The book covers the theory of Michell structures being the lightest and fully stressed systems of bars, designed within a given domain, possibly within the whole space, transmitting a given load towards a given support. Discovered already in 1904 by A.G.M. Michell, the structures named after him have attracted constant attention due to their peculiar feature of disclosing the optimal streams of stresses equilibrating a given load and thus determining the optimal layout of bars. The optimal layouts emerge from among all possible structural topologies, thus constituting unique designs being simultaneously light and stiff. The optimal structures turn out to be embedded in optimal vector fields covering the whole feasible domain. Key features include: a variationally consistent theory of bar systems, thin plates in bending and membrane shells; recapitulation of the theory of optimum design of trusses of minimum weight or of minimal compliance; the basis of 2D Michell theory for a single load case; kinematic and static approaches; 2D benchmark constructions including Hemp’s structures and optimal cantilevers; L-shape domain problems, three forces problem in 2D, bridge problems; revisiting the old - and delivering new - 3D benchmark solutions; extension to multiple load conditions; Prager-Rozvany grillages; the theory of funiculars and archgrids; the methods of optimum design of shape and material inspired by the theory of Michell structures, industrial applications. The book can be useful for graduate students, professional engineers and researchers specializing in the Optimum Design and in Topology Optimization in general.

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 book commemorates the 80th birthday of Prof. W. Pietraszkiewicz, a prominent specialist in the field of general shell theory. Reflecting Prof. Pietraszkiewicz’s focus, the respective papers address a range of current problems in the theory of shells. In addition, they present other structural mechanics problems involving dimension-reduced models. Lastly, several applications are discussed, including material models for such dimension-reduced structures.