Abstract
For a structural system composed of functional components in a vibration environment, it is of great importance to suppress the dynamic war** deformation of these local regions to ensure the performance and functionality of the system. Especially for a vibrating structure under a resonance response with critical deformations, such dynamic shape preserving design (SPD) problem is addressed to maintain local performances using topology optimization in this paper. The structure is assumed to be linear and elastic, with Rayleigh dam**, and subjected to a time-harmonic external excitation with a resonant frequency. The elastic work describing the maximum strain energy in a vibration period is defined to quantitatively measure the extreme war** deformation of local functional components. A normalized constraint on local elastic work is further introduced into a dynamical topology optimization model while maximizing the first-order eigenfrequency. Moreover, to preserve the outlines of void regions (e.g., openings), a dynamic artificial weak element (AWEdyn) technique is proposed to help measure and suppress the local deformation of voids. Numerical tests show that the dynamic elastic work could accurately describe the deformations of resonance structures. The effects of shape preservation are successfully achieved through topology optimization by suppressing war** deformations in subdomains.
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Acknowledgements
This work is supported by Key Project of NSFC (51790171, 51761145111, 51735005) and NSFC (11725211).
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The topology optimization procedure was developed on a Python platform, using the MMA algorithm. The FEM problem is also solved in Python. Other finite element solvers can be alternatively used to carry out the shape preserving design proposed in this paper. The open-source MMA optimization algorithm accomplished by Professor Krister Svanberg from KTH Royal Institute of Technology is recommended. Fortran and MATLAB versions are available. We have verified the finite element results and functional sensitivities of a simple structure with other commercial finite element software and the Fortran version MMA, and the same results were obtained. We are confident that sufficient details on methodology and implementation are contained in this paper, and readers who have difficulties and questions to replicate the results are welcome to contact the authors.
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Wang, YL., Zhu, JH., Li, Y. et al. Shape preserving design with topology optimization for structures under harmonic resonance responses. Struct Multidisc Optim 65, 145 (2022). https://doi.org/10.1007/s00158-022-03218-9
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DOI: https://doi.org/10.1007/s00158-022-03218-9