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# Elasticity, 3rd edition, J.R.Barber

Springer has just published the third edition of my book

`Elasticity'.

This new edition contains four additional chapters, including two concerned with the use of complex-variable methods in two-dimensional elasticity. In keeping with the style of the rest of the book, I have endeavoured to present this material in a such a way as to be usable by a reader with minimal previous experience of complex analysis who wishes to solve specific elasticity problems. I have emphasised the relation between the complex and real (Airy and Prandtl) stress functions, including algorithms for obtaining the complex function for a stress field for which the real stress function is already known. The complex variable methods and notation are also used in the development of a hierarchical treatment of three-dimensional problems for prismatic bars of fairly general cross-section in a later chapter. The other major addition is a new chapter on variational methods, including the use of the Rayleigh-Ritz method and Castigliano's second theorem in developing approximate solutions to elasticity problems. The full Table of Contents, a sample chapter, and other information can be accessed here. For purchasing information or to request inspection copies, please contact the publisher.

As in the second edition, I encourage the reader to become familiar with the use of symbolic mathematical languages such as Maple and Mathematica, since these tools open up the possibility of solving considerably more complex and hence interesting and realistic elasticity problems. They also enable the student to focus on the formulation of the problem (e.g. the appropriate governing equations and boundary conditions) rather than on the algebraic manipulations, with a consequent improvement in insight into the subject and in motivation. Finally, they each posess post-processing graphics facilities that enable the user to explore important features of the resulting stress state. The reader can access numerous files for this purpose at my University of Michigan homepage http://www-personal.umich.edu/~jbarber/elasticity/book.html, including the solution of sample problems, electronic versions of the tables in Chapters 21,22, and algorithms for the generation of spherical harmonic potentials. Some hints about the use of this material are contained in Appendix A, and more detailed tips about programming are included at the above website.

A solution manual is available, containing detailed solutions to all the problems, in some cases involving further discussion of the material and contour plots of the stresses etc. Bona fide instructors should contact me at jbarber@umich.edu if they need the manual and I will send it out as zipped .pdf files. Please let me know whether you have the second edition or the third edition.

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## Comments

## well done, Jim!

A congratulation for continuing effort to improve the book, which is certainly the "standard" of Elasticity today, alongside with the classical Timoshenko's Theory of Elasticity book, and perhaps the more "web-friendly" book of Allan Bower using the Brown notation. The 3 together certainly are more than what most people need in their library for the relatively

classicalelasticity problems today.Michele

## Re: Elasticity, 3rd edition, J.R.Barber

Dear Jim:

I have the second edition and like its simplicity and clarity of presentation. A quick comment/question: On pages 26-28 you discuss compatibility equations for multiply-connected domains. This is a good discussion and is rarely seen in any book (with the exception of Classical and Computational Solid Mechancis by Fung and Tong). On page 28 you explain why intuitively one can have all the compatibility equations satisfied but yet the strain field is incompatible for a body with a hole. Again, very good explaination. Then you mention that compatibility of a body with holes requires additional six equations for each hole. I think this is not correct; you would need three extra equations for each hole. Fung and Tong present a similar argument (with the correct number of extra equations) though their proof is not completely rigorous.

Regards,

Arash