elasticity who wish to gain an overall feeling for the type of problem involved and some techniques used in the solution. ALAN I. SOLER Towne School of Mechanical Engineering University of Pennsylvania Philadelphia, Pa.

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