Introduction to Structural Optimization: Course Held at the by William Prager (auth.)

By William Prager (auth.)

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Extra info for Introduction to Structural Optimization: Course Held at the Department of Mechanics of Solids, October 1974

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44) For numerical examples, the reader is referred to papers by Chern and Prager3 , Martin4 , and Chern and Martins • 3. 1. Optimal design of other elastic structures subject to compliance constraints. For ease of exposition, only beams were treated in Chapter 2, but the method by which the various optimality conditions were derived applies equally well to other elastic structures subject to compliance constraints. The following examples will illustrate this remark. (a) Sandwich member subject to axial force and bending moments.

23) ~ For examples of optimal design with frequency constraint, the reader is referred to papers by Niordson7, TurnerS, Taylor9, SheulO, McCart Haug, and Streeter 11 , Zarghamee 12 , and Karihaloo and Niordson13. (b) Design for given load factor for plastic collapse. Consider a rigid, perfectly plastic truss of given layout that is subject to a given loading. Length and cross-sectional area of the i-th bar will be denoted by ~. ~ and A. 15) is to be minimized subject to the con- straint that the load factor for plastic collapse is to have a given value A .

44b) are R = Pl7 and R = 2PI5 . 46) (P-2R)~, furnish Q = 2P~I3 for any value of R satisfying 117 5 RIP 5 215 . So far, we have regarded B as given in advance. 45), however, are readily used to determine the value of B that minimizes rl(S) . One finds that Q(S) has a minimum in each of the intervals 0 < B < 213 and 213 < B < 1 . 5% smaller than the maximal value Q assumed for S = 0, 213, and 1. P~ 2 3-li . Note that = 2P~ 2 13 , which is 50 Optimal Division into Elements of Prescribed Shape The use of a condition derived by Rozvany 35 somewhat shortens the determination of the S-value that minimizes change of the yield moment at from Y1 at = ~ Imagine the discontinuous = ~O replaced by a gradual transition ~ - E to Y2 at ~0 ~(S) ~ = ~0 + E .

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