Indexed by:期刊论文

Date of Publication:2014-07-01

Journal:STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION

Included Journals:SCIE、EI、Scopus

Volume:50

Issue:1

Page Number:113-128

ISSN No.:1615-147X

Key Words:Skeletal structures; Integrated size and topology optimization; Frequency constraint; Singular optimum; Dynamic stiffness

Abstract:The present paper studies the integrated size and topology optimization of skeletal structures under natural frequency constraints. It is found that, unlike the conventional compliance-oriented topology optimization problems, the considered problem may be strongly singular in the sense that the corresponding feasible domain may be disconnected and the global optimal solutions are often located at the tips of some separated low dimensional sub-domains when the cross-sectional areas of the structural components are used as design variables. As in the case of stress-constrained topology optimization, this unpleasant behavior may prevent the gradient-based numerical optimization algorithms from finding the true optimal topologies. To overcome the difficulties posed by the strongly singular optima, some particular forms of area/moment of inertia-density interpolation schemes, which can restore the connectedness of the feasible domain, are proposed. Based on the proposed optimization model, the probability of finding the strongly singular optimum with gradient-based algorithms can be increased. Numerical examples demonstrate the effectiveness of the proposed approach.