caa a22 4500 463243994 CHVBK 20180405153320.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s00158-006-0092-0 doi (NATIONALLICENCE)springer-10.1007/s00158-006-0092-0 Achtziger Wolfgang Institute of Applied Mathematics, University of Dortmund, Vogelpothsweg 87, 44221, Dortmund, Germany aut On simultaneous optimization of truss geometry and topology [Elektronische Daten] [Wolfgang Achtziger] The paper addresses the classical problem of optimal truss design where cross-sectional areas and the positions of joints are simultaneously optimized. Se-veral approaches are discussed from a general point of view. In particular, we focus on the difference between simultaneous and alternating optimization of geometry and topology. We recall a rigorously mathematical approach based on the implicit programming technique which considers the classical single load minimum compliance problem subject to a volume constraint. This approach is refined leading to three new problem formulations which can be treated by methods of Mathematical Programming. In particular, these formulations cover the effect of melting end nodes, i.e., vanishing potential bars due to changes in the geometry. In one of these new problem formulations, the objective function is a polynomial of degree three and the constraints are bilinear or just sign constraints. Because heuristics is avoided, certain optimality properties can be proven for resulting structures. The paper closes with two numerical test examples. Springer-Verlag Berlin Heidelberg, 2007 Truss optimization nationallicence Geometry optimization nationallicence Bilevel programming nationallicence Structural and Multidisciplinary Optimization Springer-Verlag 33/4-5(2007-04-01), 285-304 1615-147X 33:4-5<285 2007 33 158 https://doi.org/10.1007/s00158-006-0092-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00158-006-0092-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Achtziger Wolfgang Institute of Applied Mathematics, University of Dortmund, Vogelpothsweg 87, 44221, Dortmund, Germany aut NATIONALLICENCE 773 0- Structural and Multidisciplinary Optimization Springer-Verlag 33/4-5(2007-04-01), 285-304 1615-147X 33:4-5<285 2007 33 158 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer