Lagache, J.-M., (1980), ‘A geometrical procedure to design trusses in a given area,’ Eng. and Mróz, Z., (1969), ‘Optimal design of solid plates,’ Int. and Strang, G., (1986), ‘Optimal design and relaxation of variational problems,’ I, II and III, Comm Pure Appl. and Strang, G., (1983), ‘Optimal design for torsional rigidity,’ in Atluri, Gallagher et al., (Eds.), Hybrid and mixed finite element methods,(Proc. held in Southampton, UK, June 1989 ), pp. Hernandez (Eds.), Computer aided optimum design of structures: Recent advances, (Proc. Kirsch, U., (1989), ‘On the relationship between optimal structural topologies and geometries,’ in C. Hillerborg, A., (1956), ‘Theory of equilibrium for reinforced concrete slabs’ (in Swedish), Betong, 41 4, 171–182. N., (1985), ‘Prager’s layout theory: A nonnumeric computer method for generating optimal structural configurations and weight-influence surfaces,’ Comp. S., (1974), ‘Michell framework for uniform load between fixed supports,’ Eng. S., (1973), Optimum structures, Clarendon, Oxford. and Olhoff, N., (1981), ‘An investigation concerning optimal design of solid elastic plates,’ Int. Y., (1975), ‘Symmetric plane frameworks of least weight,’ In Sawczuk and Mróz (Eds.), Optimization in structural design, (Proc. P., (1989), ‘Optimal shape design as a material distribution problem,’ Struct. This process is experimental and the keywords may be updated as the learning algorithm improves.īends0e, M. These keywords were added by machine and not by the authors. In comparing the results of iterative approximate and exact layout optimization on particular examples, a 12 digit agreement is found. Applications of advanced layout theory include ‘generalized’ plates (plates with a dense system of ribs) as well as perforated and composite systems. trusses, grillages and cable nets) are considered, in which the effect of intersections on cost, stiffness and strength are neglected. Both ‘classical’ and ‘advanced’ layout theories are discussed: in the former, low density systems (e.g. This theory is based on the concepts of continuum-based optimality criteria (COC) and the ‘structural universe’ which is the union of all potential or ‘candidate’ members. (a) iterative continuum-based optimality criteria (COC) methods for approximate layout optimization of large systems with a given grid of potential members and (b) the ‘layout theory’ developed by Prager and the first author for the exact optimization of the structural topology. After reviewing some fundamental aspects of layout optimization, the lecture covers in detail two important techniques, viz.
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