Mizerna O.L., Grebenyuk S.M., Klymenko M.I. Determination of the stress-strain state of structures made of viscoelastic fibrous composite materials based on the stiffness matrix of a spatio-temporal finite element

Details

Parent Category: Geo-Technical Mechanics, 2021

Category: Geo-Technical Mechanics, 2021, № 157

Geoteh. meh. 2021, 157, 140-151

https://doi.org/10.15407/geotm2021.157.140

 

DETERMINATION OF THE STRESS-STRAIN STATE OF STRUCTURES MADE OF VISCOELASTIC FIBROUS COMPOSITE MATERIALS BASED ON THE STIFFNESS MATRIX OF A SPATIO-TEMPORAL FINITE ELEMENT

¹Mizerna O.L., ²Grebenyuk S.M., ²Klymenko M.I.

¹Zaporizhzhia Polytechnic National University, ²Zaporizhzhia National University

UDC 539.3

Language: Ukrainian

Abstract. Increase in spheres of composite materials application leads to the need to improve the methods of composite structures calculation, increase their efficiency and adequacy to real processes. The use of fibrous composite materials creates difficulties in determining the stress-strain state of the structure due to the different physical and mechanical properties of the material components. As a rule, a fibrous composite consists of two components: a matrix and a fiber. The matrix ensures the material monolithicity fixing the shape of the product and the relative position of the reinforcing fibers. The fibers absorb the main stresses that occur during operation, and provide rigidity and strength of the composite. The combination of the matrix and fiber properties allows creating special types of composites to be used in various equipment. The use of rubber as a matrix gives the structure viscoelastic properties, which can be seen in the deformation creeping and stress relaxation in the material, which complicates the calculation of the stress-strain state of the whole structure greatly. The paper proposes an approach that is the development of a moment scheme of finite elements in the form of the displacements method based on the Lagrange principle. Using this approach, a special space-time finite element has been developed that takes into account the viscoelastic properties of the material matrix and the fiber elastic properties. The proposed numerical approach allows obtaining a solution to the problems of viscoelasticity of composite materials mechanics in three-dimensional model. Using the applications package created on the basis of this approach, the calculation of the stress-strain state of a single-cavity pneumatic cylinder with a rubber cord shell has been done. The influence of the reinforcement scheme and rubber viscoelastic properties on the parameters of the pneumatic cylinder deformation has been analyzed. In particular, it becomes possible to adjust the structure stiffness properties by changing the orientation, type and concentration of fibers, as well as the type of matrix and other material characteristics.
Keywords: fibrous composite material, viscoelasticity, space-time finite element.

REFERENCES:

1. Korneyev, V.S. and Shalay, V.V. (2019), “Mathematical model of rubber-cord shell of rotation for pneumatic shock absorbers”, Omsk Scientific Bulletin. Series “Aircraft missile and power engineering”, vol. 3? no. 1, pp. 22-41. https://doi.org/10.25206/2588-0373-2019-3-1-22-41

2. Martynenko, V.H. and Lvov, H.I. (2016), “Numerical method for determining anisotropic viscoelastic properties of orthogonally reinforced composite material”, Bulletin of the National tech. KhPI University. Ser.: Dynamics and strength of machines, no. 46 (1218), pp. 44-51. https://doi.org/10.20998/2078-9130.2016.46.88049

3. Levin, V.A. et al. (2015), “Numerical analysis of effective mechanical properties of rubber-cord composites under finite strains”, Composite Structures, vol. 131, pp. 25-36. https://doi.org/10.1016/j.compstruct.2015.04.037

4. Svetashkov, A. et al. (2017), “The hybrid effective modules of viscoelastic composites”, Key Engineering Materials, vol. 743, pp. 217-222. https://doi.org/10.4028/www.scientific.net/KEM.743.21

5. Papanicolaou, G.C. and Zaoutsos, S.P. (2019), “Viscoelastic constitutive modeling of creep and stress relaxation in polymers and polymer matrix composites”, Creep and fatigue in polymer matrix composites, pp. 3-59. https://doi.org/10.1016/B978-0-08-102601-4.00001-1

6. Yvonnet, J. (2019), “Linear viscoelastic materials”, Computational homogenization of heterogeneous materials with finite elements. Solid mechanics and its applications, vol. 258, pp. 123-144. https://doi.org/10.1007/978-3-030-18383-7_7

7. Kupriyanov, N.A., Simankin, F.A. and Manabaev, K.K. (2016), “New effective moduli of isotropic viscoelastic composites. Part II. Comparison of approximate calculation with the analytical solution”, IOP Conf. Series: Materials Science and Engineering, International Conference on Mechanical Engineering, Automation and Control Systems, Tomsk, Russia, 1-4 December 2015, vol. 124, pp. 1-6. https://doi.org/10.1088/1757-899X/124/1/012100

8. Kirichevskiy, V.V. and Sakharov, A.S. (1992), Nelineynyye zadachi termomekhaniki konstruktsiy iz slaboszhimayemykh elastomerov [Nonlinear problems of thermomechanics of structures made of weakly compressible elastomers], Naukova dumka, Kiev, Ukraine.

9. Kirichevskiy, V.V. (2002), Metod konechnykh elementov v mekhanike elastomerov [Finite element method in elastomer mechanics], Naukova dumka, Kiev, Ukraine.

10. Onufriyenko, A.V. (2018), Vibration isolation of machine aggregates using sleeve stretch dampers, Ph.D. Thesis, Dynamics, strength of machines, devices and equipment, Omsk, Russia.

About the authors:

Mizerna Olena Leonidivna, Senior Lecturer of the Department of Applied Mathematics, Zaporizhzhya Polytechnic National University, Zaporizhzhya, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Grebenyuk Serhii Mykolaiovych, Doctor of Technical Sciences (D. Sc.), Head of the Department of Fundamental Mathematics in Zaporizhzhya National University, Zaporizhzhya, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Klymenko Mykhailo Ivanovych, Associate Professor of the Department of Fundamental Mathematics, Zaporizhzhya National University, Zaporizhzhya, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

• < Prev
• Next >