Principal Computer Methods in Applied Mechanics and Engineering Mathematical models for the analysis and optimization of elastic plastic structures: A.A. Čyras...
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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING NORTH-HOLLAND 44 (1984) 365-366 BOOK REVIEW Mathematical Models for the Analysis and Optimization of Elastic Plastic Structures, A.A. Cyras (Ellis Horwood Ltd., Chichester, 1983), 121 pages, ISBN O-85312-629-1 (Ellis Horwood Ltd.) ISBN 0-470-20020-O (Halsted Press). Discrete, respectively discretized structures which behave in an elastic pegectly plastic manner are considered in the book with respect to their limit equilibrium, optimization as well as with respect to elastic plastic states. These problems are dealt with individually in three chapters constituting the main part of the text. They are preceded by a characterization of discrete systems which opens the subject. Matrix notation is introduced for static and kinematic quantities referred to arbitrarily discretized structures and is used throughout the An additional chapter demonstrating essential apvolume, facilitating the presentation. plications of the theory on selected examples closes the book. Each of the three main tasks addressed in the book, i.e. limit equilibrium, optimization, elastic plastic analysis, is treated for three different types of quasi-static loading. Thus, monotonic loading is followed by the consideration of the cyclic loading condition and subsequently, movable Zouding is handled and is seen to constitute a special case of cyclic loading. Following his intention, the author does not deal with physical details but is merely guided by the point of view of mathematical programming in formulating the respective problems. Nevertheless, the reader is often confronted with remarks on the mechanics of the subject. In each case, a statement of the particular task is followed by the formulation of an extremum problem in terms of the static variables. Mechanical extremum principles provide the basis for the respective static formulation which is considered as the primal one. The kinematic approach is subsequently derived by duality considerations. The extremum problem so stated; in terms of the kinematic variables is then associated with a mechanical extremum principle. The dual static and kinematic solutions are finally compared and the corresponding mechanical extremal principles are unified. A discussion of different aspects and a summary at the end of each chapter appear helpful to the reader. Futhermore, comparisons between different separately deduced formulations support a general view of the matter. As a matter of fact, the overall arrangement of the text is didactically advantageous. Restricted explanations and a frequent assumption of terms to be well known presume the apparent knowledge of the reader. The small volume at hand may thus be understood as a synopsis of formulations of mathematical programming problems for discrete elastic plastic structures rather than an introduction into the subject. It offers a link between the mechanical 00457825/84/$3.00 @ 1984, Elsevier Science Publishers B.V. (North-Holland) 366 Book Review fundamentals of elastic plastic structures and mathematical programming algorithms which are not presented in the book. Certainly, a revision of various details would improve the conciseness of the volume providing a standard on the subject. J. St. Doltsinis