By George I. N. Rozvany
`This booklet can certainly be suggested to all people who are prepared to immerse themselves in a single of an important components of structural optimization,`
H. Eschenauer, ZFW Köln,1990
`Das Buch kann in jedem Fall all denen empfohlen werden, die bereit sind, sich eines der wichtigen Gebiete der Strukturoptimierung einzuarbeiten.'
Zeitschrift für Flug und Weltraumforschung, 14:1/2, 1990
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Additional resources for Structural Design via Optimality Criteria: The Prager Approach to Structural Optimization
L~ (c) (f) Fig. 3 Optimal plastic design. be calculated by the method illustrated on a rectangular cross-section in Fig. 3g. a. in Fig. 3g) which is normal to the plane of the bending moment and divides the cross-section into two areas of equal magnitude. For sections having an axis of symmetry normal to the plane of the moment, such an axis becomes the neutral axis (Fig. 3g). Next we determine the lever arm between the centroids of the part cross-sections above and below the neutral axis (d/2 in Fig.
We can see, therefore, that the static-kinematic method has shown relatively easily that only layouts (a) and (c) can be optimal. In addition, it supplied the optimal value of PB for layout (c) and the range of validity of both types of optimal layouts in terms of a, l, k, Land P. Note: In the above problem, the system of potential members ("structural universe") consisted of two members only. As will be seen in Chapter Eight this method for eliminating non-optimal members from the solution is particularly efficient when the structural universe consists of a very large (or infinite) number of potential members.
At a simple end support S3' we have M = u = 0 and at an end 8 4 with a vertical guide (allowing vertical translation but no rotation), the end conditions become M' = u' = O. The latter two examples represent partly static, partly kinematic constraints. 1, loads and stresses that satisfy static continuity (equilibrium) conditions and static constraints (static boundary conditions) are said to be statically admissible and are denoted by (pS, QS), while kinematically admissible displacements and strains (UK, qK) satisfy kinematic continuity (compatibility) conditions and kinematic constraints (kinematic boundary conditions).