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1

Modeling of photochemical and photothermal effects in soft tissue subjected to laser irradiation

Jasiński Marek, Zadoń Maria

Computer Assisted Methods in Engineering and Science

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2024

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Vol. 31, no. 1

29--50

EN

The purpose of this study is to analyze the phenomena that occur in biological tissueduring photodynamic therapy (PDT). Under the influence of the laser, triplet oxygen istransformed into singlet oxygen, which is cytotoxic to cancer tissue. The impact of thelaser on the tissue may also be accompanied by changes in the thermophysical parameters,e.g., perfusion, which can affect the supply of oxygen to the tissue and, consequently,the outcome of the therapy. The proposed model uses the optical diffusion equation,the Pennes bioheat transfer equation, and reactions equations for PDT. The connectionbetween bioheat transfer and PDT models is taken into account through the respectiverelationships between perfusion rate, capillary blood velocity, and the maximum oxygensupply rate. Furthermore, a method is proposed to model abnormal vascular patterns inthe tumor subdomain. The boundary element method and the finite difference methodwere used in the numerical implementation stage.

2

Modelling of the acoustic wave scattering on the aircraft surface using the boundary element method

Nowicki Dawid, Suder-Dębska Katarzyna, Czajka Ireneusz

Vibrations in Physical Systems

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2023

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Vol. 34, nr 1

art. no. 2023107

EN

Sound localization tools are important in the environmental protection and the human searches. The article is one of the stages of the implementation of the concept of using aircraft to localize sound sources. The use of a fixed-wing aircraft instead of a multirotor would increase the total flight time, and expand the surveyed area. It is important to determine the most favourable positions of the receivers on the surface of the aircraft. The scattering effects of the sound waves coming from the ground source and aircraft engine on the acoustic field on the aircraft surface are not homogeneous. In the article the authors present the modelling of the scattering of the sound waves over the airplane surface with the usage of boundary element methods. After determining the effects from the sound source on earth and from the aircraft engine the conclusion was made, that the influence from the engine noise is greater than that from the ground source, and in order to localize the low amplitude signals, the aircraft need to glide. Considering only the effects of the ground source, the optimal areas for the microphones placement were determined.

3

Applications of the second-order edge element method versus zero order in optical diffusion tomography

Rymarczyk Tomasz, Sikora Jan

Przegląd Elektrotechniczny

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2022

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R. 98, nr 1

107--110

EN

This paper presents an approximation of two boundary elements by analysing numerical aspects of such an approximation. Diffusion optical tomography with defined region geometry was used for this purpose. The Helmholtz equation in the frequency domain was transformed to integral form. The inverse problem was defined as an optimal shape design problem. The conversion of the imaging problem to an inverse task required the solution of the PDE by the BEM. Remesh in the optimisation process is not required in contrast to the solution of the MES. Two different approximations are compared, and the results of the research work are presented. The proposed method depends on the configuration of the object or objects within the region and the starting position and dimensions of the circular inclusion.

PL

W artykule przedstawiono aproksymację dwóch elementów brzegowych analizując numerycznych aspekty takiego przybliżenia. Wykorzystano do tego dyfuzyjną tomografię optyczną z określoną geometrią regionu. Równanie Helmholtza w dziedzinie częstotliwości przekształcono do postaci całkowej. Problem odwrotny został zdefiniowany jako problem projektowania optymalnego kształtu. Konwersja problemu obrazowania na zadanie odwrotne wymagała rozwiązania PDE przez BEM. Remesh w procesie optymalizacji nie jest wymagany w przeciwieństwie do rozwiązania MES. Porównano dwa różne przybliżenia. Proponowana metoda silnie zależy od konfiguracji obiektu lub obiektów wewnątrz regionu oraz pozycji wyjściowej i wymiarów wtrącenia kołowego.

