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........ published in NEWSLETTER # 46
TOPOLOGY DESIGN OF STRUCTURES
by Professor Martin P. Bendsoe, The Technical University of Denmark (Denmark) and Professor C.A. Mota Soares, CEMUL, Instituto Superior Tecnico, Lisboa (Portugal)
The efficient use of materials is of great importance, and the choice of the basic topology for the design of structures and mechanical elements is crucial for the performance of sizing or shape optimization. This volume (NATO ASI SERIES E227) provides a comprehensive review of the state-of-the-art in topology design, spanning fundamental mathematical, mechanical and implementation issues.
Topology design of discrete structures (trusses, frames, etc.) involves large scale computational problems and the need to select structural elements from a discrete set of possibilities. The formulation and solution of discrete design problems are described, including new applications of genetic algorithms and dual methods. Several papers in this book show that there is a considerable potential in developing special purpose numerical optimization methods which use the unique form of the structural topology problems.
For continuum problems the book emphasizes the `Homogenization Method' which employs composite materials as the basis for defining shape in terms of material density, unifying macroscopic structural design optimization and micromechanics. A main focus of the book is the use of the latter in assisting the former.
Computational aspects of topology design are a focal point of the presentations, and the large-scale nature of the problems means that it is essential to develop a special type of optimization algorithm. Finally, the use of the homogenization method in a computer-aided design environment is addressed, illustrating the effectiveness of the topology optimization as compared to simple sizing and shape optimization. Also presented are various techniques for transforming the material density shape information of the topology optimization into a standard boundary of solid modelling form of CAD systems.
At present, topology optimization based on an energy criterion (compliance/global stiffness) for linear elastic structures under a single loading condition is well established. A number of papers in this volume address possible extensions to multiple loading cases, vibration problems, elasto-plastic problems and thermo-elastic problems. Also, the derivation of effective medium characterization for such problems is presented, as a first step in establishing the necessary rigorous background for treating such problems.
The book underlines the immense potential of topology design methods, and at the same time emphasizes the need for further research into the computational aspect of treating such large-scale problems, as well as for research that will allow for expansion of the scope of the present technology, which is limited to rather simple design situations.
Reference books: E74, E215, E227, F27