TY - JOUR

T1 - Parameter and Topology Optimization of Structures in the Frequency Domain under Nevanlinna–Pick Interpolation Constraints

AU - Kara, Aliyye

AU - Eksin, Ibrahim

AU - Mugan, Ata

N1 - Publisher Copyright:
© 2024 by the authors.

PY - 2024/2

Y1 - 2024/2

N2 - The design optimization of structures can be conducted in either the time domain or the frequency domain. The frequency domain approach is advantageous compared to its time domain counterpart, especially if the degree of freedom is large, the objectives and/or constraints are formulated in the frequency domain, or the structure is subject to random loading. In this paper, an attempt is undertaken to obtain feasible optimal solutions by implementing the Nevanlinna–Pick (NP) interpolation theory across multi-objective structural optimization problems in the frequency domain. The NP equations introduce a trade-off that originates from the interpolation theory for complex variables. According to the NP theory, a complex function cannot have an independent amplitude from its derivative at a certain frequency. Consequently, the frequency response of a physical system cannot be shaped arbitrarily at discrete frequencies. Our objectives within this paper include calculating the weight, natural frequency, fatigue life, frequency domain response, and its derivative. To illustrate our claims, sample parameter and topology optimization problems were formulated and solved, both with and without the NP constraints. It was found that the inclusion of NP constraints induced a considerable improvement in the optimal solutions, while also causing the convergence to the optimal solution to become smoother.

AB - The design optimization of structures can be conducted in either the time domain or the frequency domain. The frequency domain approach is advantageous compared to its time domain counterpart, especially if the degree of freedom is large, the objectives and/or constraints are formulated in the frequency domain, or the structure is subject to random loading. In this paper, an attempt is undertaken to obtain feasible optimal solutions by implementing the Nevanlinna–Pick (NP) interpolation theory across multi-objective structural optimization problems in the frequency domain. The NP equations introduce a trade-off that originates from the interpolation theory for complex variables. According to the NP theory, a complex function cannot have an independent amplitude from its derivative at a certain frequency. Consequently, the frequency response of a physical system cannot be shaped arbitrarily at discrete frequencies. Our objectives within this paper include calculating the weight, natural frequency, fatigue life, frequency domain response, and its derivative. To illustrate our claims, sample parameter and topology optimization problems were formulated and solved, both with and without the NP constraints. It was found that the inclusion of NP constraints induced a considerable improvement in the optimal solutions, while also causing the convergence to the optimal solution to become smoother.

KW - frequency domain fatigue life

KW - multi-objective optimization

KW - optimization in the frequency domain

KW - parameter optimization

KW - structural optimization

KW - topology optimization

UR - http://www.scopus.com/inward/record.url?scp=85192495894&partnerID=8YFLogxK

U2 - 10.3390/app14031278

DO - 10.3390/app14031278

M3 - Article

AN - SCOPUS:85192495894

SN - 2076-3417

VL - 14

JO - Applied Sciences (Switzerland)

JF - Applied Sciences (Switzerland)

IS - 3

M1 - 1278

ER -