1R19. Inverse and Crack Identification Problems in Engineering Mechanics. Applied Optimization Series, Vol 46. - GE Stavroulakis (Dept of Civil Eng, Inst of Appl Mech, Tech Univ Carolo Wilhelmina, Braunschweig, Germany). Kluwer Acad Publ, Dordrecht, Netherlands. 2001. 223 pp. ISBN 0-7923-6690-5. $122.00.

Reviewed by G Maier (Dept of Struct Eng, Tech Univ Politecnico, Piaza Leonardo Da Vinci 32, Milan, 20133, Italy).

Inverse problems undoubtedly represent, nowadays, a broad area of applied mechanics; an area which is growing in all its three subdomains, namely parameter identification, optimum design and structural control. The first one, especially, which is dealt with in this book, exhibits a variety of basic concepts and a multiplicity of approaches. An interdisciplinary character arises in it from the confluence of experimental methodologies with recent developments in mathematics (such as regularization of ill-posedness and nonconvex constrained minimization) and in computational mechanics (such as sensitivity analysis). In many applications, deterministic approaches have to be replaced by stochastic ones, in view of important roles played by noisy experimental data and modeling uncertainties. Batch exploitations of experimental data to simply minimize a discrepancy norm between measured and corrupted quantities may be satisfactory in many practical situations. Other situations suggest sequential techniques like in Kalman filter, which consists of a sequence of stochastic estimations along a flow of noisy measurements starting from an expert’s a priori estimates. From an engineering point of view, a sharp distinction operatively and otherwise exists between material parameter identification based on laboratory testing and diagnostic identification of damages in structures on the basis of in situ monitoring.

In the inhomogeneous field of inverse mechanical problems, this volume basically focuses on structural parameter identification problems in statical and dynamical regimes endowed with the following peculiarities: unilateral contacts and cracks as primary sources of nonlinearities; consequent central role of complementarily problems or variational inequalities; and (in view of the nonlinearity confinement to lesser dimensionality loci) frequent recourse to boundary element methods for field modeling in space.

The purpose pursued by the author in this book (which was originated by his “Habilitation” thesis), clearly, is not to provide a textbook nor a broad conspectus of the subject. In fact, after a brief introduction on the conceptual framework of the topics to be expounded, three chapters are devoted to the theoretical and computational tools of later use, namely: linear and nonlinear complementarity problems; convex and nonconvex quadratic and nonlinear programing; mathematical programing “under equilibrium constraints” (MPEC); space discretization by boundary elements; evolutionary and soft computing techniques, such as genetic algorithms and neural networks.

The tools presented in the first half of the book, are put to work in the second half for the numerical solution of identification problems concerning flaws and cracks, in statics, steady-state dynamics, and transient dynamics (Chs 5, 6, and 7, respectively).

The pertinent literature is abundantly cited in reference lists at the end of each chapter. The style is clear and terse. The presentation is properly illustrated by meaningful (though mostly academic) examples and by numerous good figures.

In this reviewer’s opinion, this up-to-date monograph by Georgios Stavroulakis substantially supplements the quantitatively still limited (but qualitatively excellent) set of general treatises, such as those by Bui and Tarantola. Its readership will hopefully include not only researchers and doctoral students interested in inverse mechanical problems, but also libraries of universities and companies. In fact, though deliberately restricted in coverage and purposes, Inverse and Crack Identification Problem in Engineering Mechanics presents systematically, with a reasonable balance between theoretical and computational aspects, very recent developments in its subject, and it illustrates concepts and methods which are partly novel and partly are now being transferred from mathematics to mechanics and from mechanics to engineering.