9R19. Nonlinear Problems in Machine Design. - E Zahavi (Ben-Gurion Univ, Beer Sheva, Israel) and D Barlam (Israel Aircraft Indust, Israel). CRC Press LLC, Boca Raton FL. 2001. 406 pp. ISBN 0-8493-2037-2. $99.95.

Reviewed by PJ Eagle (Exp and Comput Mech, DaimlerChrysler Corp, 800 Chrysler Dr, Auburn Hill MI 48326-2757).

This book is a monograph devoted to methods for solving mechanical design problems using hand-calculated and computer-based nonlinear analytical techniques. The stated aim of the text is to “acquaint readers with the modern analytical methods of machine design, enabling them to use them in daily applications.” The book intends to divide the emphasis between the theoretical basis of machine design methods and practical applications (generally within the context of commercial FEM codes). While the intended audience is not clearly spelled out, it would appear to be senior undergraduate or master’s level mechanical engineering students. This audience might use this text as a reference in design projects, but not as a primary course textbook.

The book consists of two main sections, Theoretical Fundamentals and Design Cases, divided over 12 chapters. There is an exhaustive list of nomenclature and symbols, a fairly elaborate index, and three appendices. The appendices are strangely selected for a text that is clearly not a teaching textbook. The first appendix is a review of very basic tensor calculus. No reader who would be capable of following the presentation on solid mechanics would benefit from this summary. The second appendix is a three-page review of matrix fundamentals that is incomplete and overly elementary. The third appendix is a collection of tabular data that is apparently not referred to anywhere in the text. There are relatively few typesetting irregularities and typographic errors. While the abundant figures are clearly and consistently executed, some are quite fuzzy in their reproduction suggesting that they may have been copied from a less than camera-ready source.

The Theoretical Fundamentals section provides an extensive review of basic solid mechanics with less extensive coverage of the finite element method, nonlinear problems, plasticity, contact, and fatigue. The review of solid mechanics is very concise and well written and would serve as an excellent teaching resource, except for the shortage of examples. The overview of energy methods in elastic problems is especially well written and documented with illustrations. The coverage of plasticity is equally clear, but suffers from no clear connection to any applications. It appears to be an edited version of some instructional materials that may have been used in lectures. The section on contact problems goes into greater depth than most machine design texts and ends with a commentary on the pluses and minuses of various solution methods. Unfortunately, without more extensive theoretical development and solved examples, any reader who would benefit from this terse review of contact stresses would not appreciate this critical review of the techniques. The review of fatigue methods lacks any derivation whatsoever and is simply a presentation of formulas and diagrams available in numerous other sources.

The Design Cases section considers applications that include leaf springs, threaded fasteners, flanges, and fatigue. Each case study section reviews (without derivation), the principal design equations related to each application area followed by an example of a finite element solution. There are no additional problems for consideration by the reader (as one would use a textbook) and only limited information about the construction of the finite element models (precluding their reconstruction in most cases).

This text claims to provide access to the author’s experience in applying both theoretical methods to practical problems in the area of machine design. In many cases, the practical grounding of the case studies is in question. For example, there is no attention paid to significant figures in any solved problem. Calculations of circular areas are reported to seven significant figures in cases where only two have any practical meaning. One especially troubling example is in the section on flanged connections. Comparisons are made between standard hand calculations and the results of an extensive finite element model. The authors observe that the hand calculation results in a critical pressure of 50.462 MPa whereas the MSC.NASTRAN result produces 56.242 MPa. (No standard practices on the use of significant figures were followed in this example. The five reported here do not have any justification.) The apparent 10% discrepancy is regarded as a justification for the application of the elaborate computer modeling of the flange. There is a significant “practical” matter which appears to be overlooked here: in any reasonable application (excepting missiles or race cars where every gram of excess weight is torturously sought out), a 10% error resulting from hand computations would be absorbed in the factor of safety, and the engineering team would move on to the next problem. How could a week-long (or longer) modeling excise be justified in such a case?

In summary, this reviewer would not recommend Nonlinear Problems in Machine Design to students or libraries seeking mechanical design reference texts. More complete and practical sources are available in traditional texts such as Shigley and Norton. The addition of examples in this text which use computer-aided engineering do not justify its selection as a learning resource. A second edition of this book should be considered with a more extensive review process and the addition of more example problems.