On the Exploitation of Geometrical Symmetry in Structural Computations of Space Power Stations ALAIN BOSSAVIT Summary The paper describes how to take advantage of geometrical symmetry of space structures to save on the computational cost of their mechanical characteristics. Fifty years from now, some of our energy will come from satellite power stations. Maybe this is just a dream [8]. But the design of such stations is today's reality. They are currently studied in several research institutes with today's technology and knowhow. In particular, ‘structural computations' of stations, which include the numerical prediction of some static or dynamic characteristics (vibration modes, stresses induced by solar heating or microgravity, reaction to impacts, etc.) are done with tools which have been developed and well tested in conventional, ‘ground-based' civil engineering. Such tools may not fully take into account peculiarities of spatial structures. The most striking of these peculiarities is their high degree of repetitivity. How to take advantage of this is the point of the present paper. After a short and simplified account of the principles of computational structural analysis (section 1), we describe in section 2 some methods suggested by group theory, which have been used extensively in classical physics over almost a century. Their application to our field raises specific difficulties, which are examined in section 3. The emphasis is less on the description of new methods than on ideas which may help to generate such methods. Therefore, technical details have been discarded. Some imprecision may result for such omissions, that we hope specialists will forgive. 1. Computational Structural Analysis Consider, as a typical example, an assembly of beams, jointed at some points, the ‘nodes' of the structure. The deformation resulting from an applied load may be characterized by displacements (changes in position and orientation) of all nodes with respect to some reference configuration. Let us use v as a symbol for the values of this set of parameters, which characterize the deformed state of the structure. In the case of Fig. 1, and provided all forces and thus displacements are in the vertical plane, v, would consist in 7 times 3, that is 21 real-valued parameters (7 nodes, 2 parameters to describe translations and one for rotation, for each node). One may consider v as a Alain Bossavit, Conseiller Scientifique, Service IMA, Etudes et Recherches, Electricite de France, 1, avenue du General de Gaulle, 92141 Clamart, France.
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