Advances in Computational Design

  • 제5권3호
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  • Pages.305-321
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  • 2020
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  • 2383-8477(pISSN)
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  • 2466-0523(eISSN)
테크노프레스 (Techno-Press)
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Algorithm of solving the problem of small elastoplastic deformation of fiber composites by FEM

  • Polatov, Askhad M. (Department of Mathematics, National University of Uzbekistan) ;
  • Khaldjigitov, Abduvali A. (Samarkand branch of Tashkent University of Information Technologies) ;
  • Ikramov, Akhmat M. (Department of Mathematics, National University of Uzbekistan)
  • 투고 : 2019.03.11
  • 심사 : 2020.01.04
  • 발행 : 2020.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper is presented the solution method for three-dimensional problem of transversely isotropic body's elastoplastic deformation by the finite element method (FEM). The process of problem solution consists of: determining the effective parameters of a transversely isotropic medium; construction of the finite element mesh of the body configuration, including the determination of the local minimum value of the tape width of non-zero coefficients of equation systems by using of front method; constructing of the stiffness matrix coefficients and load vector node components of the equation for an individual finite element's state according to the theory of small elastoplastic deformations for a transversely isotropic medium; the formation of a resolving symmetric-tape system of equations by summing of all state equations coefficients summing of all finite elements; solution of the system of symmetric-tape equations systems by means of the square root method; calculation of the body's elastoplastic stress-strain state by performing the iterative process of the initial stress method. For each problem solution stage, effective computational algorithms have been developed that reduce computational operations number by modifying existing solution methods and taking into account the matrix coefficients structure. As an example it is given, the problem solution of fibrous composite straining in the form of a rectangle with a system of circular holes.

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참고문헌

  1. Bolshakov, V.I., Andrianov, I.V. and Danishevsky, V.V. (2008), Asymptotic Methods for Calculating Composite Materials Taking into Account the Internal Structure, Thresholds, Dnepropetrovsk, Ukraine. 196. (in Russian).
  2. Brovko, G.L., Bykov, D.L., Vasin, R.A., Georgievskii, D.V., Kiiko, I.A., Molodtsov, I.N. and Pobedrya, B.E. (2011), "A.A. Il'yushin's scientific heritage and development of his ideas in mechanics", Mech. Solids, 46(1), 3-14. https://doi.org/10.1016/j.prostr.2017.11.022.
  3. Kamel, Kh.A. and Eisenstein, G.K. (1974), "Automatic grid generation in two-and three-dimensional composite areas", High Speed Computing of Elastic Structures, Shipbuilding, Leningrad, Russia. 2, 21-35. (in Russian).
  4. Karpov, E.V. (2002), "Influence of the fibrous structure on stress concentration near a circular hole in borallum", Dynam. Continuous Medium, 120, 137-144.
  5. Khaldjigitov, A. and Adambaev, U.I. (2004), "Numerical and mathematical modeling of elastic plastic transversally isotropic materials", the 11th European Conference of Composite materials, Greece, Rhodes, May-June.
  6. Khaldjigitov, A.A. (2003), "Plasticity theories for transversely isotropic materials", COMPLAS VII 7-th International Conference on Computational Plasticity, Barcelona, April.
  7. Laurie, D. (2007), "Calculation of Radau-Kronrod and Lobatto-Kronrod quadrature formulas", Numerical Algorithms, 45(1-4), 139-152. https://doi.org/10.1007/s11075-007-9105-3.
  8. Meleshko, V.A. and Rutman, Y.L. (2017), "Generalized flexibility method by the example of plane elastoplastic problem", Procedia Structural Integrity, 6, 140-145. https://doi.org/10.1016/j.prostr.2017.11.022.
  9. Palizvan, M., Sadr, M.H. and Abadi, M.T. (2018), "A numerical method to evaluate the elastoplastic material properties of fiber reinforced composite", World Academy Sci., Eng. Technol. J. Mater. Metallurgical Eng., 12(11), 586-595.
  10. Pobedrya, B.E. and Gorbachev, V.I. (1984), "Stress and strain concentration in composite materials", Mech. Compos. Mater., 20(2), 141-148. https://doi.org/10.1007/BF00610353
  11. Pobedrya, B.Y. (1994), "The problem in terms of a stress tensor for an anisotropic medium", J. Appl. Math.Mech., 58(1), 81-89. https://doi.org/10.1016/0021-8928(94)90032-9.
  12. Polatov, A.M. (2013), "Numerical simulation of elastic-plastic stress concentration in fibrous composites", Coupled Syst. Mech., 2(3), 271-288. https://doi.org/10.12989/csm.2013.2.3.271.
  13. Polatov, A.M. (2019), "Finite element modeling of fibrous composites stress", Globe Edit, OmniScriptum Publishing, 133.
  14. Rutman, Y.L., Meleshko, V.A. and Ivanov, A.Yu. (2018), "Elastoplastic Analysis Methods and Capacity Curve Developing Features", Adv. Civil Eng. Technol., 2(3), 216-218. https://doi.org/10.31031/ACET.2018.02.000543.
  15. Tandon, G.P. and Weng, G.J. (1988), "A theory of particle-reinforced plasticity", J. Appl. Mech., 55(1), 126-135. https://doi.org/10.1115/1.3173618.
  16. Tomashevsky, S.B. (2011) "The influence of elastic-plastic deformations on the results of solving contact problems of railway transport", Bullet. Bryansk State Technical University, 3. 17-23.
  17. Zienkiewicz, O.C. and Taylor, R.L. (2005), The Finite Element Method for Solid and Structural Mechanics, Butterworth-Heinemann, United Kingdom. 631.

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