IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2023i1p71-d1307289.html
   My bibliography  Save this article

Formulation and Numerical Solution of Plane Problems of the Theory of Elasticity in Strains

Author

Listed:
  • Dilmurod Turimov

    (Department of Computer Engineering, Gachon University, Sujeong-gu, Gyeonggi-do, Seongnam-si 461-701, Republic of Korea)

  • Abduvali Khaldjigitov

    (Department of Mechanics and Mathematical Modeling, Faculty of Mathematics, National University of Uzbekistan, St. Universitetskaya 4, Tashkent 100174, Uzbekistan)

  • Umidjon Djumayozov

    (Department of Software Engineering, Faculty of Computer Engineering, Samarkand Branch of Tashkent University of Information Technologies, St. Shokhrukh Mirzo 47A, Samarkand 140100, Uzbekistan)

  • Wooseong Kim

    (Department of Computer Engineering, Gachon University, Sujeong-gu, Gyeonggi-do, Seongnam-si 461-701, Republic of Korea)

Abstract

This article is devoted to the formulation and numerical solution of boundary-value problems in the theory of elasticity with respect to deformations. Similar to the well-known Beltrami–Michell stress equations, the Saint-Venant compatibility conditions are written in the form of differential equations for strains. A new version of plane boundary-value problems in strains is formulated. It is shown that for the correctness of plane boundary value problems, in addition to the usual conditions, one more special boundary condition is required using the equilibrium equation. To discretize additional boundary conditions and differential equations, it is convenient to use the finite difference method. By resolving grid equations and additional boundary conditions with respect to the desired quantities at the diagonal nodal points, we obtained convergent iterative relations for the internal and boundary nodes. To solve grid equations, the elimination method was also used. By comparing with the Timoshenko–Goodyear solution on the tension of a rectangular plate with a parabolic load, the validity of the formulated boundary value problems in strains and the reliability of the numerical results are shown. The accuracy of the results has been increased by an average of 15%.

Suggested Citation

  • Dilmurod Turimov & Abduvali Khaldjigitov & Umidjon Djumayozov & Wooseong Kim, 2023. "Formulation and Numerical Solution of Plane Problems of the Theory of Elasticity in Strains," Mathematics, MDPI, vol. 12(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:71-:d:1307289
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/1/71/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/1/71/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nima Ahmadi & Sajad Rezazadeh, 2023. "An Innovative Approach to Predict the Diffusion Rate of Reactant’s Effects on the Performance of the Polymer Electrolyte Membrane Fuel Cell," Mathematics, MDPI, vol. 11(19), pages 1-25, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:71-:d:1307289. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.