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Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Hongliang Liu1, Peijin Wang1, Yuan Liang2,*, Kai Long3, Dixiong Yang2
1 Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation, College of Aerospace Engineering, Shenyang Aerospace University, Shenyang, 110136, China
2 State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116023, China
3 State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206, China
* Corresponding Author: Yuan Liang. Email: yuanliangdut@dlut.edu.cn

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2023.024921

Received 13 June 2022; Accepted 15 August 2022; Published online 20 September 2022


Continuum topology optimization considering the vibration response is of great value in the engineering structure design. The aim of this study is to address the topological design optimization of harmonic excitation structures with minimum length scale control to facilitate structural manufacturing. A structural topology design based on discrete variables is proposed to avoid localized vibration modes, gray regions and fuzzy boundaries in harmonic excitation topology optimization. The topological design model and sensitivity formulation are derived. The requirement of minimum size control is transformed into a geometric constraint using the discrete variables. Consequently, thin bars, small holes, and sharp corners, which are not conducive to the manufacturing process, can be eliminated from the design results. The present optimization design can efficiently achieve a 0–1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies. Additionally, the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric, which is a distinct difference from the static optimization design. Hence, one-half of the design domain cannot be selected according to the load and support symmetry. Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization, and to improve the design manufacturability


Discrete variable topology optimization; harmonic excitation; minimum length scale control; geometric constraint; manufacturability
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