Читать книгу Metaheuristics for Structural Design and Analysis - Yusuf Cengiz Toklu - Страница 15

In the beginning, the design of all types of edifices was being carried out without any form of analysis since structural calculations were not available by any means. Due to the field iterations mentioned in the above sections, some empirical rules were being brought forward, which were, mostly geometric (Cowan 1977). An example of these rules is the one about vaults (see Figure 1.4) noted by Leonardo de Vinci (1452–1519). This stated that the chords connecting the top of the structure to the extreme points at the bottom should not cross the inner arch, in order to prevent failure (Benvenuto 1990, p. 9).

Figure 1.4. Empirical rule on vaults: lines ab and bc will remain within the wall

Empirical rules were in use until the 18th century. As time went on, structural computations began to come onto the scene. One of the starting points of this trend, advanced by Robert Hooke (1635–1703), was the rule “ut tensio, sic vis”, “extension is directly proportional to force”, which was the starting point of the theory of elasticity. We can assume that iterations of structures have begun, first in terms of dimensions, second in terms of shapes, with the introduction and advent of structural computations. But since the structural theory was only at a primitive level, and computational tools were not available, the iterations were very naïve at the beginning. A method known as the cross method, advanced in 1930 by Hardy Cross (1885–1959), which is technically known as the “moment distribution method”, became a very important tool for engineers in structural computations (Cross 1930; Eaton 2001). The introduction of computers in 1960 enabled designers to do their computations in a much more efficient way. Finally, the FEMinization, defined above, being advanced towards the end of that decade (Felippa 2001), enabled engineers to analyze all types of structures in a very efficient way, eliminating the fear of a higher number of unknowns and of complex structures.

With these appropriate tools and theory, engineers started to make efficient iterations in designing structures, since it was now possible to repeat analyses easily by changing the dimensions of the members and even their placements.