Abstract
The ‘lattice space structure’ is one of the groups of space structures and a typical structure of this type consists of a large number of elements of different lengths. The objective of this thesis is to regularise these different element lengths, which is desirable in practice. To this end, the nodal positions of the structure are altered, such that the required geometry will be obtained. This process is referred to as the ‘traviation process’. Normally, this process involves a number of constraint conditions. To solve this non-linear optimisation problem, one of the optimisation techniques, namely the ‘genetic algorithm’, is used because this technique is robust and is found to be suitable for the geometric optimisation problem. The fundamental procedure of the genetic algorithm is first introduced and its advantages are discussed. Then, the procedure is applied to the regularisation of element lengths using a number of new concepts that are required for the operation. The effectiveness of the proposed algorithm is investigated through a number of examples and it is found that it is capable of regularising element lengths. The genetic approach established for the regularisation of element lengths is found to be suitable for generating a new structural system, ‘nexorade’. That process is described in this thesis as another application of the geometric optimisation. Although finding the geometry of nexorades is generally difficult, the proposed method, referred to as the ‘fanning process’, can achieve this objective. The results are discussed through a number of examples. The above two processes are implemented as ‘formex functions’, which make it possible to use them in conjunction with the other concepts of ‘formex algebra’. This gives rise to a large number of possibilities of generating configurations. Also, several outcomes of the research are described in this thesis such as random number generators.