Reverse and direct methods for solving the characteristic equation

Lozhkin, Alexander; Božek, Pavol; Lyalin, V. E.; Tarasov, V. F.; Tóthová, Mária; Sultanov, R. K.

doi:10.1063/1.4954935

Cited by 3 publications

(2 citation statements)

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“…For the three-dimensional stress state, the criterion characterizing the transition of a material from the elastic to the plastic state can be described by the condition of plasticity, expressed by the function [ 15 , 19 , 20 ]:

where:

is the stress vector with three normal and three shear stress components and

are constants sufficiently describing properties of the material.…”

Section: An Analytical Description Of Elastic–plastic Materials Behmentioning

confidence: 99%

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Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic–Plastic Regime under Cyclic Loading

et al. 2020

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In exact analyses of bodies in the elastic–plastic regime, the behavior of the material above critical stress values plays a key role. In addition, under cyclic stress, important phenomena to be taken into account are the various types of hardening and the design of the material or structure. In this process, it is important to define several groups of characteristics. These include, for instance, the initial area of plasticity or load which defines the interface between elastic and plastic deformation area. The characteristics also include the relevant law of plastic deformation which specifies the velocity direction of plastic deformation during plastic deformation. In the hardening condition, it is also important to determine the position, size and shape of the subsequent loading area. The elasto-plastic theory was used for the analysis of special compliant mechanisms that are applied for positioning of extremely precise members of the Compact Linear Collider (CLIC), e.g., cryomagnets, laser equipment, etc. Different types of deformation hardening were used to simulate the behavior of particular structural elements in the elastic–plastic regime. Obtained values of stresses and deformations may be used in further practical applications or as default values in other strain hardening model simulations.

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where:

is the stress vector with three normal and three shear stress components and

are constants sufficiently describing properties of the material.…”

Section: An Analytical Description Of Elastic–plastic Materials Behmentioning

confidence: 99%

Section: Initial Area Of Plasticitymentioning

confidence: 99%

Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic–Plastic Regime under Cyclic Loading

et al. 2020

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The Newton problem solution of the transformed complex curve parameters

Lozhkin

Korobeynikov

Khaziyakhmetov

2019

J. Phys.: Conf. Ser.

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Many tasks from the natural and engineering sciences require precision solutions with complex curves. The main obstacle is the lack of the necessary mathematical apparatus. The analysis of symmetries on the Euclidean plane by Dieudonne and the figure by Weyl allowed us to formulate a new method for obtaining the parameters of linear transformation alternative to classical. It can be used for an ellipse, hyperbola, as well as complex flat curves. The method is analyzed for trajectories having symmetries. A theorem to obtain the parameters of the transformed curve in the general case is formulated. Theoretical calculations and the results of experimental studies using the method of geometric modeling are given. The method is very new, so it may not work for some curves. There is the possibility of obtaining it, since the research uses the simplest apparatus.

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