By G. I. N. Rozvany (eds.)
Topology optimization is a comparatively new and swiftly increasing box of structural mechanics. It bargains with one of the most tricky difficulties of mechanical sciences however it can be of substantial useful curiosity, since it can in attaining a lot larger mark downs than mere cross-section or form optimization.
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Example text
25e. The real and adjoint displacements Ua and Ua in the direction of member "a" can be calculated from the work equation: 'f' -'f'- ' 50 Ua ii. N. 3 Another Nonoptimal Layout (a, c) For the sake of eliminating any other possible optimum in this nonconvex problem, we shall also investigate the layout (a, c). r and (a) Solution with two active constraints {nonoptimal). The real internal forces virtual internal forces j: and j; for this layout are shown in Figs. 25g-i. 2 = 10 = ( _fixa)2 + )2xc)2) J210.
Nonzero member force (F) or cross-sectional area (A), but suddenly changes to infinity for A = F = 0. For a compression bar this singularity is even more severe, because the permissible stress for small cross-sectional areas (with high slenderness values) tends to zero, but it again changes to infinity at A = F = 0. One method of overcoming this problem is also shown in Fig. g. g. Rozvany and Sobieski 1992). As a result of this modification, the "narrow passage" FD in Fig. 27 widens out considerably (see the modified design space in Fig.
1, 13]). That means, we start with a set of N nodal points (or nodes) in space (dim = 3) or in the plane (dim = 2). At some of these nodes given ("external") forces apply, at some nodes support conditions are defined. Moreover, a grid of m potential bars is given where each bar connects two of the nodal points. This grid (including forces and boundary conditions) is called ground structure. The task is to find a good (optimal) truss structure that satisfies all load- and support conditions, and whose bar connections are given by a subset of bars and nodes from the given ground structure.