Fig. 2. A typical problem. In this slightly idealized design for a space power station, many copies of a few basic moduli would be put together to build the solar-cells array. At one end, an orientable parabolic antenna sends microwaves to the ground. The overall size is a few miles. The zoom (in (b)) shows how the basic elements are put together. Note that some of them may be shared by several cells (the ‘symmetry cell' is shown as a box, in dotted lines). The numbers in (d) refer to the ‘indices' of the elements (see text). The numbers displayed are not the indices themselves, but the orders of the ‘small groups' of the elements. The original big structural problem is replaced by a family of independent simple structural problems relative to the elementary structure shown in (c). crystallography or solid physics. We have in mind the theory of group representation, as developed in particular by Wigner [12] to suit the needs of quantum physics. Such methods prove well adapted to structural computations. They still leave something to be desired, for reasons to be seen below. But overall, the obstacles to such a transfer of methods from one domain to another seem to lie in the different backgrounds of people concerned. We have tried to address this problem in [2], to which we also refer for all technical details. 2. The Exploitation of Symmetry 2.1. Bilateral Symmetry Consider the simplest case of bilateral symmetry (Fig. 3). Let v be a displacement. Let us call Sv the displacement ‘symmetric' to v, according to the following definition: the value of Sv at node x (this value is an ordinary vector) is obtained by taking the mirror
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