Abstract
The present research deals with extending the repertoire of shapes and forms for space structures using computer aided techniques. A major part of the research concerns the introduction of certain composite transformations. These are termed "paragenic transformations" which combine the effects of cylindrical and spherical transformations to create families of new shapes. It is shown that surfaces obtained from paragenic transformations may be used for a variety of structural forms such as grids, vaults, domes, cable nets, membranes and shell surfaces. Another important area covered by the present research is concerned with pattern generation. For this purpose, the concept of a "protomorph" is introduced. A protomorph acts as an underlying pattern which can be used as a starting point to create a continuum of patterns. The patterns studied represent cable, bar or beam elements or finite elements for modelling of plate, shell or membrane structures. The research aims at developing a methodology for generating and manipulating space structure forms. The material in the Thesis is presented as follows: Chapter One contains a brief examination of some notable space structures built world-wide. Chapter Two describes the basic concepts of "formex algebra", a mathematical tool which is ideally suited for the purpose of representing and manipulating forms. Formex algebra is used in conjunction with the programming language Formian which is described in the second part of Chapter Two. A strategy for pattern generation is presented in Chapter Three. Examples in the study include patterns for single layer, double layer and multilayer space structures. Paragenic transformations are introduced in Chapter Four with the help of a number of examples. This part of the study is a major contribution towards expanding the repertoire of available shapes and forms for different classes of space structures. Chapter Five presents the conclusions of the work together with some ideas for future research.