George I. N. Rozvany - Böcker

Topology optimization of structures and composite materials is a new and rapidly expanding field of mechanics which is now coming to play a major role in most branches of engineering, such as aerospace, mechanical, structural, civil and materials. There are also significant implications for energy production and the building and material sciences. It a truly "high-tech" field, requiring advanced computer facilities and computational methods, while involving unusual theoretical considerations in pure mathematics. Topology optimization deals with some of the most intractable problems in the mechanical sciences, but is also of considerable practical interest in that it can achieve far greater savings than conventional (sizing or shape) optimization. Extensive research into topology optimization is being conducted in most developed countries. The present book describes the state of the art, bringing together researchers from a diversity of backgrounds: mathematicians, information scientists, aerospace, automotive, mechanical, structural and civil engineers.

Topology optimization of structures and composite materials is a new and rapidly expanding field of mechanics which is now coming to play a major role in most branches of engineering, such as aerospace, mechanical, structural, civil and materials. There are also significant implications for energy production and the building and material sciences. It a truly "high-tech" field, requiring advanced computer facilities and computational methods, while involving unusual theoretical considerations in pure mathematics. Topology optimization deals with some of the most intractable problems in the mechanical sciences, but is also of considerable practical interest in that it can achieve far greater savings than conventional (sizing or shape) optimization. Extensive research into topology optimization is being conducted in most developed countries. The present book describes the state of the art, bringing together researchers from a diversity of backgrounds: mathematicians, information scientists, aerospace, automotive, mechanical, structural and civil engineers.

The book covers new developments in structural topology optimization. Basic features and limitations of Michell’s truss theory, its extension to a broader class of support conditions, generalizations of truss topology optimization, and Michell continua are reviewed. For elastic bodies, the layout problems in linear elasticity are discussed and the method of relaxation by homogenization is outlined. The classical problem of free material design is shown to be reducible to a locking material problem, even in the multiload case. For structures subjected to dynamic loads, it is explained how they can be designed so that the structural eigenfrequencies of vibration are as far away as possible from a prescribed external excitation frequency (or a band of excitation frequencies) in order to avoid resonance phenomena with high vibration and noise levels. For diffusive and convective transport processes and multiphysics problems, applications of the density method are discussed. In order to take uncertainty in material parameters, geometry, and operating conditions into account, techniques of reliability-based design optimization are introduced and reviewed for their applicability to topology optimization.

The classical problem of free material design is shown to be reducible to a locking material problem, even in the multiload case.

"During the last two decades, research on structural optimization became increasingly concerned with two aspects: the application of general numeri- cal methods of optimization to structural design of complex real structures, and the analytical derivation of necessary and sufficient conditions for the optimality of broad classes of comparatively simple and more or less ideal- ized structures. Both kinds of research are important: the first for obvious reasons; the second, because it furnishes information that is useful in testing the validity, accuracy and convergence of numerical methods and in assess- ing the efficiency of practical designs. " (Prager and Rozvany, 1977a) The unexpected death of William Prager in March 1980 marked, in a sense, the end of an era in structural mechanics, but his legacy of ideas will re- main a source of inspiration for generations of researchers to come. Since his nominal retirement in the early seventies, Professor and Mrs. Prager lived in Savognin, an isolated alpine village and ski resort surrounded by some of Switzerland's highest mountains.It was there that the author's close as- sociation with Prager developed through annual pilgrimages from Australia and lengthy discussions which pivoted on Prager's favourite topic of struc- tural optimization. These exchanges took place in the picturesque setting of Graubunden, on the terrace of an alpine restaurant overlooking snow-capped peaks, on ski-lifts or mountain walks, or during evening meals in the cosy hotels of Savognin, Parsonz and Riom.

"During the last two decades, research on structural optimization became increasingly concerned with two aspects: the application of general numeri- cal methods of optimization to structural design of complex real structures, and the analytical derivation of necessary and sufficient conditions for the optimality of broad classes of comparatively simple and more or less ideal- ized structures. Both kinds of research are important: the first for obvious reasons; the second, because it furnishes information that is useful in testing the validity, accuracy and convergence of numerical methods and in assess- ing the efficiency of practical designs. " (Prager and Rozvany, 1977a) The unexpected death of William Prager in March 1980 marked, in a sense, the end of an era in structural mechanics, but his legacy of ideas will re- main a source of inspiration for generations of researchers to come. Since his nominal retirement in the early seventies, Professor and Mrs. Prager lived in Savognin, an isolated alpine village and ski resort surrounded by some of Switzerland's highest mountains.It was there that the author's close as- sociation with Prager developed through annual pilgrimages from Australia and lengthy discussions which pivoted on Prager's favourite topic of struc- tural optimization. These exchanges took place in the picturesque setting of Graubunden, on the terrace of an alpine restaurant overlooking snow-capped peaks, on ski-lifts or mountain walks, or during evening meals in the cosy hotels of Savognin, Parsonz and Riom.

Proceedings of the IUTAM Symposium on Structural Optimization, Melbourne, Australia, February 9-13, 1988