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1

Assessment of sinkhole hazard in the post-mining area using the ERT method and numerical modeling

Ścigała Roman, Szafulera Katarzyna, Jendryś Marek

Zeszyty Naukowe Akademii Morskiej w Szczecinie

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2023

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nr 75 (147)

20--34

EN

The loss of stability of shallow voids existing in the rock mass often results in the formation of sinkholes on the surface. This has a significant impact on the threat to public safety. Therefore, it is crucial to recognize the presence of such voids, especially in old post-mining areas, where shallow extraction was previously conducted, and there is a lack of mapping documentation indicating the location of underground workings. This paper presents an example illustrating a proposed procedure for recognizing shallow voids, which consists of two research works: geophysical research combined with numerical analyzes used as a kind of forward modeling. This combination increases the possibility of accurately locating potential sinkhole occurrences. The first part of this article provides selected literature information on the occurrence of sinkhole hazards. The second part presents the results of subsurface layer investigations of the rock mass conducted using electrical resistivity tomography (ERT). The third part focuses on assessing the threat of sinkhole formation by using forward numerical modeling performed with the FLAC 3D software to confirm the subsurface structures identified through the ERT method. The results of the analyzes conducted with both methods are then discussed in terms of their suitability for assessing the associated risk. The research conducted within the framework of this study confirms the effectiveness of the ERT method combined with numerical modeling for evaluating the state of the rock mass. This method can be considered a valuable tool for supporting decision-making in identifying post-mining areas that are particularly at risk of sinkhole formation.

2

The Temperature Field Effect on Dynamic Stability Response of Three-layered Annular Plates for Different Ratios of Imperfection

Pawlus Dorota

Studia Geotechnica et Mechanica

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2023

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Vol. 45, nr 2

158--173

EN

The paper presents the temperature field effect on the dynamic stability problem of plates with imperfection. The main objective is to conduct numerical investigations which show the relations between the imperfection ratio and plate dynamic response in a thermal environment. The plate is composed of three layers: thin facings and a thicker core. The plate can be loaded mechanically and thermally or only thermally. The facings are mechanically compressed with the forces acting in a plane. The temperature field model is defined by the temperature difference, which occurs between the plate edges. Two plate models are examined as follows: built using the approximation methods – orthogonalization and finite differences – and composed of finite elements. The analytical and numerical solution procedure is the main one, which is the proposal to perform the problem analysis. The plate reaction is described by the obtained values of the critical temperature differences for plates loaded only thermally and by the critical mechanical load sand the corresponding temperature differences for plates loaded mechanically and subjected to the uncoupled temperature field. The effect of the plate imperfection ratio under time-dependent loads is shown by numerous observations and results, which are shown graphically. The importance of the imperfection ratio on the plate’s dynamic stability response in complex loading conditions is studied.

3

A blow up of solutions for a system of Klein-Gordon equations with variable exponent : theoretical and numerical results

Gözen Sedanur Mazi, Yılmaz Nebi, Pişkin Erhan, Okutmustur Baver

Mathematica Applicanda

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2023

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Vol. 51, no. 2

143--164

EN

In this paper, we consider a system of Klein-Gordon equations with variable exponents. The first part of the manuscript is devoted to the proof of the blow up of solutions with negative initial energy under suitable conditions on variable exponents and initial data. The theoretical part is supported by numerical experiments based on P1-finite element method in space and the BDF and the Generalized-alpha methods in time illustrated in the second part. The numerical and analytical results of the blow up solutions agree with each other.

PL

Praca poświęcona jest układowi równań Kleina-Gordona ze zmiennymi wykładnikami. W pierwszej części pokazano, że rozwiązania o ujemnej energii początkowej uciekają do nieskończoności przy odpowiednich warunkach na wykładniki oraz dane początkowe. Część teoretyczną uzupełniają obliczenia numeryczne oparte na metodzie elementu skończonego dla zmiennych przestrzennych oraz metodzie różniczkowania wstecz (Backward Differentiation Formula, BDF). Wyniki numeryczne i analityczne dotyczące wybuchowego charakteru rozwiązań wzajemnie potwierdzają się.

