Mathematical Modeling of Inverse Problems of Forming Taking into Account the Incomplete Reversibility of Creep Strain

  • K. S. Bormotin
  • N. A. Taranukha


Functionals of direct and inverse problems of forming structural components are constructed taking into account the theory of incomplete reversibility of deformations. Formulations of these problems are given, and the uniqueness of their solutions is proved. An iterative method for solving inverse problems of forming structural components is proposed. Numerical solutions of these problems are obtained using a finite-element method.


inverse problems of forming variational inequalities uniqueness theory of incomplete reversibility of creep strain convergence finite-element method iterative method 


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  1. 1.
    T. Adachi, S. Kimura, T. Nagayama, et al., “Age Forming Technology for AircraftWing Skin,” Materials Forum 28, 202–207 (2004).Google Scholar
  2. 2.
    Z. Lihua, K. Jianguo, and H. Minghui, “Study on Springback Behavior in Creep Age Forming of Aluminium Sheets,” Adv. Sci. Lett. 19 (1), 75–79 (2013).CrossRefGoogle Scholar
  3. 3.
    B. D. Annin, A. I. Oleynikov, and K. S. Bormotin, “Modeling of Forming theWing Panels the SSJ-100 Aircraft,” Prikl. Mekh. Tekh. Fiz. 51 (4), 155–165 (2010) [J. Appl. Mech. Tech. Phys. 51 (4), 579–589 (2010)].Google Scholar
  4. 4.
    A. I. Oleinikov and K. S. Bormotin, “Modeling of the Forming of Wing Panels in a Creep Mode with Strain Aging in Solutions of Inverse Problems,” Uchen. Zap. Komsomolsk-na-Amure Gos. Tekh. Univ., No. II-1, 5–12 (2015).Google Scholar
  5. 5.
    I. Yu. Tsvelodub, Stability Postulate and Its Application in the Theory of Creep of Metallic Materials (Lavrentyev Inst. of Hydrodyn., USSR Acad. of Sci., Novosibirsk, 1991) [in Russian].Google Scholar
  6. 6.
    Yu. P. Samarin, Equation of State for Materials with Complex Rheological Properties (Kuibyshev State Univ., Kuibyshev, 1979) [in Russian].Google Scholar
  7. 7.
    V. P. Radchenko and M. N. Saushkin, Creep and Relaxation of Residual Stresses in Reinforced Structures (Mashinostroenie-1, Moscow, 2005) [in Russian].zbMATHGoogle Scholar
  8. 8.
    K. S. Bormotin, “An Iterative Method for Solving Inverse Problems of Forming Structural Components in Creep,” Vychisl. Metody Program. 14, Sec. 1, 141–148 (2013).Google Scholar
  9. 9.
    K. S. Bormotin, “An Iterative Method for Solving Geometrically Nonlinear Inverse Problems of Forming Structural Components in Creep,” Zh. Vychisl. Mat. Mat. Fiz. 53 (12), 145–153 (2013).MathSciNetzbMATHGoogle Scholar
  10. 10.
    S. N. Korobeinikov, Nonlinear Deformation of Solids (Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2000) [in Russian].zbMATHGoogle Scholar
  11. 11.
    R. Hill, “On Uniqueness and Stability in the Theory of Finite Elastic Strain,” J. Mech. Phys. Solids. 5 (4), 229–241 (1957).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    F. P. Vasil’ev, Optimization Methods (Faktorial Press, Moscow, 2002) [in Russian].Google Scholar
  13. 13.
    S. N. Korobeinikov, A. I. Oleinikov, B. V. Gorev, and K. S. Bormotin, “Mathematical Modeling of Creep Processes in Metals Having Different Properties in Tension and Compression,” Vychisl. Metody Program. 9, 346–365 (2008).Google Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Komsomolsk-on-Amur State Technical UniversityKomsomolsk-on-AmurRussia
  2. 2.Institute of Engineering and Metallurgy, Far East BranchRussian Academy of SciencesKomsomolsk-on-AmurRussia

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