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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

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.

9

Transient dynamic analysis of functionally graded micro-beams considering small-scale effects

Eshraghi I., Dag S.

Archives of Mechanics

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2021

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Vol. 73, nr 4

303--337

EN

A domain-boundary element method, based on modified couple stress theory, is developed for transient dynamic analysis of functionally graded micro-beams. Incorporating static fundamental solutions as weight functions in weighted residual expressions, governing partial differential equations of motion are converted to a set of coupled integral equations. A system of ordinary differential equations in time is obtained by domain discretization and solved using the Houbolt time marching scheme. Developed procedures are verified through comparisons to the results available in the literature for micro- and macro-scale beams. Numerical results illustrate elastodynamic responses of graded micro-beams subjected to various loading types. It is shown that metal-rich micro-beams and those with a smaller length scale parameter ratio undergo higher displacements and are subjected to larger normal stresses.

10

Acoustic Attenuation Performance Analysis and Optimisation of Expansion Chamber Coupled Micro-perforated Cylindrical Panel Using Response Surface Method

Alisah Mohamad Izudin, Ooi Lu Ean, Ripin Zaidi Mohd, Yahaya Ahmad Fadzli, Ho Kelvin

Archives of Acoustics

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2021

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Vol. 46, No. 3

507--517

EN

This paper describes the boundary element method (BEM) and the experimental and optimisation studies conducted to understand the potential of expansion chamber coupled micro-perforated cylindrical panel (MPCP) in enhancing the acoustic attenuation for in-duct noise control issues. Owing to the complex structure of the MPCP and to achieve the correct prediction of acoustic attenuation, BEM is adopted on the basis of the Simcenter 3D software to compute the sound transmission loss (TL), As the MPCP is cylindrical in shape with numbers of sub-milimeter holes, additive manufacturing-based 3D printing is utilised for the model prototyping to reduce current design limitation and enable fast fabrication. The TL measurement-based two-load method is adopted for model validation. Subsequently, parametric studies of the MPCP concerning the perforation hole diameter, perforation ratio and depth of air space are carried out to investigate the acoustic performance. Optimisation via response surface method is used as it allows for evaluating the effects of multiple parameters as required in this study. The model validation result shows that the error between the BEM and the measured values is relatively small and shows good agreement. The R-square value is 0.89. The finding from the parametric studies shows that a wider peak attenuation can be achieved by reducing the perforation hole diameter, and one way to increase the TL amplitude is by increasing the air cavity depth. Finally, the optimised MPCP model is adopted to the commercial vacuum cleaner for verification. The sound pressure level of the vacuum cleaner is significantly attenuated within the objective frequency of 1.7 kHz.

11

Gas flow simulation in the working gap of impulse gas-barrier face seal

Kuznetsov Eduard, Nahornyi Volodymyr, Krenický Tibor

Management Systems in Production Engineering

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2020

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nr 4 (28)

298--303

EN

Numerical simulation method of the working process of a centrifugal unit contactless face impulse seal is proposed. A seal functioning physical model was created. Its operation key aspects that are not taken into account in the traditional methods of calculating contactless impulse seals are identified. A numerical simulation of seal working process based on the Reynolds equation solution for the medium vortex-free motion in the gap between moving surfaces is proposed. Hypothesis that simplify the equation's numerical solution for the face impulse seal is formulated. The numerical solution is obtained using the boundary element method. Based on the obtained numerical solution, the distribution of the working medium pressure field in the seal gap is simulated.

12

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.

13

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.

14

Liquid vibrations in cylindrical tanks with and without baffles under lateral and longitudinal excitations

Strelnikova E., Kriutchenko D., Gnitko V., Tonkonozhenko A.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 3

117--132

EN

The paper is devoted to issues of estimating free surface elevations in rigid cylindrical fluid-filled tanks dunder external loadings. The possibility of baffles installation is provided. The liquid vibrations caused by lateral and longitudinal harmonic loadings are under consideration. Free, forced and parametrical vibrations are examined. Modes of the free liquid vibrations are considered as basic functions for the analysis of forced and parametric vibrations. The modes of the free liquid vibrations in baffled and un-baffled cylindrical tanks are received by using single-domain and multi-domain boundary element methods. Effects of baffle installation are studied. The problems of forced vibrations are reduced to solving the systems of second order ordinary differential equations. For parametric vibrations the system of Mathieu equations is obtained. The numerical simulation of free surface elevations at different loadings and baffle configurations is accomplished. Beat phenomena effects are considered under lateral harmonic excitations. The phenomenon of parametric resonance is examined under longitudinal harmonic excitations.

