Customer Reviews

Elasticity (Solid Mechanics and Its Applications)

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This is a superb graduate level textbook on linear elasticity, by an author well-recognized for his own research on this topic. Please notice that the 2nd edition of the book is greatly expanded and improved from the 1st edition. Elasticity is a "classic" subject of advanced mechanics education, and the older classic books by Timoshenko and Sokolnikoff take the subject to the mid-20th century. Since then, however, important "broad" solutions have been added, such as singular stresses in cracks/dislocations/disclinations, or micromechanics-type of problems dealing with inhomogeneities and transformation strains in the spirit of Eshelby. Beyond that, symbolic math packages now allow the instruction of elasticity in a very different manner from, say, 15 years ago. Barber has written his book in a way that allows, I believe, this easy incorporation of symbolic math packages into the course material.

We have used Barber's book three times for teaching a graduate course on elasticity, and the students (both MS and PhD levels) have found the book lucid and succinct. It contains a good number of homework problems, ranging from easier to quite challenging. A very attractive feature of the book is that a complete, detailed solution manual is available to instructors (from the author at the Univ. of Michigan.) A very extensive list of symbolic math files for computation of stresses and displacements from 2-D and 3-D potentials is also available from the author.

Contrary to other books on elasticity, Barber's book does not devote too much space on tensor analysis in the beginning. Students are most likely exposed to these tools in a course on continuum mechanics. I like this approach (Timoshenko follows the same view in his classic monograph), since it allows the instructor to jump right into solving elasticity problems.

One advantage of the book is its modern approach: There are chapters on crack-tip singular stresses, and dislocations. The standard material on 2-D problems are presented both in rectangular and polar coordinates. Barber has a beautiful discussion on generating independent solutions of the biharmonic equation that is clear and presented from first principles. The discussion of the St. Venant assumption in the context of the cantilever loaded by a shear force at its end is also an educational gem, combining the solution of the half-plane loaded by sinusoidal tractions with an estimate of the decay rate of the equilibrated "corrective" tractions. The discussion of the Williams singular stresses in the wedge and in the crack limit is also highly educational, one of the best I have seen in a textbook.

The 3-D presentation is also well written. This topic may seem incomprehensible and arbitrary to many beginning grad students, but Barber starts from simple solutions (Lame potential) and then proceeds to more involved potentials (solving biharmonic equations, i.e. Love, Galerkin, or harmonic equations, i.e. Papkovich-Neuber). The extension of these ideas to solving half-space problems is presented very systematically (the clearest approach I have seen in a textbook) by building a list of solutions each of which identifies a specific type of traction that is easily made to vanish at the half-space boundary. There is also a well-written section on sphere problems using spherical harmonics, on the complex variable formulation of 2-D problems, as well as on thermal stresses.

The contact section is also well written. The presentation of 2-D contact is systematic and very educational, hinging on the use of Fourier analysis and the half-plane point force solutions to solve contact with flat punches and cylinders.

A useful educational feature of the 2-D section is a feature that many instructors will find attractive: A list of all the biharmonic solutions in terms of polynomial or polar coordinate functions, including both stresses and displacements. Students love these tables: They allow the quick "building"of solutions by inspection.

In summary, this is a well-written textbook, greatly recommended for an advanced undergrad and certainly for a grad-level course on elasticity. I would love to see a greater number of problems, both medium and more challenging, and, perhaps, an expanded section on energy principles, mostly minimum potential energy.

Unfortunately, Barber's Elasticity is marred by a good deal of errata and does not make clear important assumptions in several derivations, most notably in dealing with curved beams. There are better texts available on this subject.

This book will introduce governing equations of linear elasticity and will focus on solutions of boundary value problems in both two and three dimensions using several different methods.