Stresses in composite plates with riveted bars used for aircraft construction

• Autorzy: Maksymovych Marta , Dutkiewicz Maciej , Maksymovych Olesia

Identyfikatory

DOI

10.20858/sjsutst.2024.122.12

• Języki publikacji: EN

Abstrakty

EN

Summary. Reinforcement of plates with rod systems is widely used in engineering, especially in aircraft construction. For example, An-178 aircraft. Removable panels on the lower surface of the wing half, located between the rear spar and the flaps. The method of calculating stresses and deformations in composite plates reinforced with rods is developed in the work. It is assumed that the rod is elastic, attached with rivets. Rivets were considered as rigid inclusions to which unknown forces were applied. These forces were determined from the condition of compatibility of plate and rod deformations. The singular integral equations' method was used to determine stresses and strains in the plate. Integral equations were solved numerically and reduced to a system of algebraic equations. To obtain the forces and moments acting on the rivets, the equations of equilibrium of the rivets and the conditions that ensure the same displacements between the rivets in the plate and in the rods are added to these equations. Examples of calculating stresses near circular and elliptical rivets, magnitudes of forces acting on rivets depending on the rigidity of the rods are given. The reduction of the stress concentration near the elliptical hole, which is placed between two rods, was studied.

Słowa kluczowe

EN

stress concentration factors; SCF; anisotropic plates; elastic rod; rivets; rigid inclusions; stress-strain state; SSS; stress concentration

PL

współczynniki koncentracji naprężeń; SCF; anizotropowe płyty; pręt sprężysty; nit; kolumna sztywna; stan naprężenia-odkształcenia; SSS; koncentracja naprężeń

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Zeszyty Naukowe. Transport / Politechnika Śląska
• Rocznik: 2024
• Tom: z. 122
• Strony: 221--237
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Maksymovych Marta

• Faculty of Mechanical Engineering and Transport, Lviv Polytechnic National University, Stepana Bandera 12 Street, 79013 Lviv, Ukraine

• https://orcid.org/0009-0005-7967-0975

autor

Dutkiewicz Maciej

• Faculty of Civil, Environmental Engineering and Architecture, Bydgoszcz University of Science and Technology, Al. Prof. Sylwestra Kaliskiego 7, 785-796 Bydgoszcz, Poland

• https://orcid.org/0000-0001-7514-1834

autor

Maksymovych Olesia

• Faculty of Civil, Environmental Engineering and Architecture, Bydgoszcz University of Science and Technology, Al. Prof. Sylwestra Kaliskiego 7, 785-796 Bydgoszcz, Poland

