trusses, etc. Let Ae be the stiffness matrix of element e, and E the set of elements. One has if one assumes that all Ae are extended by zero entries in order to be of the same size as A. So assembly is just computing the sum in (12) from a description of the elements. In order for a structure to be symmetric, not only the nodes but also the elements should correspond by the symmetry operations. More precisely, if a beam-element e of stiffness Ae links nodes i and j and if a symmetry g transforms i and j into g{i) and g{j}, a beam of the same rigidity should link g(i) and g(j). A way to use symmetry could be to assemble the whole structure first, then to take advantage of symmetry. This seems to be how the method is conceived by the Swiss school [10]. This is not optimal, since the costly assembly of A is done in vain: only the stiffness of the symmetry cell should be necessary. So one would prefer to perform a partial assembly. But what about elements (like the beams in the symmetry plane of Fig. 3) which are not entirely in the symmetry cell, but overlap on the symmetrical images of the cell? Should they be treated like other elements (unlikely), or counted several times, or be attributed a fraction of their actual stiffness? The difficulty has been perceived [13], but could not be solved without a bit of group theory. The solution to this problem is as follows [2]. Let Ge be the ‘small group' of element e, i.e. the subgroup of G made of all transformations g such that g(e) = e, and let ie be its ‘index': i€=(order of G)/(order of Ge). (13) This index is an integer (‘Lagrange theorem', [1]). Now the rule is: All elements which encounter the symmetry cell should be considered in the assembly process, but their stiffness matrix should be multiplied by the weighting factor ie. and this factor is one only for the elements which lie entirely in the cell. 3. Some Difficulties If one wants to apply the previous notions to the computation of space structures, there is an obvious difficulty: such structures (cf. Fig. 2) are ‘almost' symmetrical, they do have a lot of repetitivity, but they are not truly symmetrical in the very precise definition of the word - there is no equivariance with respect to a group. It is true that a translation of the structure of Fig. 2(a) by the length of a module will give a structure which is almost identical, but the previous theory does not account for ‘almost': it assumes exact invariance. The existence of the antenna, on the other hand, is also an alteration of symmetry, which is not allowed by the theory. So, in presence of repetitivity (but no true symmetry) and/or of slight departures from symmetry, what to do? Can ‘near-symmetry' be exploited? We shall proceed in two steps. First, forget about the antenna and try to make something out of repetitivity. Next, find a method to hook back the antenna. 3.1 Equivariant Imbedding We shall consider the example (Fig. 5) of a plane structure, with repetitivity, made up
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