Published since 1923
DOI: 10.33622/0869-7019
Russian Science Citation Index (RSCI) на платформе Web of Science


  • STRUCTURAL MECHANICS
  • Approaches And Principles Of Mathematical Modeling In Structural Mechanics
  • UDC 539.3
    doi: 10.33622/0869-7019.2023.11.86-90
    Boris V. GUSEV1, info-rae@mail.ru
    Vasiliy V. SAURIN2, saurin@ipmnet.ru
    1 Russian University of Transport, ul. Obraztsova, 9, str. 9, Moscow 127994, Russian Federation
    2 Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, prospekt Vernadskogo, 101, korð. 1, Moscow 119526, Russian Federation
    Abstract. Some approaches and principles of mathematical modeling in the structural mechanics are discussed. When describing phenomena occurring in the mechanics of solids, dual variational principles are used. Variables can always be divided into two groups: the first group consists of so-called measurable variables, the second contains non-measurable quantities. At the same time, the governing equations can be divided into three groups: constitutive equations, laws of balance and continuity, initial and boundary conditions. It is shown how the initial-boundary value problem can be reduced to minimizing a quadratic non-negative (energy) functional with respect to all admissible variables. The essence of this functional is that it consists of six energy states. An energy principle is formulated that determines the true state of the system. This approach also allows us to naturally formulate criteria for the accuracy of approximate solutions and construct solutions for complex non-stationary dynamic systems with an irregular shape with a predetermined accuracy.
    Keywords: structural mechanics, mathematical modeling, variational principles, numerical methods, linear theory of elasticity
  • REFERENCES
    1. Kostin G. V., Saurin V. V. Integrodifferential relations in linear elasticity. Berlin, De Gruyter, 2012. 280 p.
    2. Kostin G. V., Saurin V. V. Dynamics of solid structures. Method using integrodifferential relations. Berlin, De Gruyter, 2017. 305 p.
    3. Kostin G. V., Saurin V. V. The method of integro-differential relations in the linear theory of elasticity. Izvestiya Rossijskoj akademii nauk. Mekhanika tverdogo tela, 2007, no. 2, pp. 36-49. (In Russ.).
    4. Saurin V. V. On variational approaches in the linear theory of elasticity. Doklady Akademii nauk, 2007, vol. 415, no. 4, pp. 486-490. (In Russ.). Available at: https://naukarus.com/o-variatsionnyh-podhodah-v-lineynoy-teorii-uprugosti (accessed 2.09.2023). (In Russ.).
    5. Vasidzu K. Variacionnye metody v teorii uprugosti i plastichnosti [Variational methods in the theory of elasticity and plasticity]. Moscow, Mir Publ., 1987. 542 p. (In Russ.).
  • For citation: Gusev B. V., Saurin V. V. Approaches And Principles Of Mathematical Modeling In Structural Mechanics. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering], 2023, no. 11, ðp. 86-90. (In Russ.). doi: 10.33622/0869-7019.2023.11.86-90

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