Saint-Venant's problem / Dorin Ieşan

Saint-Vénant’s problem was posed in 1855-1856 and since then has generated a vast literature and still today offers a lot of challenge. The book under review is a welcome addition to the literature since it presents a wealth of information previously disposed in several books and articles. It will certainly estimulate research in this area.

The book has an introduction, 5 chapters and a bibliography of 160 entries. The introduction is concise, clear and guides well the reader through the book. The main chapter, the first, concerns results where Saint-Vénant’s solutions are involved. These solutions are constructed and some characterizations are given. Saint-Vénant’s principle is proved. Truesdell’s problem is discussed and it serves to show that the subject is very much alive and well. Chapter 2 presents the Almansi- Mitchell problem that considers the case where there are body forces and surfaces fractions on the lateral boundary. The next 3 chapters discuss some generalizations of Saint-Vénant’s problem for anisotropic elastic bodies, for heterogeneous elastic cylinders and for Cosserat elastic bodies. The book also shows some applications of the theory to thermoelastostatics. (Zentralblatt)