The term Av can be interpreted as the vector of reaction forces. The total energy J= W-E is and, as easily seen, Problem (1) is equivalent to the following system of linear equations: To check this, differentiate J with respect to v in (4). The derivative Av-f should be zero at u, thus (5), which also means that reaction forces and applied load should balance at equilibrium. Remark. One may extend the meaning of symbols in (1) or (5) in order to cover the case of a field of displacements (with an infinity of degrees of freedom). If so, in order to apply the methods described here, one should first replace the problem by a suitable approximation with a finite number of freedoms. A standard technique for this is ‘finite elements analysis', which we shall only mention. There are two problems in (5). One which is documented in thousands of references (see e.g. [6]), is to solve (5), a non-trivial task since the number of degrees of freedom may be well over 106, or more. The second, known as ‘assembly', is to compute the entries of A. It contributes a lot to the size and complexity of computer codes in structural analysis. The display of results is also a factor of complexity. These codes may be gigantic software systems, with as many as 106 instruction lines, and their design and maintenance are in some respects an industry. As this description suggests, powerful tools now exist for the computation of satellite stations (and they are effectively in use). But since they were not specifically designed for such tasks, one may suspect that relatively new problems will arise with spatial structures. One of these problems is the exploitation of the obvious repetitivity of some spatial structures in order to save on computational costs. For obvious reasons, spatial structures will be made up from many identical copies of a few number of modules. As nothing in space will oppose extensive application of such modularity principles, the number of degrees of freedom may reach millions. Taking advantage of repetitivity may thus yield much more substantial savings than in the case of ground structures. This justifies the search for new concepts. One of these, not addressed here, may be ‘homogenization' [4]. The idea is that, seen from some distance, a repetitive structure will look like a continuous medium. So one could first look for the mechnical characteristics of this equivalent medium, then make use of the finite element technique. The whole point is that such characteristics can be obtained by a computation on the ‘symmetry cell' of the structure (this cell is indicated by the dotted lines in Fig. 2(c)). By this method, one could, for the purpose of computation, replace the main part of the station (Fig. 2(a)) by a thick homogeneous plate, whose elastic coefficients would be given by the computation on the cell. As the number of degrees of freedom needed to accurately model this plate is much less than in the original structure, there is a gain. Another idea (and this is our point) is to transfer to the field of structural computations a body of methods well established in other fields of applied physics, like
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