#### 624.04 A new method for calculating the torsional stiffness of a naturally twisted bar

##### Temis Y. M. (Центральный институт авиационного моторостроения им. П.И. Баранова), Ziyatdinov I. Z. (Центральный институт авиационного моторостроения им. П.И. Баранова)

doi: 10.18698/2309-3684-2023-1-6480

At the initial stages of designing compressor blades, screws, cutting tools, it is advisable to use a finite element model based on a model of a naturally twisted beam. This model takes into account the influence of the angle of natural twist on the rigidity of the part. The torsional stiffness of a bar significantly affects the stiffness parameters of the finite element model. It is shown that the torsional stiffness correction obtained on the basis of the relations of the technical theory of naturally twisted beams makes it possible to obtain results at small angles of natural twist that are in good agreement with the three-dimensional calculation of a twisted FEM beam. At large specific angles of initial twist, the technical theory gives overestimated values of the torsional stiffness. The article proposes a modification of the relations of the technical theory to determine the torsional rigidity, taking into account large angles of initial twist.

Темис Ю.М., Зиятдинов И.З. Новый метод вычисления жесткости на кручение в модели естественно-закрученного стержня. Математическое моделирование и численные методы, 2023, No 1, с. 64–80

#### 517:519.6 Computation of stress-strain condition of free body by finite element method

##### Temis Y. M. (Центральный институт авиационного моторостроения им. П.И. Баранова), Azmetov K. K. (Baranov Central Institute of Aviation Motor Development/Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2018-3-95113

The technique of computation of stress-strain condition of free bodies by finite element method was offered. Implementation of suggested algorithm in two-dimensional formulation and calculation examples are given.

Темис Ю.М., Азметов Х.Х. Расчет напряженно-деформированного состояния свободных тел методом конечных элементов. Математическое моделирование и численные методы, 2018, № 3, с. 95–113.

#### 539.374 Model of non-isothermal elastoplastic deformation of structural materials under complex loading

##### Temis Y. M. (Центральный институт авиационного моторостроения им. П.И. Баранова), Hudyakova A. D. (Центральный институт авиационного моторостроения им. П.И. Баранова/Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2017-3-2035

The study introduces a model of elastoplastic deformation of structural alloys under conditions of complex nonisothermal loading. The model is based on the plastic flow theory. Within the research we derived the relations that made it possible to determine the parameters of the model using the results of sample tests according to the program of rigid symmetric cyclic deformation. Moreover, we developed an algorithm for determining the plasticity parameters from a limited set of experimental data. Based on the algorithm developed, we obtained the plasticity parameters for the nickel alloy IN738LC over a wide temperature range.

Temis Yu.M., Khudyakova A.D., Model of non-isothermal elastoplastic deformation of structural materials under complex loading.Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 20–37

#### 539.374 Numerical simulation of nonisothermal elastoplastic deformation processes of structural materials

##### Temis Y. M. (Центральный институт авиационного моторостроения им. П.И. Баранова), Hudyakova A. D. (Центральный институт авиационного моторостроения им. П.И. Баранова/Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2018-2-4769

The algorithm of the loading surface equation account during integration of constitutive equations system of invariant nonisothermal plasticity theory, based on returning of a representing point to a loading surface equation on each step of calculation was offered. Efficiency of proposed algorithm in combination with different linearization schemas for number of proportional and nonproportional thermomechanical deformation trajectories was explored. Results of simulation of the processes of tubular nickel-based alloy IN738LC specimens testing under proportional (tension-compression, tension-compression with torsion) and nonproportional («circle» and «diamond» with out-of-phase axis strain and temperature changing) cyclic thermomechanical deformation trajectories in operating-temperature range from 450 to 950°C.

Темис Ю.М., Худякова А.Д. Численное моделирование процессов неизотермического упругопластического деформирования конструкционных материалов. Математическое моделирование и численные методы, 2018, № 2, с. 47–69.