Optimization in mechancis: Problems and methods.

*(English)*Zbl 0659.73073
North-Holland Series in Applied Mathematics and Mechanics, 34. Amsterdam etc.: North-Holland. xii, 279 p. $ 97.25; Dfl. 185.00 (1988).

The book deals with a discussion of the basic optimization problems and methods in mechanics. The subjects under study are as varied as minimization of masses, stresses and displacements, maximization of loads, vibration frequencies or critical speeds of rotating shafts.

The book contains seven chapter. The first chapter contains only the examples of some optimization problems like a reinforced shell, a robot, a booster. Also it is shown how to discretize by finite element techniques some optimization problems of structures and how to solve a strength maximization of a structure under stability constraints. The second chapter deals with the mathematical concepts and justification of the methods and algorithms of optimization. They are illustrated by some examples of structures subject to several loadings and to fundamental vibration frequencies. Chapter 3 is devoted to the Kuhn-Tucker theorem and to duality. Chapter 4 deals with the so-called associated problems, it means pairs of problems. Chapter 5 presents the basis of classical numerical methods of mathematical programming. The gradient and conjugate gradient methods, the Newton and the so-called quasi-Newton methods, the linearization, penalty and projection methods are analysed. Chapter 6 contains the so-called optimality criteria: the techniques of fully- stressed design, the classical optimality criteria, then the generalized optimality criteria and the mixed methods. Chapter 7 combines methods and techniques offered above in order to solve some optimization of discrete or continuous structures subject to dynamical effects. Particular attention is paid to mass minimization and fundamental eigenvalue problems.

This is an excellent book covering a fairly wide range of topics and addressed to engineers, researchers, but it may as well be used as an auxiliary text in teaching a graduate course in structural optimization.

The book contains seven chapter. The first chapter contains only the examples of some optimization problems like a reinforced shell, a robot, a booster. Also it is shown how to discretize by finite element techniques some optimization problems of structures and how to solve a strength maximization of a structure under stability constraints. The second chapter deals with the mathematical concepts and justification of the methods and algorithms of optimization. They are illustrated by some examples of structures subject to several loadings and to fundamental vibration frequencies. Chapter 3 is devoted to the Kuhn-Tucker theorem and to duality. Chapter 4 deals with the so-called associated problems, it means pairs of problems. Chapter 5 presents the basis of classical numerical methods of mathematical programming. The gradient and conjugate gradient methods, the Newton and the so-called quasi-Newton methods, the linearization, penalty and projection methods are analysed. Chapter 6 contains the so-called optimality criteria: the techniques of fully- stressed design, the classical optimality criteria, then the generalized optimality criteria and the mixed methods. Chapter 7 combines methods and techniques offered above in order to solve some optimization of discrete or continuous structures subject to dynamical effects. Particular attention is paid to mass minimization and fundamental eigenvalue problems.

This is an excellent book covering a fairly wide range of topics and addressed to engineers, researchers, but it may as well be used as an auxiliary text in teaching a graduate course in structural optimization.

Reviewer: St.Jendo

##### MSC:

74P99 | Optimization problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

74E30 | Composite and mixture properties |

74S05 | Finite element methods applied to problems in solid mechanics |