About Stability of First Kind Equation Solving

Shyshkanova, Gannа

doi:10.1109/saic.2018.8516805

Cited by 9 publications

(9 citation statements)

References 5 publications

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“…The analytical solution was obtained using a variant of the perturbation method, based on the small-parameter expansion of the potential of a simple layer distributed over a doubly connected region. In this way, the problem of pressing a flat punch in the form of a non-circular ring is reduced to a sequence of problems for a punch in the form of a circular ring [9][10][11][12]21]. Special software for calculations and analysis of the results was developed in the publicly available C++ language (USA).…”

Section: The Study Materials and Methodsmentioning

confidence: 99%

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Construction of mathematical and computer models for calculating contact characteristics of interaction between a rigid punch and an elastic half-space

Zaytseva,

Zhushman

2024

EEJET

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The subject of this study is a punch-elastic half-space system under compressive force. The paper solves the problem of determining contact stresses and displacements. The content of results is the constructed models and the assessment of their adequacy. This work considers the problem of pressing a rigid plane double-connected punch on a homogeneous and isotropic elastic half-space. To obtain an analytical solution, a variant of the perturbation method based on the expansion of the potential of a simple layer distributed over a double-connected region by a small parameter was applied. The problem of pressing a flat punch in the form of a non-circular ring is reduced to a sequence of problems for a punch in the form of a circular ring. This allows us to use a known solution for a circular ring. Finite element models were built using ANSYS. A group of models was constructed to take into account possible damage in the event that the punch-elastic half-space system is exposed to difficult natural conditions or an aggressive environment during a certain time of modeling. A database was formed for the purpose of further transferring it to CLIPS. Sets of rules and knowledge were compiled. A generalizing algorithm was developed for the problems of constructing and analyzing mathematical and computer models of contact interaction between a rigid cylindrical punch with a flat double-connected base with an elastic half-space under the action of a compressive force. The problem of determining the geometric shape of the cross-section of an annular punch in the plan for the punch-elastic half-space system was solved for the case when the contact zone is not known in advance. The devised approach could be employed in engineering calculations for strength and durability

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Section: The Study Materials and Methodsmentioning

confidence: 99%

“…However, as a drawback, it can be pointed out that the study of the stability of the solution obtained by such an analytical method was not considered there. This was done in work [12].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Construction of mathematical and computer models for calculating contact characteristics of interaction between a rigid punch and an elastic half-space

Zaytseva,

Zhushman

2024

EEJET

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“…We propose to reduce the problem for the domain  to sequences of similar problems for a circular domain D analogically to the reduction of a problem for a non-circular ring to the circular ring developed in [23,24]. Because the domain  is circular without friction, the equation of the boundary  of the contact domain  could be assumed as…”

Section: Solution Methods For the General Problemmentioning

confidence: 99%

Simple layer potential expansion for optimization of contact interaction taking into account friction and adhesion

Shyshkanova,

Walther

2023

J. Phys.: Conf. Ser.

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Friction plays a crucial role in the formation of contact problems, particularly through adhesion. This paper focuses on a quasi-static three-dimensional problem of a punch movement along the boundary of an elastic half-space. The investigation considers friction and adhesion forces, employing a two-term friction law. The objective is to optimize the pressure distribution beneath the punch. The shape of the punch serves as the design variable, while the deviation of the pressure distribution, originating from a given one, is minimized. The optimization problem can be divided into two sequentially solvable sub-problems. The first task involves finding a pressure distribution that minimizes the performance functional, which has a known solution. The second problem entails searching for the optimal shape of the punch to achieve the previously determined pressure distribution. A numeric-analytical solution is developed based on the expansion of the simple layer potential. The coefficients characterizing friction and adhesion act as small parameters. The proposed method gives the ability to obtain closed-form formulas in each approximation, enabling convenient qualitative analysis and practical engineering applications. The calculations and analytical dependence reveal an asymmetric distribution of pressure on the contact area, during the movement of an axisymmetric punch.

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“…The method of least squares is often used to generate estimators and other statistics in regression analysis. It was shown how difficult questions could be answered by developing simple models with simple interpretation of parameters for diversity of applications [23,24].…”

Section: Calculation Methodologymentioning

confidence: 99%

Efficiency forecasting for municipal solid waste recycling in the context on sustainable development of economy

et al. 2020

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Ukraine's further economic growth should be directed by Government Sustainable Development Strategy for harmonization of economy, environmental and social protection. One of the important modern problems is pollution by waste. The feasibility of introducing an eco-project for the municipal solid waste recycling is substantiated at the present research. The complex mathematical model of profit forecast is developed, which shows the tariffs influence on profitability of eco-project on construction of the plant for municipal solid waste recycling in Poltava region of Ukraine. The authors determine and analyse the dependences of the expected eco-project revenue from the change in tariffs for waste management services for each of the consumer categories. Two scenarios of economic development (inertial and innovative) are compared and resulted that the both scenarios have environmental and economic effect, so they are investment attractive. Emphasis is placed on the shortcomings and gaps of the existing tariff policy. The paper demonstrates lack of incentives for the development of business recycling under the existing tariff policy, so to establish a single tariff is proposed uniting the services cost for the removal, sorting, processing and disposal of the waste and also without dividing by consumer categories.

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About Stability of First Kind Equation Solving

Cited by 9 publications

References 5 publications

Construction of mathematical and computer models for calculating contact characteristics of interaction between a rigid punch and an elastic half-space

Construction of mathematical and computer models for calculating contact characteristics of interaction between a rigid punch and an elastic half-space

Simple layer potential expansion for optimization of contact interaction taking into account friction and adhesion

Efficiency forecasting for municipal solid waste recycling in the context on sustainable development of economy

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