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Optimal Grillage Layouts

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Book cover Shape and Layout Optimization of Structural Systems and Optimality Criteria Methods

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 325))

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Abstract

The theory of optimal structural layouts was discussed in Chapter 6 and its iterative applications to large systems in Chapter 7. In order to check the validity and accuracy of such numerical methods, however, it is necessary to obtain exact, analytical solutions for relatively complex layout problems. One of the most successful applications of the exact layout theory was the optimization of grillage layouts, as can be seen from the following remark by Prager: “Although the literature on Michell trusses” “(i.e. least-weight trusses)” “is quite extensive, the mathematically similar theory of grillages of least-weight was only developed during the last decade. Despite its late start, this theory advanced farther than that of optimal trusses. In fact, grillages of least-weight constitute the first class of plane structural systems for which the problem of optimal layout can be solved for almost all loadings and boundary conditions” (Prager and Rozvany, 1977b). The problem of grillage optimization can be described as follows (Fig. 58): A structural domain D, bound by two horizontal planes and some vertical surfaces, is subject to a system of vertical loads which are to be transmitted to given supports by beams of rectangular cross-section having a given depth and variable width. The beams are to be contained in the structural domain and are to take on a minimum weight (or volume). The beam system is to be designed plastically (see Chapter 2, Fig. 1).

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  1. Essen University, Essen, Germany

    G. I. N. Rozvany

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    G. I. N. Rozvany

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Rozvany, G.I.N. (1992). Optimal Grillage Layouts. 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_8

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