Download Topology Optimization in Structural Mechanics by G. I. N. Rozvany (eds.) PDF

By G. I. N. Rozvany (eds.)

Topology optimization is a comparatively new and swiftly increasing box of structural mechanics. It offers with essentially the most tough difficulties of mechanical sciences however it can be of substantial functional curiosity, since it can in attaining a lot larger discount rates than mere cross-section or form optimization.

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0) and they become invalid if a member vanishes (A = 0) in the optimal solution. This discontinuity in the design procedure was first pointed out by Sved and Ginos (1968). It was first stated by Cheng and Jiang (1992) that for such problems the feasible set is not disjoint, but the optimal solution is connected to the rest of the feasible set by a line segment. This can be shown on a simple example, which was introduced by Kirsch (1990) and is reproduced in Fig. 26. The feasible set for this problem consists of the shaded area BCD E and of the line segment F D, the optimal solution being at F.

TOPOLOGY OPTIMIZATION OF DISCRETE STRUCTURES AN INTRODUCTION IN VIEW OF COMPUTATIONAL AND NONSMOOTH ASPECTS W. Achtziger University of Erlangen-Nuremberg, Erlangen, Germany Abstract We discuss standard problems of topology optimization of discrete structures. This paper is an attempt to provide an (almost) self-contained introduction and stresses the techniques of reformulating problems and mathematical tools needed for a successful numerical treatment. First, relations between several classical formulations of single load problems are shown in order to illustrate the mathematical techniques used, such as minimax- Theorems, duality etc.

From an engineering point of view, it is more practical to aim at solutions with only solid and empty elements at the macro-level (SE topologies). (a) Discretized SE topologies {0-1 type problem). It has been demonstrated by the author and his associates that for SE topologies a powerful method is the combination of the discretized continuum-type optimality criteria (DCOC) method and solid isotropic microstructures with penalty (SIMP} for intermediate densities. Compelling evidence of the effectiveness of this approach was given in Figs.

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