Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-05-121-47
DOI: https://dx.doi.org/10.15863/TAS.2023.05.121.47
Language: English
Citation: Djumayozov, U. Z., & Eshmanova, N. F. (2023). Numerical solution of three-dimensional boundary value problems of the theory of elasticity in finite deformations. ISJ Theoretical & Applied Science, 05 (121), 321-330. Soi: http://s-o-i.org/1.1/TAS-05-121-47 Doi: https://dx.doi.org/10.15863/TAS.2023.05.121.47 |
Pages: 321-330
Published: 30.05.2023
Abstract: Usually, when determining the safety margins and reliability of structures and their elements, it is sufficient to solve the boundary value problem of the theory of elasticity at small deformations. With the development of innovative technologies and the widespread use of composite materials, the calculation of materials at large deformations is required. Usually, to solve boundary value problems with finite deformations, variation methods based on potential energy are used. The article formulates a three-dimensional boundary value problem of the theory of elasticity in finite deformations for a parallelepiped with different natural and kinematic boundary conditions. The grid equations are constructed by the finite-difference method. To solve nonlinear difference equations, the method of elastic solutions of Ilyushin is used, i.e. first, the elastic (linear) problem is solved, and then the same problem is solved with a new right-hand side, taking into account the nonlinear part of the original equations. In this case, the finite-difference analogue of the linear problem solved with respect to central nodal values is the basis for an iterative process of the Jakobi type with an approximation order of 2. Using the received numerical results, the distribution of displacements and stresses in a parallelepiped is investigated.
Key words: finite deformation, elasticity, displacement, boundary value problem, difference equation.
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