Identification of the elastic characteristics of a composite material based on the results of tests for the stability of panels made from it
R.A. Kayumov a, b∗, B.F. Tazyukov c∗∗, I.Z. Muhamedova a∗∗∗, F.R. Shakirzyanov a∗∗∗∗
a Kazan State University of Architecture and Engineering, Kazan, 420043 Russia
b A.N. Tupolev Kazan National Research Technical University, Kazan, 420111 Russia
c Kazan Federal University, Kazan, 420008 Russia
E-mail: ∗kayumov@rambler.ru, ∗∗bulat.tazioukov@kpfu.ru, ∗∗∗muhamedova-inzilija@mail.ru, ∗∗∗∗faritbox@mail.ru
Received November 28, 2018
DOI: 10.26907/2541-7746.2019.1.75-85
For citation: Kayumov R.A., Tazyukov B.F., Muhamedova I.Z., Shakirzyanov F.R. Identification of the elastic characteristics of a composite material based on the results of tests for the stability of panels made from it. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 1, pp. 75–85. doi: 10.26907/2541-7746.2019.1.75-85. (In Russian)
Abstract
The problem of identifying the mechanical characteristics of a fibrous compo site material (FCM), from which cylindrical panels or pre-curved plates are made by superposition at an angle to the edge, has been considered. The problem has been solved using the analysis of the results of the tests of structures with bringing them to the loss of bearing capacity due to loss of stability.
The advantage of the proposed approach is no necessity to measure the deformation or movement of these structural elements during experiments (this does not require the presence of complex measuring devices, their calibration, long-term debugging of the experimental techniques). Only the critical values of the load, which can be tested in a short period of time, must be determined. In addition, such tests are not destructive under loading, which enables the repeated use of the sample under different types of load and conditions of fixing. The identification technique is based on minimizing the quadratic discrepancy between the results of solving direct problems of stability and the results of experiments. By introducing the discrepancy of possible errors in experimental data measurement, an extended formulation of the problem has been obtained. Numerical solutions of the model problems show that the solution of the problem is stable to variations of the original data. The proposed approach allows to obtain the calculated mechanical characteristics of the composite material close to true even in the case of a considerable variation in the stiffness characteristics of the composite material from sample to sample and errors in determining the critical load.
Keywords: fiber composite, identification method, minimization, stability, critical load, stiffness characteristics, numerical experiment
Acknowledgments. The study was performed as part of the state assignment of the Ministry of Science and Higher Education of the Russian Federation no. 9.5762.2017/VU (project no. 9.1395.2017/PCh) and supported by the Russian Foundation for Basic Research (project no. 19-08-00349) and the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (project no. 1.12878.2018/12.1.).
References
1. Vol'mir A.S. Ustoichivost' deformiruemykh sistem [Stability of Deformable Systems]. Moscow, Nauka, 1967. 984 p. (In Russian)
2. Kayumov R.A. The extended problem of identification of mechanical characteristics of materials based on the results of testing of constructions. Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, 2004, no. 2, pp. 94–105. (In Russian)
3. Teregulov I.G., Kayumov R.A., Safiullin D.Kh. Modeling the operation of shells from a nonlinearly viscoelastic composite material. Tr. Mezhdunar. konf. po teorii obolochek i plastin [Proc. Int. Conf. on the Theory of Shells and Plates]. Nizhny Novgorod, 1994, vol. 3, pp. 227–235. (In Russian)
4. Alekseev K.P., Kayumov R.A., Mukhamedova I.Z., Teregulov I.G. Experimental study of the creep of composite materials on tubular Plexiglas samples. Mekh. Kompoz. Mater. Konstr., 2004, vol. 10, no. 2, pp. 199–210. (In Russian)
5. Giannadakis K., Mannberg P., Joffe R., Varna J. The sources of inelastic behavior of Glass Fibre/Vinylester non-crimp fabric [
45]s laminates. J. Reinf. Plast. Compos., 2011, vol. 30, no. 12, pp. 1015–1028. doi: 10.1177/0731684411412644.
6. Paimushin V.N., Firsov V.A., Gyunal I., Egorov A.G., Kayumov R.A. Theoretical-experimental method for determining the parameters of damping based on the study of damped flexural vibrations of test specimens. 3. Identification of the characteristics of internal damping. Mech. Compos. Mater., 2014, vol. 50, no. 5, pp. 633–646. doi: 10.1007/s11029-014-9451-x.
7. Diveyev B., Butiter I., Shcherbina N. Identifying the elastic moduli of composite plates by using high-order theories. 2. Theoretical-experimental approach. Mech. Compos. Mater., 2008, vol. 44, no. 2, pp. 139–144. doi: 10.1007/s11029-008-9003-3.
8. Kayumov R.A., Tazyukov B.F. Stability of bent thin elastic plate loaded by transverse force. Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., 2001, no. 4, pp. 12–15. (In Russian)
9. Kayumov R.A., Nezhdanov R.O., Tazyukov B.F. Opredelenie kharakteristik voloknistykh kompozitnykh materialov metodami identifikatsii [Determination of Fiber Composite Material Characteristics by the Identification Methods]. Kazan, Izd. Kazan. Univ., 2005. 258 p. (In Russian)
10. Vasil'ev V.V. Mekhanika konstruktsii iz kompozitsionnykh materialov [Mechanics of Composite Structures]. Moscow, Mashinostroenie, 1998. 269 p. (In Russian)
11. Nordin L.O., CityplaceVarna J. Methodology for parameter identification in nonlinear viscoelastic material model. Mech. Time-Depend. Mater., 2005, vol. 9, no. 4, pp. 57–78. doi: 10.1007/s11043-005-9000-z.
12. Kayumov R.A., Muhamedova I.Z., Tazyukov B.F. Parameter determination of hereditary models of deformation of composite materials based on identification method. J. Phys.: Conf. Ser., 2018, vol. 973, art. 012006, pp. 1–8. doi: 10.1088/1742-6596/973/1/012006.
13. Kayumov R.A., Teregulov I.G. Structure of the constitutive relations for hereditarily elastic materials reinforced by hard fibers. J. Appl. Mech. Tech. Phys., 2005, vol. 46, no. 3, pp. 405–411. doi: 10.1007/s10808-005-0090-9.
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