• https://orcid.org/0000-0002-2892-7735

Bibliografia

• 1. Koiter Warner. 1955. "On the diffusion of load from a stiffener into a sheet". The Quarterly Journal of Mechanics and Applied Mathematics 8(2): 164-178. DOI: 10.1093/qjmam/8.2.164.
• 2. Alblas Johannes Bartholomeus. 1966. "On the diffusion of load from a stiffener into an infinite wedge-shaped plate". Applied Scientific Research, Section A 15(1): 429-439. DOI: 10.1007/bf00411576.
• 3. Muki Rokuro, Eli Sternberg. 1967. "Transfer of load from an edge-stiffener to a sheet – a reconsideration of Melan’s problem". Journal of Applied Mechanics. DOI: 10.1115/1.3607761.
• 4. Franco Annalisa, Gianni Royer-Carfagni. 2014. "Effective bond length of FRP stiffeners". International Journal of Non-Linear Mechanics 60: 46-57. DOI: 10.1016/j.ijnonlinmec.2013.12.003.
• 5. Budiansky Bernard, Wu Tai Te. 1961. "Transfer of load to a sheet from a rivet-attached stiffener". Journal of Mathematics and Physics 40(1-4): 142-162. DOI: 10.1002/sapm1961401142.
• 6. Черепанов Г.П. 1983. Механика разрушения композиционных материалов. Москва: Наука. [In Russian: Cherepanov G.P. 1983. Mechanics of destruction of composite materials. Moscow. Nauka].
• 7. Zhou Kun, Hoh, Hsin Jen, Wang Xiaowei, Keer Leon, Pang John HL, Song Byron, Wang Qi . 2013. "A review of recent works on inclusions". Mechanics of Materials 60: 144-158. DOI: 10.1016/j.mechmat.2013.01.005.
• 8. Li Peng, Xikun Zhang, Yuanyuan An, Rui Zhang, Xiaoqing Jin, Nan Hu, Leon Keer. 2020. "Analytical solution for the displacement of a polygonal inclusion with a special application to the case of linear eigenstrain". European Journal of Mechanics-A/Solids 84: 104049. DOI: 10.1016/j.euromechsol.2020.104049.
• 9. Kattis Makinos, Elli Gkouti, Paraskevas Papanikos. 2020. "The elliptic homoeoid inclusion in plane elasticity". Meccanica 55: 1509-1523. DOI: 10.1007/s11012-020-01180-8.
• 10. Mattei Ornella, Mikyoung Lim. 2021. "Explicit analytic solution for the plane elastostatic problem with a rigid inclusion of arbitrary shape subject to arbitrary far-field loadings". Journal of Elasticity 144: 81-105. DOI: 10.1007/s10659-021-09828-6.
• 11. Chen Yun Zhi. 2021. "On debonding at interface in the Eshelby’s elliptical inclusion under remote loading". Engineering Fracture Mechanics 255: 107910. DOI:https://doi.org/ 10.1016/j.engfracmech.2021.107910.
• 12. Chen Yun Zhi. 2022. "Solution for elliptic inclusion in an infinite plate with remote loading and Eshelby’s eigenstrain of polynomial type". Mathematics and Mechanics of Solids 27(7): 1153-1163. DOI: 10.1177/10812865211060070.
• 13. Wang Xiaowei, Peter Schiavone. 2022. "New solutions for an Eshelby inclusion of arbitrary shape in a plane or two jointed half‐planes". Journal of Applied Mathematics and Mechanics/ZAMM 102(1): e202100297. DOI: 10.1002/zamm.202100297.
• 14. Sánchez-Reyes González. 2020. "Implementation in MATLAB of the Iso-Geometric Boundary Elements Method for the resolution of 2D anisotropic elastostatic problems". Master’s Degree Final Project. Industrial Engineering. Continuum Mechanics and Theory of Structures. School of Engineering. Universidad de Sevilla. DOI: 10.1016/j.enganabound.2020.04.006.
• 15. Yang Ping, Xu Wang, Peter Schiavone. 2021. "An Eshelby inclusion of parabolic shape in an anisotropic elastic plane". Mechanics of Materials 155: 103733. DOI: 10.1016/j.engfracmech.2021.107910.
• 16. Samal Sneha, Ignazio Blanco. 2021. "Investigation of dispersion, interfacial adhesion of isotropic and anisotropic filler in polymer composite". Applied Sciences 11(18): 8561. DOI: 10.3390/app11188561.
• 17. Shanz Martin, Olaf Steinbach. 2007. Boundary Elements Analysis. Berlin: Springer-Verlag. 352 p. DOI: 10.1007/978-3-662-26400-3.
• 18. Yin Yin, Huiming Song, Yaoming Zhang, Chunlin Wu. 2022. The inclusion-based boundary element method. Academic Press. DOI: 10.1016/b978-0-12-819384-6.00012-7.
• 19. Beer Gernot, Christian Dünser, Eugenio Ruocco, Vincenzo Mallardo. 2020. "Efficient simulation of inclusions and reinforcement bars with the isogeometric Boundary Element method". Computer Methods in Applied Mechanics and Engineering 372: 13409. DOI: 10.1016/j.cma.2020.113409.
• 20. Ting Thomas Chi-Tsai, Wang Minzhong. 1992. "Generalized Stroh formalism for anisotropic elasticity for general boundary conditions". Acta Mechanica Sinica 8(3): 193-207.7. DOI: 10.1007/bf02489242.
• 21. Liu Wei, Ki Hong. 2014. "A Clifford algebra formulation of Navier-Cauchy equation". Procedia Engineering 79: 184-188. DOI: 10.1016/j.proeng.2014.06.329.
• 22. Maksymovych Olesia, Jerzy Jaroszewicz. 2018. "Determination of stress state of anisotropic plates with rigid inclusions based on singular integral equations". Engineering Analysis with Boundary Elements 95: 215-221. DOI: 10.1016/j.enganabound.2018.07.004.
• 23. Lekhnitskii Sergei Georgievich. 1987. Anisotropic Plates. New York London Paris Montreux Tokyo Melbourne.
• 24. Chawla Man Mohan, Ramakrishnan Radha. 1974. "Numerical evaluation of integrals of periodic functions with Cauchy and Poisson type kernels". Numer. Math 22 (4): 317-323. DOI: 10.1007/bf01406970.
• 25. Megson Thomas. 2016. Aircraft structures for engineering students. Butterworth-Heinemann. DOI: 10.1016/b978-0-08-096905-3.00073-5.
• 26. Jones Robert. 1999. Mechanics of Composite Materials. Taylor, Francis. DOI: 10.1201/9781498711067-1.
• 27. Hwu Chyanbin, Wen Yen. 1991. "Green's Function of Two-dimensianal anisotropic plates containing an Elliptic Hole". Int. J. Solids Structures 27(13): 1704-1719. DOI: 10.1016/0020-7683(91)90070-v.
• 28. Савин Г.Н. 1968. Pаспределение напряжений около oтверстий. Наукова думка, Киев. [In Russian: Savin G.N. 1968. Stress distribution around holes. Naukova Dumka, Kiev].