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A strategy based on the strain‐to‐kinetic energy ratio to ensure stability and convergence in topology optimization of globally resonating one‐material structures
Author(s) -
Silva Olavo M.,
Neves Miguel M.
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6374
Subject(s) - topology optimization , convergence (economics) , topology (electrical circuits) , maximization , harmonic , resonance (particle physics) , power (physics) , control theory (sociology) , constraint (computer aided design) , mathematical optimization , process (computing) , mathematics , stability (learning theory) , vibration , computer science , physics , engineering , geometry , finite element method , acoustics , structural engineering , control (management) , particle physics , combinatorics , quantum mechanics , artificial intelligence , machine learning , economics , economic growth , operating system
Summary The authors propose a new formulation of SIMP‐based topology optimization problems aiming to obtain resonating one‐material structures through a stable maximization process. The new formulation is capable of achieving globally resonant lightly damped “0‐1” structures for frequencies close to those of interest. The proposed strategy successfully deals with known issues like design “degeneration” and instability of the gradient‐based optimization process around the resonance frequency (which is a local maximum when maximizing vibration responses) at which harmonic excitation forces shall be applied. In this work, the authors use the concept of complex input power to overcome the mentioned issues. It is proposed a topology optimization procedure where a weighted sum between the active input power (real part of the complex input power) and the static compliance is minimized with a constraint on the reactive input power (imaginary part of the complex input power), which is converted to a ratio between the time‐averaged potential and kinetic energies of the system named quotient R . By this way, it is possible to ensure viability to the procedure by preventing the resonance frequency from reaching exactly the excitation frequency throughout the process, which otherwise causes difficulties on convergence. The process achieves resonance frequencies very close to given values of interest by keeping the “side” of R <1 or R >1. Several examples are presented to illustrate the potential of the proposed method.