This report describes a rapid reanalysis technique (reducing analysis costs by factors between 2 and 100) and a rapid search procedure (reducing the number of design steps by a factor of 25) for obtaining optimum designs. Reanalysis is an approximate procedure based on extremum energy principles and leading, monotonically, to results as exact as desired. THe desing process is an allocation procedure. Each element of the structure is sized in turn. Optimization is addressed toward least weight design of truss systems with multiple loadings and a discrete set of admissible sizings (materials). The new technique can easily include prestress as a design variable. It can be extended to treat any set of finite elements and is based on use of the force or displacement method or both. Because of the modularity of calculations, it is well suited to computer implementation for multi-element structural systems.

The report considers the state of the art in methods of structural optimization. Mathematical programming based methods, while extremely successful with problems of moderate size tend to become prohibitively costly when applied to large scale structures. A novel approach to the weight optimization of indeterminate structures under multiple loading conditions with strength and displacement constraints has been developed and is presented herein. Using this method significant improvements in computational time have been achieved over direct numerical search methods. In some cases the numbers of iterations required to determine the least weight have been reduced by factors of over 20. The rate of convergence is independent of problem size permitting application to large scale structures. Examples of application of the new approach to a number of problems are included.

This book is intended to serve all those who are interested in structural opti mization, whether they work in this field or study it for other purposes. Rapid growth of interest in the cognitive aspects of optimization and the increas ing demands that the present day engineer has to meet in modern design have created the need of a monographic treatment of the subject. The vast number and wide range of structural optimization problems formulated and investigated in the last twenty years call for an attempt to sum up the pres ent state of knowledge in this domain and to outline the directions of its further development. The present authors undertook this task, hoping that the result would stimulate further work towards finding new methods and solutions and increasing the range of applications of the optimization methods to structural design. The immediate aim of the book is to present the basic criteria and methods of optimization and to provide a reference guide to the most important publications in the field. 'The book consists of fourteen chapters. Chapter 1 introduces the basic concepts, definitions and assumptions relating to structural optimization. Chapter 2 gives the foundations of optimization for minimum elastic strain potential or maximum rigidity, and sets a basis for optimization of bar, plate and lattice structures. Chapter 3 presents criteria of strength design and their applications to plane structures.

This volume contains the Proceedings of the Twelfth International Congress of Applied Mechanics, held at Stanford University on August 26 to 31, 1968. The Congress was organized by the International Union of Theoretical and Applied Mechanics; members of the IUTAM Congress Committee and Bureau are listed under Congress Organization. The members of the Stanford Organizing Committee, which was responsible for the detailed organization of the Congress, are also given, as are the names of the sponsors and the industrial and educational organizations that contributed so generously to the financial support of the meeting. Those attending the Congress came from 32 countries and totaled 1337 persons, plus wives and children. A list of the registered participants is included in the volume. The technical sessions of the Congress comprised four General Lectures and 281 contributed papers, the latter being presented in groups of five simultaneous sessions. The final choice of the contributed papers was made on the basis of abstracts by an International Papers Commit tee of IUTAM consülting of G. K. BATCHELOR, E. BECKER, N. J. HOFF, and W. T. KOlTER.

Function minimization methods in structural analysis and optimum design are discussed. A computer program which implements the energy search method of nonlinear finite element analysis is presented. Several recent weight optimization methods based on finite element analysis are reviewed. Special characteristics of the finite element method relevant to automated design are identified. Some efficient approximate analysis methods for optimization applications are explored. Applications of some of these methods to plane frames and finite-deflection trusses are presented.

This book presents the integrated approach of analysis and optimal design of structures. This approach, which is more convenient than the so-called nested approach, has the difficulty of generating a large optimization problem. To overcome this problem a methodology of decomposition by multilevel is developed. This technique, which is also suitable for implementation on parallel processing computers, has the advantage of reducing the size of the optimization problem generated. The geometric programming for both equality and inequality constraints is used in the optimization.