Buckling and Geometrically Nonlinear Deformation of Compact Near-Surface Delaminations in Composite Panels with an Asymmetric Anisotropic Layup

Аuthors

Mitrofanov O. V., Shkurin M. V.^*

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

*e-mail: m.shkurin@mai.ru

Abstract

The emergence of defects and damages, requiring exact evaluation of the stress-strain condition (SSS) for their non-propagation prediction, while the structures from composite materials being operated is inevitable in modern aviation industry. Particular attention is being paid to the delamination type compact rectangular subsurface defects in smooth composite skins. Unlike the traditional regular zones design, where symmetric balanced structures are employed, actual subsurface delaminations often exhibit an anisotropic (unbalanced) and asymmetric layup. Analysis of such zones requires application of complex mathematical models as bending and plane stress states are not being separated in them.
The primary objective of this study consists in obtaining an analytical solution to the problem of buckling and post-buckling (geometrically nonlinear) deformation of the compact rectangular delaminations with account for the impact of structural anisotropy and asymmetry under the action of the compressive and shear loads.
Basic relations of the composite panel generalized mathematical model are being employed as a methodological foundation. Physical equations incorporate membrane, bending, and mixed stiffnesses. A system of two nonlinear von Kármán-type differential equations for asymmetric unbalanced structures is derived based on the equilibrium and strain compatibility equations, and by the Airy stress function introduction. To solve the boundary value problem of a simply supported panel, the Bubnov-Galerkin method was applied. The deflection function is approximated as a two-term series. Analytical integration of the equations allowed reducing the initial problem to a system of the two nonlinear algebraic equations with respect to the deflection amplitudes.
As the result of the research, a closed-form analytical solution was successfully obtained. The explicit analytical relationships and governing integration coefficients were derived for the stress-strain state computing at the post-buckling stage. Besides, compact analytical formulas for determining critical compressive and shear fluxes were established.
The obtained results are of significant practical interest for damage tolerance engineering in the aerospace sector. The derived analytical relationships allow for a rapid and reliable evaluation of the defects nonlinear behavior under combined loading conditions. Furthermore, they facilitate multivariant verification computations of the stress-strain state for the subsurface delaminations. This mathematical framework enables structural engineers to quickly and accurately assess the critical necessity of repair interventions. Ultimately, the proposed approach can be seamlessly integrated into the overarching survivability methodology of modern composite aviation structures, ensuring their reliable verification and safety while rigorously accounting for their complex asymmetric structural characteristics.

Keywords:

composite panel compression; anisotropic asymmetric layup; geometrically nonlinear deformation; near-surface defects

References

1. Advisory Circular AC20-107В Composite aircraft structure. U.S. Department of Transportation Federal Aviation Administration, 08.09.2009.

2. Korolev VI. Layered anisotropic plates and shells made of reinforced plastics. Moscow: Mashinostroenie; 1965. 272 p. (In Russ.).

3. Ashkenazi EK, Ganov EV. Anisotropy of structural materials: Handbook. Leningrad: Mashinostroenie. Leningradskoe otdelenie; 1980. 247 p. (In Russ.).

4. Lehnitsky SG. Anisotropic plates. Moscow: OGIZ; 1947. 354 p. (In Russ.).

5. Vasiliev VV. Mechanics of structures made of composite materials. Moscow: Mashinostroenie; 1988. 270 p. (In Russ.).

6. Vasiliev VV, Morozov EV. Advanced mechanics of composite materials and structures. 4th ed. Elsevier; 2018. 882 p.

7. Mitrofanov OV. Applied geometrically nonlinear problems in the design and calculations of composite aircraft structures. Moscow: MAI; 2022. 164 p. (In Russ.).

8. Dudchenko AA, Elpatyevsky AN, Lurie SA, et al. Calculation of plates made of composite materials. Moscow: MAI; 1993. 68 p. (In Russ.).

9. Gavva LM, Firsanov VV. Mathematical models and methods for calculating the stress-strain state of aircraft panels from composite materials taking into account the production technology. Mechanics of Solids. 2020;55(3):403-412. (In Russ.).

10. Khayer M. Mechanics of plates made of asymmetric layered composites. In: Applied mechanics of composites. New in foreign science: A collection of articles. No. 44. Moscow: Mir; 1989. p. 143–175. (In Russ.).

11. Azikov NS. Stability and bearing capacity of plates and panels made of layered composites under compression and shear. Doctoral thesis. Moscow: MATI; 1998. 439 p. (In Russ.).

12. Adegova LA, Bobrysheva MV, Shcherbinina AE. Investigation of shell stability loss depending on the laying of composite material layers. Materialy XIII Vserossiiskoi nauchno-prakticheskoi konferentsii s mezhdunarodnym uchastiem “Rossiya molodaya” (April 20–23, 2021; Kemerovo). Kemerovo: KuzGTU; 2021. p. 627071–627077. (In Russ.).

13. Badrukhin YuI, Terekhova ES. Rational design of thin-walled load-bearing laminated composite panels under combined loading. Aerospace MAI Journal. 2023;30(4):130–139. (In Russ.). URL: https://vestnikmai.ru/eng/publications.php?ID=177614 

14. Terekhova ES. Certain design and technological features in rational design of the thin-walled load-bearing panels made of laminated composite influencing their load capacity. Engineering Journal: Science and Innovation. 2024(10). (In Russ.).

15. Terekhova ES. Rational design of panels made of laminated composite material in terms of strength and stability. PhD thesis. Novosibirsk: SibNIA named after S.A. Chaplygin; 2025. 140 p. (In Russ.).

16. Shkurin MV, Mitrofanov OV, Gavva LM. Refined mathematical model for designing anisotropic composite panels for small aircraft airframe structures while ensuring stability and strength taking into account geometrically nonlinear behavior. Materialy  IX Mezhdunarodnoi konferentsii “Problemy mekhaniki sovremennykh mashin” (July 07–13, 2025; Ulan-Ude). Ulan-Ude: ESSUTM; 2025. p. 287–298. (In Russ.).

17. Ushakov AE. Methodology for Ensuring Operational Survivability and Safety of Aircraft Structures Made of Polymer Composite Materials. Moscow: Fizmatlit; 2012. 204 p. (In Russ.).

18. Pogosyan MA, Turbin NV, Staroverov OA, Melnikova VA. Investigation of the Damage Tolerance of Aircraft Polymer Composite Structures under Conditions of Cyclic Compression after Impact. Aerospace MAI Journal. 2025;32(4):126-136. (In Russ.). URL: https://vestnikmai.ru/eng/publications.php?ID=186674

19. Mitrofanov OV, Glagovsky AA, Turbin NV, et al. Design support of tests for the operational survivability of aircraft structures from PCM. Materialy V Vserossiiskoi nauchno-prakticheskoi konferentsii “Problemy prochnosti aviatsionnykh konstruktsii i materialov” (February 25–28, 2026; Sedova Zaimka). Novosibirsk: SibNIA; 2026. p. 53–54 (In Russ.).

20. Mitrofanov O. Evaluation of the Buckling Stability and Geometrically Nonlinear Behavior of Square Composite Panels of an Unsymmetrical Structure in Shear. Mechanics of Composite Materials. 2021;57(3):301-308. DOI: 10.1007/s11029-021-09955-0 EDN RGMKWU

21. Mitrofanov OV, Shkurin MV, Dudchenko AA. Assessing geometrically nonlinear behavior of the anisotropic structure short surface defects in composite panels under compression. Engineering Journal: Science and Innovation. 2024(4). (In Russ.).