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**Structural optimization. Vol. 1: Optimality criteria.**
*(English)*
Zbl 0649.73042

Mathematical Concepts and Methods in Science and Engineering, 34. New York - London: Plenum Press. XII, 334 p.; $ 49.50 (1985).

This book is written as a first volume in a treatise devoted to structural optimization including analytical formulations and numerical applications. Particular chapters are written separately or jointly by Prager and Save with one chapter elaborated by Sacchi.

Basic concepts of structural analysis and variational theorems are presented in Chapter 1, where theorems of minimum potential and complementary energies, the Rayleigh principle for free vibrations, and the mutual energy theorem for elastic structures are demonstrated, and next limit analysis and shakedown theorems for plastic structures are proved. The formulation of problems of optimal design is presented in Chapter 2. Chapter 3 is devoted to optimal design of beams and frames with emphasis laid on optimal plastic design. Some examples of optimization of elastic beams with deflection, stress, or stability constraints are also treated in this chapter. In Chapter 4, which is devoted to optimal design of trusses, problems of optimal layout (Michell trusses) are considered. Both exact and approximate solutions are presented for some simple cases. Chapter 5 is concerned with optimal plastic design of grillages (or reinforced concrete plates). The principal curvature lines and deflection fields are presented for a variety of boundary value problems of polygonal plates. Chapter 6 is concerned with optimal design of plates, shells and disks mostly for plastic design with limit load constraints. Chapter 7 provides the derivation of optimality criteria using Lagrange multiplier techniques with both equality and inequality constraints. In Chapter 8, some extensions to other optimal design problems are considered and in Chapter 9 solutions to selected problems are provided.

This book provides a valuable introduction to optimal structural design problems with emphasis on analytically derived optimality criteria with illustrative examples treated analytically. It also summarizes an extensive original research conducted by the late Professor Prager and his coworkers during the last two decades in the field of structural optimization. The optimal layout theory for both plane trusses and grillages constitutes an example of new important developments essential not only for further applications in optimal structural design, but also for optimal synthesis of engineering material structure or in the study of the mechanics of biomaterials with optimality conditions incorporated in the growth process.

Basic concepts of structural analysis and variational theorems are presented in Chapter 1, where theorems of minimum potential and complementary energies, the Rayleigh principle for free vibrations, and the mutual energy theorem for elastic structures are demonstrated, and next limit analysis and shakedown theorems for plastic structures are proved. The formulation of problems of optimal design is presented in Chapter 2. Chapter 3 is devoted to optimal design of beams and frames with emphasis laid on optimal plastic design. Some examples of optimization of elastic beams with deflection, stress, or stability constraints are also treated in this chapter. In Chapter 4, which is devoted to optimal design of trusses, problems of optimal layout (Michell trusses) are considered. Both exact and approximate solutions are presented for some simple cases. Chapter 5 is concerned with optimal plastic design of grillages (or reinforced concrete plates). The principal curvature lines and deflection fields are presented for a variety of boundary value problems of polygonal plates. Chapter 6 is concerned with optimal design of plates, shells and disks mostly for plastic design with limit load constraints. Chapter 7 provides the derivation of optimality criteria using Lagrange multiplier techniques with both equality and inequality constraints. In Chapter 8, some extensions to other optimal design problems are considered and in Chapter 9 solutions to selected problems are provided.

This book provides a valuable introduction to optimal structural design problems with emphasis on analytically derived optimality criteria with illustrative examples treated analytically. It also summarizes an extensive original research conducted by the late Professor Prager and his coworkers during the last two decades in the field of structural optimization. The optimal layout theory for both plane trusses and grillages constitutes an example of new important developments essential not only for further applications in optimal structural design, but also for optimal synthesis of engineering material structure or in the study of the mechanics of biomaterials with optimality conditions incorporated in the growth process.

### MSC:

74P99 | Optimization problems in solid mechanics |

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

74R20 | Anelastic fracture and damage |

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