Topology Optimization of Structures and Composite Continua

Topology optimization of structures and composite materials is a new and rapidly expanding field of mechanics which now plays an ever-increasing role in most branches of technology, such as aerospace, mechanical, structural, civil and ma­ terials engineering, with important implications for energy production as well as building and environmental sciences. It is a truly "high-tech" field which requires advanced computer facilities and computational methods, whilst involving unusual theoretical considerations in pure mathematics. Topology optimization deals with some of the most difficult problems of mechanical sciences, but it is also of consid­ erable practical interest because it can achieve much greater savings than conven­ tional (sizing or shape) optimization. Extensive research into topology optimization is being carried out in most of the developed countries of the world. The workshop addressed the state of the art of the field, bringing together re­ searchers from a diversity of backgrounds (mathematicians, information scientists, aerospace, automotive, mechanical, structural and civil engineers) to span the full breadth and depth of the field and to outline future developments in research and avenues of cooperation between NATO and Partner countries. The program cov­ ered • theoretical (mathematical) developments, • computer algorithms, software development and computational difficulties, and • practical applications in various fields of technology. A novel feature of the workshop was that, in addition to shorter discussions after each lecture, a 30 minutes panel discussion took place in each sesssion, which made this ARW highly interactive and more informal.

Table of Contents:
I — Basic aspects of topology optimization.- Some recent results on topology optimization of periodic composites.- Problem classes, solution strategies and unified terminology of FE-based topology optimization.- Comparative study of optimizing the topology of plate-like structures via plate theory and 3-D theory of elasticity.- A formulation for optimal structural design with optimal materials.- On the influence of geometrical non-linearities in topology optimization.- II — Special techniques and problem classes in topology optimization.- Structural reanalysis for topological modifications — a unified approach.- Topological derivative and its application in optimal design of truss and beam structures for displacement, stress and buckling constraints.- Transmissible loads in the design of optimal structural topologies.- New formulation for truss topology optimization problems under buckling constraints.- III — Treatment of computational difficulties in topology optimization.- On singular topologies and related optimization algorithm.- An efficient approach for checkerboard and minimum member size control and its implementation in a commercial software.- Some intrinsic difficulties with relaxation and penalization methods in topology optimization.- Topology optimization subject to design-dependent validity of constraints.- IV — Emerging methods in topology optimization.- Evolutionary computing and structural topology optimization — a state of the art assessment.- Stress ratio type methods and conditional constraints — a critical review.- Advances in evolutionary structural optimization: 1992-2000.- V — Mathematical aspects of topology optimization.- Shape optimization with general objective functions using partial relaxation.- Equally stressed structures:two-dimensional perspective.- VI — Practical applications of topology optimization.- Practical aspects of commercial composite topology optimization software development.- Topology optimisation of the porous coating distribution in non-cemented hip prostheses.- A formulation in design for optimal energy absorption.- VII — Miscellaneous topics.- Optimal design with non-linear elastic materials.- Damage tolerant topology optimization under multiple damage configurations.- On topology aspects of optimal bi-material physically non-linear structures.- Brief contributions (Extended abstracts).- Model of functional adaptation of bone and design of composite structural elements.- On optimal design problems for unilaterally supported plates subjected to buckling.- Shape truss optimization in Java multithreaded genetic program.- Optimal design of material and topology based on an energy model.- Modelling and optimization of porous materials deformation process.- Topology optimization of plastic disks.- Optimality conditions in nonconservative stability problems.- About nonunique solutions in topology optimization.- Optimization of non-elastic plates and shells.- Optimisation of rigid-plastic and elastic-plastic beams under dynamic loading.- Percolation model of material viscous failure under pressure.- Topology design of the joint types and boundary conditions of the discretized structures by mathematical programming.