Download Discrete Structural Optimization by W. Gutkowski (eds.) PDF
By W. Gutkowski (eds.)
The engineering layout of buildings and machines is composed usually find the simplest resolution between a finite variety of possible judgements. This quantity contains difficulties and resolution equipment for discrete structural optimization. particular, approximate and heuristic tools are provided using deterministic and stochastic approaches.
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Sample text
In general it depends on the method applied for continuous optimization. In the case presented in the example of next chapter the bound was taken the distance of one third of all iterations. In numerical realization of the method one may specify only finite number of elements belonging to A1. In the case of linear elastic structures these elements may be limited to the number obtained from iterations performed for three distinct constraints : + g0 - D. g0 ; g0 - D. 5. Numerical Examples. A£1 $ maxAJ· (30) Truss of minimum weight Ten bar structure given ten-bar structure shown in Fig.
45744 * 105 respectively. Final results of discrete minimum design are given in Table 3. In order to verify the proposed method the results were compared with results obtained for the case when the whole list of ten member sizes was considered. In both cases the discrete minimum weights are the same. W. Gutkowski 44 Table 2. :::. :::. 25go. 0 10 number of combinations n- 2 * 7 * 3 * 2 * 7 * 7 * 3 * 2 * 2 * 7- 3495744 Table 3. Minimum weight solution for cross section areas a ten-bar truss. pre.
26). 0 j Ar-1 < Arj < Ar~1 Fig. 26. Graph with a three structure. Under above definitions vortices with the first index fo represent all possible combinations of values of the objective function W. The number n of this combinations is equal (21) In the case when all structural members are chosen from the same catalogue containing k member sizes, the number of combinations is equal to (22) According to {20) and (iv) the extreme vortices belonging to the same layer of the graph (subgraph) represent the smallest and the largest volume from all possible volumes included in the layer (Fig.