4

Projektowanie obudowy tunelu z wykorzystaniem metody kontroli konwergencji

Blajer Mateusz

Materiały Budowlane

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2023

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nr 5

10--13

PL

W artykule przedstawiono wykorzystanie metody kontroli konwergencji do weryfikacji obudowy tunelu drążonego w warunkach fliszu karpackiego. Bazuje ona na obliczeniach numerycznych MES lub MRS i stanowi rozwinięcie metod analitycznych i seminumerycznych, które wykorzystywano w początkach jej stosowania. Dzięki użyciu modeli MES lub MRS możliwe jest odwzorowanie tak skomplikowanego ośrodka, jakim jest flisz karpacki i jego (w większości przypadków) asymetrycznego oddziaływania. Obecnie jedynie przestrzenne modele MES i MRS przewyższają opisywaną metodę pod względem możliwości obliczeniowych.

EN

The paper presents the use of the convergence confinement method for designing and verifying the tunnel lining in the conditions of the Carpathian flysch. It is based on numerical calculations using FEM or FDM and it is a development of the analytical and semi-analytical methods that were used at the beginning of its application. By using FEM or FDM models, it is possible to reproduce such a complex medium as the Carpathian flysch and its (mostly asymmetric) actions. Currently, only spatial FEM and FDM models exceed the described method in terms of computational capabilities.

5

Comparison of heat transfer phenomena for two different cryopreservation methods : slow freezing and vitrification

Skorupa Anna, Piasecka-Belkhayat Alicja

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 1

57--69

EN

The purpose of the research is to prepare a mathematical and numerical model for the phenomenon of heat transfer during cryopreservation. In the paper, two popular methods, slow freezing and vitrification, are compared. Furthermore, the basic model of thermal processes is supplemented by the phenomenon of phase transitions. To determine the temperature distribution during cryopreservation processes, one uses the heat transfer equation proposed by Pennes. An integral part of the energy equation is the substitute thermal capacity (STC) performed according to the concept named one domain method (fixed domain method), The numerical model is developed using the finite difference method (FDM) connected with directed interval arithmetic. The final part of the article contains the results of numerical simulations.

6

The dynamic stability problem of composite annular plates with auxetic properties

Pawlus Dorota

Engineering Transactions

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2023

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Vol. 71, iss. 3

329--349

EN

This paper presents the effect of the auxeticity on the behaviour of a plate subjected to the loss of stability. The plate structure is composed of three layers built of auxetic or conventional facings and a conventional core. The plate is loaded mechanically in the plane of facings with forces increasing in time. The main technique of the problem solution is based on the orthogonalisation and finite differences methods. Selected examples of plates were calculated with the use of the finite difference method. The obtained results allow observing the similarities and differences between plate models, whose structures are built of conventional layers or mixed layers: auxetic-foam-auxetic. Investigations complement the knowledge of the responses of the composite structures with auxetic properties. They show the possibility of using special plate structures whose materials are characterised by the negative value of Poisson’s ratio.

7

Modeling of the influence of elevated temperature on oxygen distribution in soft tissue

Jasiński Marek, Zadoń Maria

Engineering Transactions

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2023

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Vol. 71, iss. 3

287--306

EN

The purpose of the study was to analyze the combined model of bioheat transfer and oxygen distribution in tissue during exposition to the external heat impulse. The effect of temperature and thermal damage to the tissue on the values of its thermophysical parameters was taken into account. The variable value of the perfusion coefficient affects the blood velocity in the capillary and thus the distribution of the partial oxygen pressure in the tissue. Various models of the oxygen dissociation curves were also considered and a sensitivity analysis was performed for the parameters of the oxygen distribution model. In the numerical realization stage, the finite difference method and the shooting method were used.

8

Application of genetic algorithm for double-lap adhesive joint design

Kurennov Sergei, Barakhov Konstantin, Polyakov Olexander, Taranenko Igor

Archive of Mechanical Engineering

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2023

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LXX, nr 1

27--42

EN

The problem of optimal design of symmetrical double-lap adhesive joint is considered. It is assumed that the main plate has constant thickness, while the thickness of the doublers can vary along the joint length. The optimization problem consists in finding optimal length of the joint and an optimal cross-section of the doublers, which provide minimum structural mass at given strength constraints. The classical Goland-Reissner model was used to describe the joint stress state. A corresponding system of differential equations with variable coefficients was solved using the finite difference method. Genetic optimization algorithm was used for numerical solution of the optimization problem. In this case, Fourier series were used to describe doubler thickness variation along the joint length. This solution ensures smoothness of the desired function. Two model problems were solved. It is shown that the length and optimal shape of the doubler depend on the design load.

9

Simulation of infeasible instruments in a sound synthesizer - implementation and control

Pluta Marek

Vibrations in Physical Systems

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2022

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Vol. 33, nr 2

art. no. 2022206

EN

Sound synthesis using mathematical modelling of musical instruments is a method particularly well suited for live performance using a physical controller. Depending on model complexity, it may be able to reproduce various subtle phenomena related to excitation and real time control of an instrument, providing an intuitive tool for a musician. A variant of physical modelling synthesis, referred to as the simulation of infeasible instruments, uses a model of an object that does not have a physical counterpart. Such model has some properties of a real object, which makes it still intuitive for a musician. However, other features, such as geometry, or material properties, are intentionally altered in such manner, that it could not function in reality. These infeasible features introduce new properties to the sound it produces. The study presents a few such models with a discussion regarding their implementation and control issues in a real-time sound synthesizer.

10

Wpływ konstrukcji budowlanej na propagację fal elektromagnetycznych

Choroszucho Agnieszka, Tymiński Jakub, Orzechowski Damian, Kondrusik Alan, Duchnowski Szymon Piotr

Napędy i Sterowanie

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2022

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R. 24, nr 12

22--27

PL

Praca przedstawia wpływ konstrukcji budowlanej na rozkład pola elektromagnetycznego wewnątrz części budynku. W analizowanym obszarze zamontowano źródło pola o częstotliwości związanej z komunikacją bezprzewodową (2,4 GHz). Artykuł zawiera dyskusję dotyczącą zjawisk fizycznych związanych z propagacją fali elektromagnetycznej w złożonych konstrukcjach zawierających beton, zbrojenie i cegły. Zastosowano numeryczną metodę różnic skończonych w dziedzinie czasu (FDTD). Analizowany obszar modelowano według typowych budowlanych technologii. Dokładna analiza wyników może przyczynić się do rozwiązania problemu związanego z zanikami sygnału i problemem związanym z komunikacją bezprzewodową.

11

Numerical solution of MHD channel flow in a porous medium with uniform suction and injection in the presence of an inclined magnetic field

Chutia Muhim

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

5--13

EN

In this paper, the steady fully developed MHD flow of a viscous incompressible electrically conducting fluid through a channel filled with a porous medium and bounded by two infinite walls is investigated numerically for the cases (i) Poiseuille flow and (ii) Couette-Poiseuille flow; with uniform suction and injection at the walls in the presence of an inclined magnetic field. The Brinkman equation is used for the flow in the porous channel and solved numerically using the finite difference method. Numerical results are obtained for velocity. The effects of various dimensionless parameters such as Hartmann number (M), suction/injection parameter (S), permeability parameter (α) and angle of inclination (θ) on the flow are discussed and presented graphically.

12

Numerical analysis of thermal damage and oxygen distribution in laser irradiated tissue

Jasiński Marek

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

51--62

EN

A numerical analysis of the thermal damage process that proceeds in biological tissue during laser irradiation is presented. Heat transfer in the tissue is assumed to be transient and two-dimensional. The internal heat source resulting from the laser irradiation based on the solution of optical diffusion equation is taken into account. Changes in tissue oxygen distribution resulting from temperature changes are analyzed using the Krogh cylinder model with Michaelis-Menten kinetics. A Hill model was used to describe the oxyhemoglobin dissociation curve. At the stage of numerical realization, the boundary element method and the finite difference method have been applied.

13

Numerical analysis of biological tissue heating using the dual-phase lag equation with temperature - dependent parameters

Majchrzak Ewa, Stryczyński Mikołaj

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 3

85--98

EN

The dual-phase lag equation is formulated for the case when the thermophysical parameters occurring in this equation are temperature-dependent. The axial-symmetrical domain of biological tissue heated by an external heat source is considered. The problem is solved using the implicit scheme of the finite difference method. At the stage of numerical computations, the analytical relationships taken from the literature describing changes in parameters are taken into account.

14

Mathematical modeling of the phenomena that occur in a biological tissue containing photosensitizer

Jasiński Marek, Zadoń Maria

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 4

40--51

EN

The aim of the study is to analyze photothermal and photochemical phenomena that occur during photodynamic therapy (PDT). In this type of therapy, under the influence of the laser, reactions take place related to the transformation of triplet oxygen form into its singlet form which is cytotoxic to the tissue. The increases in temperature resulting from the laser-tissue interaction during PDT are not big; however, they can lead to changes in tissue perfusion, which can affect oxygen delivery to the tissue. The proposed model uses optical diffusion equation, Pennes bioheat transfer equation, and reactions equations for PDT. The main findings of the analysis show the impact of temperature on the value of the perfusion coefficient and triplet oxygen distributions at the end of the treatment procedure.

15

An extended finite difference method for singular perturbation problems on a non-uniform mesh

Swarnakar D., Kumar V. Ganesh, Soujanya G. B. S. L.

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 1

203--214

EN

An extended second order finite difference method on a variable mesh is proposed for the solution of a singularly perturbed boundary value problem. A discrete equation is achieved on the non uniform mesh by extending the first and second order derivatives to the higher order finite differences. This equation is solved efficiently using a tridiagonal solver. The proposed method is analysed for convergence, and second order convergence is derived. Model examples are solved by the proposed scheme and compared with available methods in the literature to uphold the method.

16

Unconditionally positive NSFD and classical finite difference schemes for biofilm formation on medical implant using Allen-Cahn equation

Tijani Yusuf O., Appadu Appanah Rao

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

40--60

EN

The study of biofilm formation is becoming increasingly important. Microbes that produce biofilms have complicated impact on medical implants. In this paper, we construct an unconditionally positive non-standard finite difference scheme for a mathematical model of biofilm formation on a medical implant. The unknowns in many applications reflect values that cannot be negative, such as chemical component concentrations or population numbers. The model employed here uses the bistable Allen-Cahn partial differential equation, which is a generalization of Fisher’s equation. We study consistency and convergence of the scheme constructed. We compare the performance of our scheme with a classical finite difference scheme using four numerical experiments. The technique used in the construction of unconditionally positive method in this study can be applied to other areas of mathematical biology and sciences. The results here elaborate the benefits of the non-standard approximations over the classical approximations in practical applications.

17

Analysis of traffic load effects in railway backfilled arch bridges

Kamiński Tomasz, Machelski Czesław

Archives of Civil Engineering

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2022

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Vol. 68, nr 2

243--260

EN

The problem of the arch barrel deformation in railway backfilled arch bridges caused by their typical service loads is analysed. The main attention is paid to vertical or radial displacements of characteristic points of the arch barrel. In the study results of deflection measurements carried out on single and multi-span backfilled arch bridges made of bricks or plain concrete during passages of various typical railway vehicles are used. On the basis of such results empirical influence functions of displacements are being created. In the next step, the results are utilised to estimate bending effects within the arch. The paper includes different procedures based on measurements of displacements in various points and directions. Using empirical influence functions arbitrary virtual load cases may be also considered. In this manner the proposed methodology shows a potential to be an effective tool of comprehensive calibration of numerical models of backfilled arch bridges on the basic of field tests carried out under any live loads.

PL

Artykuł skupia się na zagadnieniu przemieszczeń sklepień mostów murowanych wywołanych ich typowymi obciążeniami użytkowymi. Szczególna uwaga zwrócona jest na pomiar przemieszczeń pionowych i radialnych w charakterystycznych punktach sklepienia. W przedstawionych przykładach rozpatrzono zachowanie jedno- i wieloprzęsłowych mostów łukowych opartych na sklepieniach murowanych i betonowych pod obciążeniem przejeżdżającymi pojazdami kolejowymi różnego rodzaju. Na podstawie otrzymanych wyników pomiarów terenowych prowadzonych na powyższych obiektach stworzono doświadczalne funkcje wpływu przemieszczeń. W kolejnym kroku uzyskane wyniki wykorzystywane są do wyznaczenia momentów zginających w sklepieniu. W artykule przedstawiono odmienne procedury postępowania bazujące na pomiarach przemieszczeń w różnych kierunkach i w różnie rozmieszczonych punktach. Szczególną zaletą przedstawionego całościowego podejścia jest możliwość wykonania pożądanych pomiarów podczas standardowej eksploatacji mostu bez jakiegokolwiek zakłócania ruchu taboru, co w wielu sytuacjach czyni przeprowadzenie tego typu badań w ogóle możliwymi. Przyjęte schematy postępowania są szczególnie skuteczne w przypadku obiektów kolejowych charakteryzujących się regularnością i łatwości w identyfikacji ich schematów obciążeń reprezentowanych zwłaszcza przez lokomotywy. Niemniej jednak przedstawione podejście może być wykorzystane również w analizie mostów drogowych. Podane procedury mogą opierać się też na innych efektach statycznych (przemieszczeniach i odkształceniach w dowolnych kierunkach) mierzonych w dowolnych punktach konstrukcji. Zaproponowaną metodykę można wykorzystywać, co również zobrazowano w artykule, jako efektywne narzędzie do wszechstronnej kalibracji modeli numerycznych mostów sklepionych obejmującej np. weryfikację ich parametrów materiałowych, niewidocznej geometrii czy, w przypadku modeli dwuwymiarowych, ich szerokości efektywnej.

18

The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters

Winnicki Ireneusz, Jasinski Janusz, Pietrek Sławomir, Kroszczynski Krzysztof

Advances in Geodesy and Geoinformation

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2022

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Vol. 71, no. 2

art. no. e23, 2022

EN

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used third-order 3x3 pixels Laplace contour filters including the difference schemes used to derive them. The authors focused on the mathematical properties of the Laplace filters. The basic reasons of the differences of the properties were studied and indicated using their transfer functions and modified differential equations. The relations between the transfer function for the differential Laplace operator and its difference operators were described and presented graphically. The impact of the corner elements of the masks on the results was discussed. This is a theoretical work. The basic research conducted here refers to a few practical examples which are illustrations of the derived conclusions.We are aware that unambiguous and even categorical final statements as well as indication of areas of the results application always require numerous experiments and frequent dissemination of the results. Therefore, we present only a concise procedure of determination of the mathematical properties of the Laplace contour filters matrices. In the next paper we shall present the spectral characteristic of the fifth order filters of the Laplace type.

19

The mathematical characteristic of the fifth order Laplace contour filters used in digital image processing

Winnicki Ireneusz, Pietrek Sławomir, Jasinski Janusz, Kroszczynski Krzysztof

Advances in Geodesy and Geoinformation

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2022

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Vol. 71, no. 2

art. no. e26, 2022

EN

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used fifth-order pixels Laplace filters including the difference schemes used to derive them (finite difference method – FDM and finite element method – FEM). The results of the research concerning third-order pixels matrices of the convolution Laplace filters used for digital processing of images were presented in our previous paper: The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters is presented byWinnicki et al. (2022). As previously, the authors focused on the mathematical properties of the Laplace filters: their transfer functions and modified differential equations (MDE). The relations between the transfer function for the differential Laplace operator and its difference operators are described and presented here in graphical form. The impact of the corner elements of the masks on the results is also discussed. A transfer function, is a function characterizing properties of the difference schemes applied to approximate differential operators. Since they are relations derived in both types of spaces (continuous and discrete), comparing them facilitates the assessment of the applied approximation method.

20

Free vibrations of Kirchhoff plates considering plate variable thickness and interaction with water including water boundaries

Lenartowicz Agnieszka, Guminiak Michał, Przychodzki Maciej

Vibrations in Physical Systems

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2021

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Vol. 32, nr 2

art. no. 2021208

EN

The natural vibrations of thin (Kirchhoff-Love) plates with constant and variable thickness and interaction with water are considered in the paper. The influence of the water free surface on natural frequencies of the coupled water-plate system is analysed too. The Finite Element Method (FEM) and the Finite Difference Method (FDM) are used to describe structural deformation and the Boundary Element Method (BEM) is applied to describe the dynamic interaction of water on a plate surface. The plate inertia forces are expressed by diagonal or consistent mass matrix. The water inertia forces are described by fully-populated mass matrix which is obtained directly from the theory of double layer potential.