[The articles of this volume will not be reviewed individually.] The book contains the edited version of lectures and contributed papers presented at the NATO Advanced Research workshop on topology optimization of structures, held at Hotel do Mar, Sesimbra, Portugal, June 20-26, 1992, and organized by the Mathematical Institute, the Technical University of Denmark and by CEMUL-Center for Mechanics and Materials of the Technical University of Lisbon. The book is organized in ten parts, each addressing a subfield of topology optimization, its relations to materials modelling and its implementation. Specifically, the ten subdivisions are: I. Topology design of discrete structures; II. Discrete design and selection problems; III. The homogenization method for topology design; IV. Alternative methods for topology design of continuum structures; V. Boundary shape design methods; VI. Relaxation and optimal shape design; VII. Effective media theory and optimal design; VIII. Extending the scope of topology design; IX. Topology design in a computer-aided design environment; X. Aspects of topology design. The computational aspect of topology design is a focal point of the papers. The large-scale nature of the problems makes it essential to develop specialized optimization algorithms. Also, the use of the so- called “homogenization method” in a computer-aided design environment is addressed, illustrating the effectiveness of the topology optimization method relative to simple sizing and shape optimization. Various techniques are also presented for transforming the material density shape information generated by topology optimization solutions into standard boundary or solid geometric descriptions for use in CAD systems. The topology design of structures presents a variety of difficulties, many of which have yet to be resolved. For discrete structures (trusses, frames, etc.) the definition of topology by a set of design variables is rather straightforward, using either discrete-valued variables or by allowing the volumes of the individual discrete elements of the structure to vanish. The main challenge in topology design problems for discrete structures is the formulation of suitable, well-posed design constraints for displacements, stresses and stability (local and global buckling). The papers address these aspects in some detail. However, the question of how to account for buckling constraints is still unsolved. Practical discrete topology design typically involves large scale computational problems and the need to select individual structural elements from a discrete set of possibilities. The papers cover various numerical approaches for the discrete design problems, including genetic algorithms and dual methods, and show how the large scale nature of the problems can be addressed through algorithms based on duality principles and non- smooth analysis. The research presented indicates considerable promise for special-purpose numerical optimization methods that take advantage of the unique form of structural topology problems. Articles on continuum problems emphasize the use of the “homogenization method”, which employs a composite material as a basis for defining shape in terms of material density. This method unifies two subjects, each of intrinsic interest and previously considered distinct. One is structural optimization at the level of macroscopic design. This approach is commonly practiced by mechanical engineers, using a macroscopic definition of geometry, typically given by thicknesses or boundaries. The other subject is micromechanics, the study of the relation between microstructure and the macroscopic behavior of a composite material. The main focus of the papers is the use of the latter in assisting the former approaches. The mathematical basis for optimal topology design of continuum structures lies within the field of relaxation of variational problems, and some results on the direct calculation of relaxed functionals and design spaces are contained in the articles.
J.Genin (Las Cruces)