Topological optimization of reinforced panels loaded with concentrated forces

DOI: 10.34759/trd-2021-120-07


Kyaw Y. K.*, Soliaev J. O.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



A method of topological optimization of geometry of reinforcing panels loaded with concentrated forces is proposed. The proposed method is based on the numerical solution of the deformation problem of a panel of variable thickness. The optimization parameter is the thickness of the panel defined by a fictitious density function. The objective minimized function is the total energy of deformation of the panel. As a result of solving the optimization problem, an arrangement of stiffening ribs is determined which provide, at their own minimum mass, a maximum increase in the stiffness of the structure. The advantages of the proposed method, as compared with the standard topological optimization approaches, are the reduced requirements to the computational resources and the possibility to obtain the geometry of the stiffening ribs, which can be manufactured, for example, by milling. The paper investigates the effectiveness of the approach used in comparison with variants of regular finning of panels. It is shown that for some loading variants mass efficiency of optimized structures can be more than 2-5 times higher in comparison with the best variants of regular finning. Application options for numerical calculations of both classical plate theory and revised theory taking into account the transversal shear are considered. It is established that in the considered optimization problems with the condition of minimization of total energy of deformations application of classical theory is more effective.


reinforced panels, topological optimization, concentrated loads, stiffening ribs, regular fins


  1. Weisheng Zhang, Ying Liu. et al. A Moving Morphable Component Based Topology Optimization Approach for Rib-Stiffened Structures Considering Buckling Constraints, Journal of Mechanical Design, 2018, vol. 140 (11), DOI:10.1115/1.4041052

  2. Riccardo Vescovini et al. A semi-analytical approach for the analysis of variable-stiffness panels with curvilinear stiffeners, International Journal of Solids and Structures, 2020, vol. 188-189, pp. 244-260. URL:

  3. Scott Townsend, H. Alicia Kim. A level set topology optimization method for the buckling of shell structures, Structural and Multidisciplinary Optimization, 2019, vol. 60, pp. 1783-1800. URL:

  4. J. Luo, H.C. Gea. A systematic topology optimization approach for optimal stiffener design, Structural Optimization, 1998, vol. 16, pp. 280 — 288. URL:

  5. Sameer B. Mulani, Wesley C.H. Slemp, Rakesh K. Kapania. EBF3PanelOpt: An optimization framework for curvilinear blade-stiffened panels, Thin-Walled Structures, 2013, vol. 63, pp. 13-26, URL:

  6. Y.C. Lam, S. Santhikumar. Automated rib location and optimization for plate structures, Structural and Multidisciplinary Optimization, 2003, vol. 25, pp.35—45. DOI:10.1007/s00158-002-0270-7

  7. Alexis Dugreacute;, Aurelian Vadean, Julien Chausseacute;e. Challenges of using topology optimization for the design of pressurized stiffened panels, Structural and Multidisciplinary Optimization, 2016, vol. 53, pp. 303-320. URL:

  8. Ahmad Alhajahmad, Christian Mittelstedt. Design tailoring of curvilinearly grid-stiffened variable-stiffness composite cylindrically curved panels for maximum buckling capacity, Thin-Walled Structures, 2020, vol. 157, pp. 107132. URL:

  9. X. Ding, K. Yamazaki. Stiffener layout design for plate structures by growing and branching tree model (application to vibration-proof design), Structural and Multidisciplinary Optimization, 2004, vol. 26 (1), pp. 99-110. URL:

  10. Shutian Liu, Quhao Li, Wenjiong Chen, Rui Hu, Liyong Tong. H-DGTP Heaviside-function based directional growth topology parameterization for design optimization of stiffener layout and height of thin-walled structures, Structural and Multidisciplinary Optimization, 2015, vol. 52, pp. 903-913. URL:

  11. Dachuan Liu, Peng Hao et al. On the integrated design of curvilinearly grid-stiffened panel with non-uniform distribution and variable stiffener profile, Materials amp; Design, 2020, vol. 190, pp. 108556. URL:

  12. Dan Wang, Mostafa M. Abdalla et al. Streamline stiffener path optimization (SSPO) for embedded stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures, Computer Methods in Applied Mechanics and Engineering, 2019, vol. 344, pp. 1021-1050. URL:

  13. Dan Wang, Si-Yong Yeo et al. Data-driven streamline stiffener path optimization (SSPO) for sparse stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures, Computer Methods in Applied Mechanics and Engineering, 2020, vol. 365, pp. 113001. URL:

  14. Gamache J., Vadean A., Dodane N., Achiche S. Topology Optimization for Stiffened Panels: A Ground Structure Method, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. 46th Design Automation Conference (DAC). August 17ndash;19, 2020. URL:

  15. Hemza Layachi, Yuan-ming Xu, Mohamed Amine Bennaceur. Topology Optimization and Design Guidelines of SubStiffened Panels in Aerospace Applications, MATEC Web Conf. International Conference on Mechanical, Material and Aerospace Engineering 2017, vol. 114. URL:

  16. Lizin V.T., Pyatkin V.A. Proektirovanie tonkostennykh konstruktsii (Design of thin-walled structures), Moscow, Mashinostroenie, 2003, 448 p.

  17. Dzyuba A.S., Lipin E.K. Uchenye zapiski TsAGI, 1980, vol. 11, no. 1, pp. 58-71.

  18. Dudchenko A.A., Kyong L.K., Lurrsquo;e S.A. Trudy MAI, 2012, no. 50. URL:

  19. Kusyakov A.Sh. Vestnik Permskogo universiteta. Seriya: Matematika. Mekhanika. Informatika, 2020, no. 4, pp. 29-33.

  20. Solyaev Y. et al. On a combined thermal/mechanical performance of a foam-filled sandwich panels, International Journal of Engineering Science, 2019, vol. 134, pp. 66-76. DOI:10.1016/j.ijengsci.2018.10.010

  21. Lurie S.A. et al. Design of the corrugated-core sandwich panel with external active cooling system, Composite Structures, 2018, vol. 188, pp. 278-286. DOI:10.1016/j.compstruct.2017.12.082

  22. Sun Z, Cui R., Cui T. et al. An Optimization Approach for Stiffener Layout of Composite Stiffened Panels Based on Moving Morphable Components (MMCs), Acta Mechanica Solida Sinica, 2020, vol. 33 (1), pp. 650-662. URL:

  23. Vasiliev V.V., Morozov E.V. Advanced mechanics of composite materials and structures, 2013, Elsevier, 829 p.

Download — informational site MAI

Copyright © 2000-2024 by MAI