Article

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Title

Topology optimization of the plate using neural networks

Authors

^1,2Yu.S. Selivanov, ²K.A. Matveev

Organizations

¹FAE “S. A. Chaplygin Siberian Research Institute of Aviation”
Novosibirsk, The Russian Federation
²Novosibirsk State Technical University
Novosibirsk, The Russian Federation

Abstract

At the moment, there are many methods of topological optimization that have become classic, including in the aviation industry. The main ones are the method of solid isotropic material with Penalization (SIMP), methods of unidirectional and bidirectional evolutionary optimization (Evolutionary topology optimization and Bi-directional evolutionary topology optimization – ESO/BESO) and the LevelSet method. The paper presents a mathematical formulation of the topological optimization problem as a statement of the problem at a conditional extremum. The function of the average pliability of the structure was chosen as the target function, the maximum value of the resulting volume was the limitation. The transformation of the problem statement into an unconditional extremum statement was performed, for this the method of quadratic penalties was used. The paper presents an algorithm that allows you to apply modern machine learning methods and neural networks in conjunction with classical methods of topological optimization. The algorithm is based on the reparametrization of virtual densities by neural network parameters, which are optimized. The method of adaptive moment estimation is used as an optimization algorithm directly by the parameter of the neural network. In this paper, two classical problems of topological optimization of plates in a plane-stressed state with different boundary conditions are solved, and the results are compared with the results obtained by other authors on similar problems using classical methods of topological optimization.

Keywords

topology optimization, neural networks, SIMP, BESO

References

[1] Kirsch U. Structural Optimization-Fundamentals and Applications, Springer-Verlag, Berlin. 1993.

[2] Bendsoe M. P., Sigmund O. Topology optimization: theory, methods and applications. Berlin: Springer, 2003. 370 p.

[3] Lei X., Liu C., Du Z., Zhang W. & Guo X. Machine learning driven real-time topology optimization under moving morphable component-based framework. Journal of Applied Mechanics, 2019. 86(1), 011004.

[4] Bujny M., Aulig N., Olhofer M. & Duddeck F. Learning-based topology variation in evolutionary level set topology optimization. In Proceedings of the Genetic and Evolutionary Computation Conference, 2018. pp. 825–832.

[5] Hoyer S., Sohl-Dickstein J. & Greydanus S. Neural reparameterization improves structural optimization. arXiv preprint arXiv:1909.04240. 2019.

[6] Zhang Z., Li Y., Zhou W., Chen X., Yao W. & Zhao Y. TONR: An exploration for a novel way combining neural network with topology optimization. Computer Methods in Applied Mechanics and Engineering, 2021a. 386, 114083.

[7] Deng H. & To A. C. Topology optimization based on deep representation learning (DRL) for compliance and stress-constrained design. Computational Mechanics, 2020. 66(2), 449–469.

[8] Chandrasekhar A., Suresh K. TOuNN: Topology Optimization using Neural Networks. Structural and Multidisciplinary Optimization, 2021. 63, 1135–1149.

[9] Chandrasekhar A. & Suresh K. Length scale control in topology optimization using Fourier enhanced neural networks. arXiv preprint arXiv:2109.01861. 2021.

[10] Chandrasekhar A., Suresh K. Multi-Material Topology Optimization Using Neural Networks. Computer-Aided Design, 2021. Vol 136.

[11] Haikin S. Neural networks. The full course: translated from English / S. Khaykin. 2nd edition, ispr. M.: Williams, 2018. 1103 p.

[12] Ioffe S., Szegedy C. Batch normalization: Accelerating deep network training by reducing internal covariate shift. 2015.

[13] Glorot X., Bengio Y. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, Sardinia, Italy, 13–15 May 2010. Vol. 9, pp. 249–256.

[14] Kingma D. P. and Ba J. “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980, 2014.

[15] Baydin Atilim Gunes, Pearlmutter Barak, Radul Alexey Andreyevich, Siskind Jeffrey. “Automatic differentiation in machine learning: a survey”. Journal of Machine Learning Research. 2018.18, pp. 1–43.

[16] Sigmund O., Maute K. Topology optimization approaches. A comparative review // Structural and Multidisciplinary Optimization. 2013. Vol. 48, no. 6, pp. 1031–1055.

[17] Nocedal J. and Wright S., Numerical Optimization, 2nd ed., Springer, New York, NY, 2006.

[18] Huang X., Xie Y. M. Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des. 2007. 43, pp. 1039–1049.

[19] Zhao F. Topology optimization with meshless density variable approximations and BESO method, Comput. Aided Des. 56, 2014. pp. 1–10.

[20] Avdonyushkin D. V., Matveeva A. I., Novokshenov A. D. Machine learning method in elastic plate topology optimization problems. PNRPU Mechanics Bulletin, 2023, no. 3, pp. 5–14.

For citing this article

Selivanov Yu.S., Matveev K.A. Topology optimization of the plate using neural networks // Spacecrafts & Technologies, 2024, vol. 8, no. 4, pp. 243-253.

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