15

Application of 1-D and 2-D discrete wavelet transform to crack identification in statically and dynamically loaded plates

Knitter-Piatkowska Anna, Guminiak Michał

Engineering Transactions

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2020

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Vol. 68, iss. 2

137--157

EN

The paper presents the problem of damage detection in thin plates while considering the influence of static and dynamic characteristics, especially with regard to the modes of vibration as well as the excitation by static loads. The problem of Kirchhoff plate bending is described and solved by the Boundary Element Method (BEM). Rectangular plates supported on boundary or plates supported on boundary and resting on the internal columns are examined. A defect is introduced by the additional edges forming a crack in the plate domain. The analyses of static and dynamic structural responses are carried out with the use of Discrete Wavelet Transform (DWT). Signal decomposition according to the Mallat pyramid algorithm is applied. To obtain a more adequate input function subjected to DWT the white noise disturbing the signal is considered together with the structural response. In the dynamic experiments the plate undergoes vibrations similar to natural modes. The measured variables are static deflections and vertical displacement amplitudes. All of them are established at internal collocation points distributed alongside the line parallel to selected plate edge.

16

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.

17

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.

18

Water entry of a wedge into waves in three degrees of freedom

Sun Shi Yan, Chen Hai Long, Xu Gang

Polish Maritime Research

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2019

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nr 1

117--124

EN

The hydrodynamic problem of a two-dimensional wedge entering into a nonlinear wave in three degrees of freedom is investigated based on the incompressible velocity potential theory. The problem is solved through the boundary element method in the time domain. To avoid numerical difficulties due to an extremely small contact area at the initial stage, a stretched coordinate system is used based on the ratio of the Cartesian system in the physical space to the distance travelled by the wedge in the vertical direction. The mutual dependence of body motion and wave loading is decoupled by using the auxiliary function method. Detailed results about body accelerations, velocities and displacements at different Froude numbers or different waves are provided, and the mutual effect between body motion and wave loading is analysed in depth.

19

A practical approach to the assessment of waterjet propulsion performance: the case of a waterjet-propelled trimaran

Zhang Lei, Zhang Jia-ning, Shang Yu-chen, Dong Guo-xiang, Chen Wei-min

Polish Maritime Research

|

2019

|

nr 4

27--38

EN

To obtain a reasonable evaluation of the performance of waterjet propulsion at the design stage, a semi-theoretical and semi-empirical method is used to calculate the fundamental parameters of waterjet propulsion performance using an iterative approach. To calculate the ship’s resistance, a boundary element method based on three-dimensional potential flow theory is used to solve the wave-making resistance, and an empirical approach is used to evaluate the viscous resistance. Finally, the velocity and pressure of the capture area of the waterjet propulsion control volume are solved based on turbulent boundary layer theory. The iteration equation is established based on the waterjet-hull force-balance equation, and the change in the ship’s attitude and the local loss of the intake duct are considered. The performance parameters of waterjet propulsion, such as resistance, waterjet thrust, thrust deduction, and the physical quantity of the control volume, are solved by iteration. In addition, a PID-controlled free-running ship model is simulated using the RANS CFD method as a comparison. We apply the proposed approach and the RANS CFD method to a waterjetpropelled trimaran model, and the simulation process and the results are presented and discussed. Although there are some differences between the two methods in terms of the local pressure distribution and thrust deduction, the relative error in the evaluation results for the waterjet propulsion performance is generally reasonable and acceptable. This indicates that the present method can be used at the early stages of ship design without partial information about the waterjet propulsion system, and especially in the absence of a physical model of the pump.

20

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

|

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.