Shape Optimization with General Objective Func- Tions Using Partial Relaxation
نویسنده
چکیده
The homogenization method for topology optimization in stru tural design is by now well established (see [2℄, [3℄, [7℄, [8℄, [15℄, [16℄, [17℄, [18℄ and referen es therein). However, the theory is restri ted to omplian e or eigenfrequen y optimization (in the single or multiple loadings ase). The problem is that optimal mi rostru tures are unknown for general obje tive fun tions. Of ourse, in numeri al pra ti e, many generalizations have appeared: they often rely on the use of titious materials (soalled power-law materials, see e.g. [18℄) or of sub-optimal materials (for example, obtained by homogenization of a perforated periodi ell). Working with a sub lass of mi rostru tures is alled a partial relaxation of the problem. This sub lass needs to be ri h enough in order to approximate as mu h as possible the true optimal mi rostru tures, whi h yields good numeri al properties (fast onvergen e, global minima). On the other hand it must be as expli it as possible for a good eÆ ien y. The idea of partial relaxation is not new but somehow has never been explored systemati ally. The purpose of this work is to des ribe su h a pro edure for the lass of soalled sequential laminates (of any order) whi h are delivered by an expli it formula and are optimal in a number of important ases. We des ribe the numeri al implementation of this method of partial relaxation and dis uss its appli ation on several examples. Part of this work was written up in Aubry's thesis [5℄.
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