Рақамли технологияларнинг назарий ва амалий масалалари Том 9 № 2 (2026) · с. 30-44
Numerical Modeling of a Boundary-Value Problem of Thermoelastoplasticity in Deformations
Джумаёзов, У.З., Рахмонова, Р., Хайтбоева, И.З.
Аннотация
In this paper, using the deformation compatibility condition, similar to the well-known displacement equation, differential deformation equations are written. These, in combination with the equilibrium equation and boundary and additional boundary conditions, form a boundary-value problem of thermoelastoplasticity in deformations. The mathematical model is formulated directly in deformations, which ensures a more robust numerical implementation when analyzing the nonlinear behavior of materials taking into account temperature effects. Ilyushin's deformation theory of plasticity is used as the theoretical basis, allowing for the description of the evolution of plastic deformations through strain tensor invariants without explicitly introducing a yield surface in the classical stress formulation. The nonlinearity of the problem is due to both plastic effects and the temperature dependence of mechanical properties. The finite difference method is applied to numerically solve the boundary-value problem. An iterative solution algorithm is developed taking into account the nonlinear components of the model. An assessment of the convergence and stability of the numerical scheme for various mesh parameters and physical and mechanical properties of the material is carried out. The numerical results obtained in the elastic domain are compared with the solutions obtained in displacement and stress domains. The proposed approach can be used in the numerical modeling of structural elements operating under combined mechanical and thermal loading. The developed model and numerical solution algorithm are designed for further integration into engineering analysis software packages and can serve as the basis for constructing more complex multidimensional thermoelastoplastic models.
условие совместностипластичностьдеформацияперемещениенапряжениеконечно-разностные уравненияитерацияметод переменных направленийcompatibility conditionplasticity
Источник метаданных: OAI-PMH архив журнала · Sindex не хранит полный текст, а даёт ссылку на источник.