caa a22 4500 463243676 CHVBK 20180405153319.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s00158-007-0117-3 doi (NATIONALLICENCE)springer-10.1007/s00158-007-0117-3 On the maximization of the fundamental eigenvalue in topology optimization [Elektronische Daten] [Wolfgang Achtziger, Michal Kočvara] The paper considers a classic formulation of the topology optimization problem of discrete or discretized structures. The objective function to be maximized is the smallest natural frequency of the structure. We develop non-heuristic mathematical models paying special attention to the situation when some design variables take zero values. These models take into account multiple load conditions, equilibrium of forces, constraints on compliance and volume, and the effect of possible non-structural mass. We discuss serious obstacles for a successful numerical treatment of this formulation such as non-Lipschitzean behavior and even discontinuity of the objective function. As a cure, we present an equivalent reformulation as a bilinear semidefinite programming problem without the pitfalls of the original problem. An algorithm is presented for finding an approximation of a globally optimal solution up to a user-defined accuracy. The key ingredient of this algorithm is the treatment of a sequence of linear semidefinite programs. Numerical examples are provided for truss structures. Examples of both academic and larger size illustrate the theoretical results achieved and demonstrate the practical use of this approach. We conclude with an extension on multiple non-structural mass conditions. Springer-Verlag Berlin Heidelberg, 2007 Topology optimization nationallicence Vibration of structures nationallicence Optimization of eigenvalues nationallicence Non-linear semidefinite programming nationallicence Achtziger Wolfgang Institute of Applied Mathematics, University of Dortmund, Vogelpothsweg 87, 44221, Dortmund, Germany aut Kočvara Michal School of Mathematics, The University of Birmingham, Edgbaston, B15 2TT, Birmingham, United Kingdom aut Structural and Multidisciplinary Optimization Springer-Verlag 34/3(2007-09-01), 181-195 1615-147X 34:3<181 2007 34 158 https://doi.org/10.1007/s00158-007-0117-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00158-007-0117-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Achtziger Wolfgang Institute of Applied Mathematics, University of Dortmund, Vogelpothsweg 87, 44221, Dortmund, Germany aut NATIONALLICENCE 700 1- Kočvara Michal School of Mathematics, The University of Birmingham, Edgbaston, B15 2TT, Birmingham, United Kingdom aut NATIONALLICENCE 773 0- Structural and Multidisciplinary Optimization Springer-Verlag 34/3(2007-09-01), 181-195 1615-147X 34:3<181 2007 34 158 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer