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Space structure configurations are elegant and impressive but, unless
one is equipped with suitable conceptual tools, they are rather
difficult to generate. The emerging branch of geometry which is called
'formex configuration processing' provides the conceptual tools that are
needed for convenient handling of space structure configurations. The
concepts of formex configuration processing allow innovative structural
engineers and architects to make full use of their creative power in
evolving imaginative as well as economical space structure forms.
In the context of formex configuration processing, the term
'configuration' is used to mean an 'arrangement of parts'. The assembly
of all the elements of a structure, for instance, is a configuration.
The most common usage of the term configuration is in reference to a
geometric composition consisting of points and/or lines and/or surfaces.
A configuration may be described using a numerical model (that is, an
arrangement of numbers). In particular, the internal computer
representation of a configuration is bound to be in terms of a numerical
model. The term 'configuration processing' is used to mean the
'creation and manipulation of numerical models that represent
configurations'. In particular, the term 'formex configuration
processing' is used to mean configuration processing with the aid of the
concepts of 'formex algebra'. Formex algebra is a mathematical system
that provides simple and elegant conceptual tools for the representation
and processing of configurations. The basic ideas from which formex
algebra has emerged were evolved in the early seventies  and the
first textbook on the subject appeared in 1984 . A concise
description of the current state of the concepts of formex algebra is
given in Ref. 9. A convenient medium for using the concepts of formex
configuration processing is the programming language 'Formian' . The
use of this programming language is illustrated through an example.
Consider the dome configurations of Figs 7b to 7h. Domes of this kind
are referred to as 'scallop domes' and are obtained by 'arching' the
segments of a normal dome in various ways . Now, suppose that one
wants to produce a scallop dome from the basic diamatic pattern of
Fig.7a. A convenient way of approaching the problem is to write a
'formex formulation' that can generate all the possible configurations
of interest with parameters representing the varying features. Such a
formex formulation is shown in Fig. 8. The formulation describes the
disposition of the elements of the dome and the coordinates of its nodal
points using the notation of formex algebra.
A reader who is not familiar with the concepts of formex algebra needs a
time investment of a few days to learn about the ideas of formex
algebra before the implications of the formulation can be followed in
detail. However, the inclusion of the formulation of Fig. 8 at this
point is only intended to give an indication of the 'general look' of a
formex formulation. Indeed, the following discussion regarding the use
of the formulation of Fig. 8 does not depend on the understanding of the
details of the formulation. The only point that needs to be noticed,
however, is that the first line of the formulation assigns values to
four parameters a, g, m and p.
Figure 7: Examples of domes configurations represented by a generic formex formulation
In an actual design situation such as the case under consideration, one
is not always completely sure about all the required details at the
outset. It is, therefore, prudent to formulate the problem 'generically'
(that is, in terms of parameters), so that the effects of variations in
different features can be examined easily.
In the formulation of Fig. 8, parameter a (standing for 'amplitude')
represents the 'rise' of the segmental arches. The value of a for the
dome of Fig. 7b is chosen to be 1 unit of length (the radius of the dome
is 10 units of length). A variant of the dome of Fig. 7b is shown in
Fig. 7c, where the amplitude is increased from 1 to 2.
The number of segments into which the dome is to be divided for
scalloping is governed by the value of parameter g (standing for 'gauge
angle'). For the dome of Fig. 7c, the gauge angle is 60° and, therefore,
the dome has 6 arched segments (to make a full circle). For the dome of
Fig. 7d, the gauge angle is chosen to be 30° resulting in 12 arched
clear; a=0; g=60; m=1; p=0;
Figure 8: A generic formex formulation for creation of dome configuration shown in fig.7
The parameter m (standing for 'mode') determines the form of the arches.
Mode 1 corresponds to a parabolic arch form as used for the domes of
Figs 7b to 7d. Mode 2 corresponds to a sinusoidal arch form as shown in
Fig. 7e. The parameter p (standing for 'prominence') controls the
'horizontal curving' of the segments. When prominence is equal to zero
then there will be no horizontal curving. A positive prominence will
create 'outward curving' of the segments, as in Fig. 7f, and a negative
prominence will give rise to an 'inward curving', as in Fig. 7g. Fig. 7h
shows a scallop dome which is identical in every respect to the dome of
Fig. 7d except for the presence of prominence.
With the formulation of Fig. 8 working in Formian, it will be easy to
examine the various possibilities and chose the combination of
parameters that gives rise to the best solution. For viewing the
configuration that corresponds to a choice of parameters, all that is
required is to enter values for the parameters and the required
configuration will appear on the Formian screen after a few seconds. The
formulation of Fig. 8 may also be used to generate data for structural
analysis. The data can be prepared by Formian in a suitable format for
input to a structural analysis package such as ABAQUS, LUSAS or SAP.
Also, information about the configuration may be sent, through Formian,
to a graphics package such as AutoCAD or Corel for further processing.
The above example of formex configuration processing relates to a
lattice space structure. However, a similar approach may be used for
continuous space structures. In such a case, the configuration to be
formulated will be a finite element mesh that represents the continuous
 Nooshin, H. Algebraic Representation and Processing of Structural
Configurations, International Journal of Computers and Structures, June
 Nooshin, H. Formex Configuration Processing in Structural
Engineering, Elsevier Applied Science Publishers, London, 1984
(Obtainable from Chapman & Hall Publishers)
 Nooshin, H and Disney, P. Formian 2, Multi-Science Publishing Co Ltd, 1997
 Nooshin, H, Tomatsuri, H and Fujimoto, M. Scallop Domes,
Proceedings of the International Symposium on Shell and Spatial
Structures: Design, Performance and Economics, Singapore, November 1997.
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