Abstract
The aim of this lecture is to discuss some fundamental aspects of continuum-based optimality criteria (COC) methods. As mentioned in the opening lecture, the above criteria are usually derived by variational or control-theoretic methods. However, Prager usually based his proofs (e.g. Prager, 1974; Prager and Rozvany, 1977a) on known energy theorems of structural mechanics. Some of these optimality criteria are then reinterpreted as equilibrium, compatibility and generalized strain-stress relations for a fictitious system called adjoint structure. This mathematical device has two advantages: first, engineers can visualize such quantities as bending moments and deflections more easily than abstract mathematical entities; second, the analysis of the adjoint structure can be carried out after discretization by using existing numerical algorithms and programs (e.g. FE software).
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Rozvany, G.I.N. (1992). Continuum-Based Optimality Criteria (COC) Methods — An Introduction. In: Rozvany, G.I.N. (eds) Shape and Layout Optimization of Structural Systems and Optimality Criteria Methods. International Centre for Mechanical Sciences, vol 325. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2788-9_2
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