Topology optimization for harmonic vibration problems using a density-weighted norm objective function
- PDF / 4,861,009 Bytes
- 27 Pages / 595.224 x 790.955 pts Page_size
- 89 Downloads / 199 Views
RESEARCH PAPER
Topology optimization for harmonic vibration problems using a density-weighted norm objective function Diego Schmitt Montero1 · Olavo M. Silva2 · Eduardo Lenz Cardoso1 Received: 18 December 2019 / Revised: 4 June 2020 / Accepted: 16 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The optimized design of structures subjected to harmonic excitation is of great interest, for both the suppression of the oscillatory response (minimization) and the design of resonant structures (maximization). This work proposes an objective function which can be used for both goals, can properly locate resonance even for large damping ratios, and can be tuned to avoid the presence of non-physical modes in regions with void or intermediate relative densities. The properties of the proposed formulation are shown using a traditional benchmark case and the formulation is compared with other two formulations presented in the literature: dynamic compliance and active power. The results show that the proposed formulation is simple to use, leading to well-defined topologies with extreme harmonic behavior, although not solving the well-known problem of discontinuous topologies. Keywords Topology optimization · Harmonic vibration · Resonance · Suppression · Norm
1 Introduction This work discusses the topology optimization of continuum structures subjected to harmonic loading with known and constant frequency, where the objective is either to minimize or to maximize some measure associated with the structural response. When a minimization of the response is desired, the purpose is usually to avoid a design with resonant frequencies close to the excitation frequency. Cases where maximizing the harmonic response is of interest are seldom, but a niche for this type of design is gradually emerging with developments in the field of energy harvesting, where strains, displacements, or relative movement of a mechanical device is transformed into electrical energy.
Responsible Editor: W. H. Zhang Eduardo Lenz Cardoso
[email protected] 1
Department of Mechanical Engineering, Santa Catarina State University, Joinville, SC, Brazil
2
Mechanical Engineering Department, Universidade Federal de Santa Catarina, Florian´opolis, SC, Brazil
The initial works in this topic refers to the maximization of the first eigenvalue of a structure (D´ıaaz and Kikuchi 1992; Krog and Olhoff 1999; Pedersen 2000), and also the maximization of a gap between adjacent modes in the response spectrum (Bendsøe and Olhoff 1985; Olhoff and Du 2009). The approaches that directly apply a modal analysis usually need great care with the control and tracking of the vibration modes of the structure during optimization, due to the presence of repeated eigenvalues (Haug and Choi 1982; Seyranian et al. 1994; Thore 2016). In this regard, it is possible to use directional derivatives (Haug and Choi 1982) or rely on alternative solution schemes, like nonsmooth optimization (Zhou et al. 2017) or semi-definited programming (Ohsaki et al. 1
Data Loading...
