Approach to construction of mathematical models of geo-massif stress-deformed state under the influence of natural and technogenic forces

2018 ◽

Vol 2 (51) ◽

pp. 73-78

Author(s):

Mykola Kuzlo

Keyword(s):

Mathematical Models ◽

Numerical Solutions ◽

Single Layer ◽

Filtration Flow ◽

Curvilinear Boundary ◽

Vertical Displacements ◽

Deformed State ◽

Water Saturated ◽

Soil Filtration ◽

Saline Solutions

The analytical solutions for the determination of vertical displacements at any point of single-layer and multilayer soil compositions under filtration water flow influence, saline solutions presence and filtration considering soil changing filtration and deformation characteristics have been obtained. The mathematical models of soil filtration and the stress-deformed state from water-saturated ground massifs and bases deformations forecast under internal volumetric forces influence (hydrodynamic forces of the filtration flow, changes in the soils own weight) have been developed and substantiated. Numerical solutions of the corresponding boundary filtration problems and SDS of soil in regions with time-varying curvilinear boundary have been obtained for these mathematical models. They have enabled to perform water-saturated soils and bases deformations forecast under the change of hydrogeological conditions and man-made factors effect.

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Mathematic Modelling of Stress in Healthy Knee Joint and After Arthroplastywith Different Typesof Endoprostheses

N N Priorov Journal of Traumatology and Orthopedics ◽

10.32414/0869-8678-2017-2-11-16 ◽

2017 ◽

pp. 11-16

Author(s):

S. M. Smetanin ◽

G. M. Kavalerskiy

Keyword(s):

Stress Distribution ◽

Knee Joint ◽

Mathematical Modelling ◽

Mathematical Models ◽

Posterior Cruciate Ligament ◽

Knee Arthroplasty ◽

Knee Flexion ◽

Cruciate Ligament ◽

Healthy Knee ◽

Deformed State

Purpose of study. To study stressed-deformed state of the healthy knee joint and after arthroplasty using endoprostheses with either preservation or substitution of the posterior cruciate ligament by the method of numerical mathematical modelling.Materials and methods.Peculiarities of stress distribution in bones were determined on three mathematical models - healthy knee joint and joint after arthroplasty using endoprostheses with either preservation or substitution of the posterior cruciate ligament at the set load (80 kg) in straightened leg and either 45° or 90° knee flexion.Results. In healthy knee joint with a straightened leg the stress in the tibia is 2.3 times higher than in the femur. With knee flexion the stress in bone tissue increases and this increase is more intensive in the femur. After arthroplasty using endoprosthesis with substitution of the posterior cruciate ligament the stress in the tibia and femur is higher at all flexion angles as compared to arthroplasty using endoprosthesis with posterior cruciate ligament preservationConclusion.The obtained data may be used for mathematical substantiation of the advantage of endoprosthesis with preservation of the posterior cruciate ligament and in complex with the data of national and international registers will enable to optimize the treatment tactics in patients to whom knee arthroplasty is indicated.

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Mathematic Modelling of Stress in Healthy Knee Joint and After Arthroplastywith Different Typesof Endoprostheses

N.N. Priorov Journal of Traumatology and Orthopedics ◽

10.17816/vto201724211-16 ◽

2017 ◽

Vol 24 (2) ◽

pp. 11-16

Author(s):

S. M Smetanin ◽

G. M Kavalerskiy

Keyword(s):

Stress Distribution ◽

Knee Joint ◽

Mathematical Modelling ◽

Mathematical Models ◽

Posterior Cruciate Ligament ◽

Knee Arthroplasty ◽

Knee Flexion ◽

Cruciate Ligament ◽

Healthy Knee ◽

Deformed State

Purpose of study. To study stressed-deformed state of the healthy knee joint and after arthroplasty using endoprostheses with either preservation or substitution of the posterior cruciate ligament by the method of numerical mathematical modelling. Materials and methods. Peculiarities of stress distribution in bones were determined on three mathematical models - healthy knee joint and joint after arthroplasty using endoprostheses with either preservation or substitution of the posterior cruciate ligament at the set load (80 kg) in straightened leg and either 45° or 90° knee flexion. Results. In healthy knee joint with a straightened leg the stress in the tibia is 2.3 times higher than in the femur. With knee flexion the stress in bone tissue increases and this increase is more intensive in the femur. After arthroplasty using endoprosthesis with substitution of the posterior cruciate ligament the stress in the tibia and femur is higher at all flexion angles as compared to arthroplasty using endoprosthesis with posterior cruciate ligament preservation Conclusion. The obtained data may be used for mathematical substantiation of the advantage of endoprosthesis with preservation of the posterior cruciate ligament and in complex with the data of national and international registers will enable to optimize the treatment tactics in patients to whom knee arthroplasty is indicated.

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NEUROCOMPUTER MODELING OF CONTACT RIGIDITY

Bulletin of Bryansk state technical university ◽

10.12737/20285 ◽

2016 ◽

Vol 2016 (2) ◽

pp. 156-166

Author(s):

Петр Тихомиров ◽

Petr Tikhomirov ◽

Елена Лемешева ◽

Elena Lemesheva ◽

Николай Булхов ◽

...

Keyword(s):

Surface Layer ◽

Mathematical Models ◽

Quality Parameters ◽

Promising Method ◽

Bolted Connections ◽

Contact Rigidity ◽

Deformed State ◽

Technical Systems ◽

To Receive

Contact rigidity of a joint is one of the main criteria of operability of forest cars. It defines vibration activity and durability of the tightened bolted connections therefore its assessment will allow to predict behavior of technical systems. In work the technique of an assessment of contact rigidity by means of the nerocomputer modeling allowing to consider parameters of quality of a blanket is presented. Results of re-searches allowed to receive mathematical models for contact rigidity. In the paper there is presented a procedure of contact rigidity estimate with the aid of neurocomputer modeling. A contact rigidity of a joint is one of the basic criteria of machine and mechanism capacity for work. It defines vibration activity and strength of tightened bolted connections therefore its estimate will allow forecasting the behavior of technical systems. Neurocomputer modeling is a promising method allowing taking into account quality parameters of a surface layer of machinery at the analysis of a deformed state.

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