4

Strength analysis of sandwich beams with linear elastic inner layer

Kimura Koichi

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 3

31--44

EN

A waterproof or water-resistant sandwich structure which consists of housing chassis and a gasket requires that gasket contact pressure, which depends on bolt axial force, is greater than the design minimum pressure on the entire circumference. However, it is also necessary that gasket contact pressure is smaller than the maximum permissible gasket pressure. If the maximum stress in chassis can be calculated from bolt axial force, gasket specifications and chassis stiffness, it is helpful for a design of such waterproof structures. In this study, chassis have been regarded as Bernoulli-Euler beams, and two simple numerical methods have thus been derived. Numerical results using the proposed method are sufficiently converged even in case that the number of partitions is about 10.

5

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.

6

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.

7

Taking account of the shift and inertia of rotation in problems of diagnostics of the spectra of critical forces mechanical systems

Orobey Viktor, Nemchuk Oleksii, Lymarenko Oleksandr, Piterska Varvara, Lohinova Liliia

Diagnostyka

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2021

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Vol. 22, No. 1

39--44

EN

Diagnostics of stability of the cores constructions, elements of the carrier system of the ship and port facilities, reduces to the definition of critical forces, excess which causes a transition of the system from one equilibrium state to another. Such a transition often leads to the destruction of the constructions or other forms of accidents, and therefore it is extremely undesirable and for practice it is important to knowledge of a specific spectrum of critical forces and their corresponding forms of loss of stability.

8

Diagnostics of the strength and stiffness of the loader carrier system structural elements in terms of thinning of walls by numerical methods

Orobey Viktor, Nemchuk Oleksii, Lymarenko Oleksandr, Piterska Varvara, Sherstiuk Olha, Romanov Oleksandr, Tkachuk Kateryna

Diagnostyka

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2021

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Vol. 22, No. 3

73--81

EN

Modern gantry cranes are an indispensable element of large industrial and transport enterprises. Port handling equipment is operated under conditions of complex spatial loading of varying intensity, as well as under conditions when the walls of structural elements are thinned in the crane carrier system. During the operation of handling equipment in ports, at construction sites, in machine-building industries, in addition to the external load, aggressive media act on the carrier system elements, which leads to various types of wear: corrosive, abrasive and mechanical. Monitoring of the state of handling equipment structures is a very important task of diagnosing the state of the material of elements of the carrier system of cranes and transporting machines. An important and urgent scientific and technical problem of taking into account the influence of aggressive environment on the stress-strain state of the metal structures of gantry cranes is considered. It is noted that during corrosion, a significant thinning of the walls of structural elements occurs. The safety of crane operation requires this factor to be taken into account. It is proposed to use modern numerical methods for this, i.e. the boundary element method (BEM) and the finite element method (FEM). The implementation of these methods is performed in the Matlab programming and modeling environment (BEM), and the FEM is used in the Ansys package. In accordance with the technologies of these methods, the design diagrams of the lower girders and the crane structure as a whole were formed. Exact models of strain of crane elements during transverse bending and constrained torsion are given. Calculations of the stressstrain state of the crane metal structures have been performed. On the basis of a preliminary field study, a numerical model is proposed for diagnosing the strength and stiffness characteristics of the carrier system of handling equipment using the BEM and FEM, which has never been used in the world. Conclusions are drawn about the influence of the thinning of the walls of metal structures on the values of normal and tangential stresses.

9

A meshless method for subsonic stall flutter analysis of turbomachinery 3D blade cascade

Prasad Chandra Shekhar, Šnábl Pavel, Pešek Luděk

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 6

art. no. e139000

EN

The analysis of subsonic stall flutter in turbomachinery blade cascade is carried out using a medium-fidelity reduced-order aeroelastic numerical model. The model is a type of field mesh-free approach and based on a hybrid boundary element method. The medium-fidelity flow solver is developed on the principle of viscous-inviscid two-way weak-coupling approach. The hybrid flow solver is employed to model separated flow and stall flutter in the 3D blade cascade at subsonic speed. The aerodynamic damping coefficient w.r.t. inter blade phase angle in traveling-wave mode is estimated along with other parameters. The same stability parameter is used to analyze the cascade flutter resistance regime. The estimated results are validated against experimental measurements as well as Navier-Stokes based high fidelity CFD model. The simulated results show good agreement with experimental data. Furthermore, the hybrid flow solver has managed to bring down the computational cost significantly as compared to mesh-based CFD models. Therefore, all the prime objectives of the research have been successfully achieved.

10

Potential-based boundary element method to calculate the hydrodynamic drift force on the floating cylinder

Ghafari Hamidreza, Motallebi Mohammad, Ghassemi Hassan

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 4

69--79

EN

This paper presents the calculation of the hydrodynamic drift force by using the potetial-based boundary element method (BEM). The potential theory and far-field wave drift forces solution will be described. The comparison of non-dimensional drift force for surge and heave motions are in good agreement between numerical and experimental data. The effect of different drafts and the radius of a cylinder on the drift forces (surge, heave and pitch) are presented and discussed.

11

Homogenization of plates with parallel cracks

Holek Mateusz, Fedeliński Piotr

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 1

31--41

EN

The paper presents an analysis of effective elastic properties of plates with parallel cracks using the finite element method (FEM) and the boundary element method (BEM). Rectangular plates with parallel or inclined cracks to the edges of plates were considered. Different distances between cracks and different angles of cracks were studied. The displacement and traction boundary conditions were applied and their influence on the accuracy of overall properties of cracked material was analysed. The results obtained by the FEM and the BEM were compared.

12

Finite and boundary element analysis of crack closure

Holek Mateusz, Fedeliński Piotr

Computer Methods in Materials Science

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2020

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Vol. 20, No. 1

7--13

EN

The aim of this work is an analysis of contact pressure between crack surfaces and its influence on effective elastic properties of materials with randomly distributed cracks. The finite element method (FEM) and the boundary element methods (BEM) are applied to the numerical analysis of materials, and the results are compared. Three numerical results are presented. The accuracy of contact pressure obtained by numerical solutions is verified for a single inclined crack in an infinite plate subjected to compression by comparison with an analytical solution. The influence of angle between cracks and directions of compressive loading on contact pressure for a branched crack in a rectangular plate is studied. The effective Young moduli and Poisson ratios for a rectangular plate with randomly distributed cracks are computed. The plate contains intersecting cracks which are in contact when the plate is subjected to tension or compression.

PL

Celem pracy jest analiza sił kontaktowych między powierzchniami pęknięć i ich wpływu na zastępcze własności sprężyste materiałów z losowo rozmieszczonymi pęknięciami. Zastosowano metodę elementów skończonych (MES) i metodę elementów brzegowych (MEB) w analizie numerycznej materiałów i porównano wyniki obliczeń. Przedstawiono trzy przykłady numeryczne. Zbadano dokładność sił kontaktowych wyznaczonych metodami numerycznymi przez porównanie z rozwiązaniem analitycznym dla pojedynczego ukośnego pęknięcia w ściskanej nieskończonej tarczy. Badano wpływ kąta między pęknięciami i kierunków obciążenia ściskającego na siły kontaktowe rozgałęzionego pęknięcia w tarczy prostokątnej. Obliczono zastępcze moduły Younga i współczynniki Poissona prostokątnej tarczy z losowo rozmieszczonymi pęknięciami. Tarcza zawierała przecinające się pęknięcia, które stykają się, gdy tarcza jest rozciągana lub ściskana.

13

Impact of nonlinear standing waves underneath a deck

Majewski D., Sulisz W.

Archives of Civil Engineering

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2020

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Vol. 66, nr 4

79--96

EN

A theoretical approach was applied to investigate the impact of nonlinear standing waves underneath a horizontal deck. A solution was achieved by applying a boundary element method. The model was applied to predict impact pressure underneath a deck. The results show that the wave impact is a very complex momentary process. The influence of initial boundary conditions, wave parameters and deck clearance on impact pressure are analysed. The analysis shows that purely sinusoidal waves of very small amplitude may cause an impact pressure several orders of magnitude higher than a pressure arising from typical applications of a linear wave theory. The analysis shows that all these non-intuitive outcomes arise from the complexity of a wave impact process and its enormous sensitivity to initial conditions what indicates serious difficulties in a reliable prediction of a wave impact for complex wave fields or other structures. Laboratory experiments were conducted to validate theoretical results.

PL

Zbadano proces uderzenia nieliniowych, stojących fal wodnych w spód poziomego pokładu. Wykorzystano podejście teoretyczne, którego rozwiązanie opiera się na Metodzie Elementów Brzegowych. Za pomocą modelu wyznaczono ciśnienia generowane uderzeniem fal wodnych. Wyniki wskazują na to, że proces jest bardzo złożony i ma charakter impulsowy. Analizowano wpływ początkowych warunków brzegowych, parametrów fali oraz wysokości zawieszenia pokładu nad powierzchnią spokoju na generowane ciśnienia. Wyniki pokazują, że nawet fale sinusoidalne, o małej amplitudzie mogą wywołać ciśnienia kilkukrotnie większe niż ciśnienia wynikające z typowych zastosowań teorii liniowej falowania. Pokazują również, że często nieintuicyjne wnioski wynikają ze złożoności procesu uderzenia fali i jego dużej czułości na początkowe warunki brzegowe. Wskazuje to na poważne trudności w wiarygodnym modelowaniu procesu uderzenia dla złożonych pól falowych oraz skomplikowanych układów geometrycznych budowli. Przeprowadzono również pomiary laboratoryjne w celu uzyskania danych do walidacji modelu numerycznego. Opracowany model zapewnia wyniki z dokładnością umożliwiającą zastosowanie go w zadaniach inżynierskich.

14

On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations

Rybarska-Rusinek L.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 1

69--76

EN

The paper presents a tool for accurate evaluation of high field concentrations near singular lines, such as contours of cracks, notches and grains intersections, in 3D problems solved the BEM. Two types of boundary elements, accounting for singularities, are considered: (i) edge elements, which adjoin a singular line, and (ii) intermediate elements, which while not adjoining the line, are still under strong influence of the singularity. An efficient method to evaluate the influence coefficients and the field intensity factors is suggested for the both types of the elements. The method avoids time expensive numerical evaluation of singular and hypersingular integrals over the element surface by reduction to 1D integrals. The method being general, its details are explained by considering a representative examples for elasticity problems for a piecewise homogeneous medium with cracks, inclusions and pores. Numerical examples for plane elements illustrate the exposition. The method can be extended for curvilinear elements.

15

An evaluation of the efficiency of endpoint control on the correction of scoliotic curve with brace : A case study

Karimi Mohammad, Rabczuk Timon, Luthfi Mauludin, Pourabbas Babak, Esrafilian Amir

Acta of Bioengineering and Biomechanics

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2019

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Vol. 21, no. 2

3--10

EN

The use of braces is one of the conservative treatment approaches recommended for scoliotic subjects. However, the main question posted here is how to improve the efficiency of braces to control the scoliotic curve or to decrease its progression. The aim of this study was to evaluate the efficiency of various boundary conditions (endpoint control) of brace on the correction of scoliotic curves. Method: CT scan images of a scoliotic subject, with double lumbar and thoracic curves, was used to produce 3d model of spine. The correction of spine (decrease in scoliotic curves) was determined following the use of transverse (lateral-to-medial direction) and the combination of transverse and vertical (upward-directed force, traction) forces on spine in Abaqus software. The effects of pelvic fixation (pelvic basket of a brace) on both sides (basket enclosed pelvic in both sides), on one side (basket enclosed the pelvis in only one side), and fixation of lumbar (part of the brace encircled the lumbar area) were evaluated in this study. Results: The results of this study showed that the effect of vertical forces (traction) was more than that of transverse force. Moreover, the combination of vertical and transverse forces on lumbar and thoracic curves correction was more than that of other conditions (only transverse forces). The best correction was achieved with lumbar fixation and with combination of vertical and transverse forces. Conclusions: The use the combination of vertical and transverse forces may be suggested to correct the scoliotic curve. Moreover, the efficiency of lumbar fixation in frontal plane seems to be more than pelvic fixation to correct scoliotic curve. The outputs of this study can be used to design new braces for scoliotic subjects.

16

Modelling of thermal damage process in soft tissue subjected to laser irradiation

Jasiński M.

Journal of Applied Mathematics and Computational Mechanics

|

2018

|

Vol. 17, nr 2

29--41

EN

The numerical analysis of thermal damage process proceeding 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 the diffusion equation is taken into account. The tissue is regarded as a homogeneous domain with perfusion coefficient and effective scattering coefficient treated as dependent on tissue injury. At the stage of numerical realization, the boundary element method and the finite difference method have been used. In the final part of the paper the results of computations are shown.

17

Numerical calculation of singular integrals for different formulations of Boundary Element

Sikora J., Polakowski K., Pańczyk B.

Przegląd Elektrotechniczny

|

2017

|

R. 93, nr 11

181--185

EN

This paper presents a method of regularization for the numerical calculation of singular integrals used in different formulations of Boundary Element Method. The singular integrals arise when elements of order higher than zero are used for discretization. Very often in the Diffusive Optical Tomography for infant head modeling, triangular or square curvilinear boundary elements of the second order are used hence, our interest in the subject of effective and accurate calculation of singular integrals. Even for the classical formulation of BEM such a problem is extremely difficult. Some authors believe that the practical application possesses only flat triangular boundary elements of zero-order, and although there is some truth in this statement, Diffusion Optical Tomography elements of the second order show a significant advantage. This issue becomes even more interesting when we deal with the Galerkin BEM formulation offering the possibility of symmetrisation of the main matrix, which has fundamental importance for inverse problems. This matter becomes critical when we start to consider the Fourier BEM formulation, introduced by Duddeck. His approach provides the possibility of a solution in the case that there is no fundamental solution. The light propagation, which is described by the Boltzmann equation is such a case. Currently and most commonly, the Boltzman equation is approximated by the diffusion equation in strongly light scattering media. In the authors opinion, the problem of numerical integration of singular integrals has not yet been fully exhausted in the classic and Galerkin BEM formulation but the Fourier BEM formulation still expects the proposals of the solutions. Such an offer we would like to present in this paper.

PL

W artykule przedstawiono metodę regularyzacji numerycznego obliczania całek osobliwych stosowanych w różnych rozwiązaniach Metody Elementu Brzegowego. Całki osobliwe powstają, gdy do dyskretyzacji zostaną użyte elementy wyższego rzędu niż zero. Bardzo często w dyfuzyjnej tomografii optycznej użytej do modelowania głowy dziecka używa się trójkątnych lub kwadratowych krzywoliniowych elementów brzegowych drugiego rzędu i dlatego nasze zainteresowanie dotyczy tematu skutecznego i dokładnego obliczenia całek osobliwych. Nawet w przypadku klasycznego sformułowania MEB ten problem jest wyjątkowo trudny. Niektórzy autorzy uważają, że praktyczne zastosowanie mają tylko płaskie trójkątne elementy brzegowe zerowego rzędu i chociaż w tym stwierdzeniu jest trochę prawdy, to dyfuzyjna tomografia optyczna stosując elementy brzegowe drugiego rzędu wykazuje znaczącą przewagę. Kwestia ta staje się jeszcze bardziej interesująca, gdy mamy do czynienia ze sformułowaniem Galerkina MEB, oferującym możliwość użycia symetrycznej macierzy współczynników, która ma fundamentalne znaczenie przy rozwiazywaniu problemów odwrotnych. Ta kwestia staje się krytyczna, gdy zastosujemy sformułowanie Fouriera w MEB, wprowadzoną przez Duddecka. Jego podejście daje szanse rozwiązania w przypadku braku rozwiązania fundamentalnego. Rozchodzenie światła, opisane przez równanie Boltzmanna jest takim przypadkiem. Obecnie, równanie Boltzmana jest przybliżane równaniem dyfuzji w ośrodkach silnie rozpraszających światło. W opinii autorów, problem numerycznego całkowania całek osobliwych nie został w pełni wyczerpany w klasycznej formule MEB i dla sformułowania Galerkina, ale formuła MEB Fouriera nadal oczekuje nowych rozwiązań. Propozycję takiego rozwiązania chcielibyśmy zaprezentować w tym artykule.

18

Static and dynamic stress intensity factors of branched cracks

Fedeliński P., Holek M.

Modelowanie Inżynierskie

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2017

|

T. 34, nr 65

23--28

EN

The boundary element method (BEM) is applied to analysis of static and dynamic stress intensity factors (SIF) of branched cracks. The numerical solution is obtained by discretization of external boundaries and crack surfaces. The problem of coincident crack boundaries is solved by the dual BEM in which for nodes on crack surfaces simultaneously the displacement and the traction boundary integral equations are applied. The dynamic problem is solved by using the Laplace transform method. Static stress intensity factors (SIF) are computed by the path independent J-integral and dynamic SIF by the crack opening displacement (COD) method. Numerical examples of a single crack and two interacting branched cracks in rectangular plates are presented. The influences of dimensions and shapes of voids in the centers of the branched cracks and the orientations and distances between two interacting cracks on SIF are analyzed.

PL

Zastosowano metodę elementów brzegowych (MEB) do analizy statycznych i dynamicznych współczynników intensywności naprężeń (WIN) pęknięć rozgałęzionych. Rozwiązanie numeryczne otrzymano w wyniku dyskretyzacji brzegów zewnętrznych tarczy i krawędzi pęknięć. Zastosowano sformułowanie dualne MEB do analizy pokrywających się krawędzi pęknięcia, w którym stosuje się jednocześnie dla węzłów pęknięcia brzegowe równanie całkowe przemieszczeń i sił powierzchniowych. Zagadnienie dynamiczne analizowano metodą transformacji Laplace’a. Statyczne współczynniki intensywności naprężeń (WIN) obliczono za pomocą J-całki niezależnej od konturu całkowania, a dynamiczne WIN na podstawie rozwarcia krawędzi pęknięcia. Przedstawiono przykłady numeryczne pojedynczego pęknięcia i dwóch oddziałujących pęknięć rozgałęzionych w tarczach. Badano wpływ wielkości i kształtu pustek w środku pęknięcia rozgałęzionego oraz orientacji i odległości między dwoma pęknięciami na WIN.

19

A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method

Freus K., Freus S.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 2

67--76

EN

The aim of this paper is to create an optimal shape of the 2D domain that is described by the Non-Uniform Rational B-Splines (NURBS) curves. This work presents a method based on the topological derivative for the Laplace equation that determines the sensitivity of a given cost function to the change of its topology. As a numerical approach, the boundary element method is considered. To check the effectiveness of the proposed approach, the example of computations was carried out.

20

Low frequency sloshing analysis of cylindrical containers with flat and conical baffles

Gnitko V., Naumemko Y., Strelnikova E.

International Journal of Applied Mechanics and Engineering

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2017

|

Vol. 22, no. 4

867--881

EN

This paper presents an analysis of low-frequency liquid vibrations in rigid partially filled containers with baffles. The liquid is supposed to be an ideal and incompressible one and its flow is irrotational. A compound shell of revolution is considered as the container model. For evaluating the velocity potential the system of singular boundary integral equations has been obtained. The single-domain and multi-domain reduced boundary element methods have been used for its numerical solution. The numerical simulation is performed to validate the proposed method and to estimate the sloshing frequencies and modes of fluid-filled cylindrical shells with baffles in the forms of circular plates and truncated cones. Both axisymmetric and non-axisymmetric modes of liquid vibrations in baffled and un-baffled tanks have been considered. The proposed method makes it possible to determine a suitable place with a proper height for installing baffles in tanks by using the numerical experiment.