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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.
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.
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.
4
Content available Homogenization of plates with parallel cracks
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.
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.
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.
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.
8
Content available Impact of nonlinear standing waves underneath a deck
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.
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.
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.
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.
EN
One of the most effective designs to control the road traffic noise is the T-shaped barrier. The aim of this study was to examine the performance of T-shape noise barriers covered with oblique diffusers Rusing boundary element method. A 2D simulation technique based on the boundary element method (BEM) was used to compute the insertion loss at the center frequency of each one-third octave band. In designer barriers, the top surface of the T-shaped noise barriers was covered with oblique diffusers. The width and height of the barrier stem and the width of its cap were 0.3, 2.7, and 1 m, respectively. Angles of the oblique diffusers were 15, 30, and 45 degrees. The oblique diffusers were placed on the top surface with two designs including same oblique diffusers (SOD) and quadratic residue oblique diffusers (QROD). Barriers considered were made of concrete, an acoustically rigid material. The barrier with characteristics of QROD, forward direction, and sequence of angles (15, 30, and 45 degrees) had the greatest value of the overall A-weighted insertion loss equal to 18.3 to 21.8 dBA at a distance of 20 m with various heights of 0 to 6 m.
EN
An isogeometric boundary element method is applied to simulate wave scattering problems governed by the Helmholtz equation. The NURBS (non-uniform rational B-splines) widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The singular integrals existing in Burton-Miller formulation are evaluated directly and accurately using Hadamard’s finite part integration. Fast multipole method is applied to accelerate the solution of the system of equations. It is demonstrated that the isogeometric boundary element method based on NURBS performs better than the conventional approach based on Lagrange basis functions in terms of accuracy, and the use of the fast multipole method both retains the accuracy for isogeometric boundary element method and reduces the computational cost.
EN
The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of certain analytic functions. In addition, with the help of it, it is possible to convert the volume integrals included in the equation into contour integrals, which, in turn, will allow the use of the method of boundary elements. For modelling of solids with thin inhomogeneities, a coupling principle for continua of different dimensions is used. Applying the theory of complex variable functions, in particular, Cauchy integral formula and Sokhotski–Plemelj formula, the Somigliana type boundary integral equations are constructed for thermoelastic anisotropic half-space. The obtained integral equations are introduced into the modified boundary element method. A numerical analysis of the influence of boundary conditions on the half-space boundary and relative rigidity of the thin inhomogeneity on the intensity of stresses at the inclusions is carried out.
EN
The barium titanate material is the most intensively studied perovskite material due to its wide use in the ceramic industry. Barium titanate is also technologically important material owing to its ferroelectric behaviour at and above room temperature. The paper presents an effective implementation of boundary element multiscale method in analyzing of fracture of piezoelectric ceramics. This method can be easily used to get a better understanding of damage mechanism in the ceramic materials in order to improve the constitutive models and to support the future design of those materials. In this method the relation of boundary element method for obtaining traction is presented. The main advantage of boundary element method is the reduction of the dimensionality of the problem. Boundary element method becomes very attractive in cases of numerically complex problems that are computationally expensive.
16
Content available remote Static and dynamic stress intensity factors of branched cracks
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.
EN
In the current study, the Laplace equation is solved for rectangular and elliptical computational domains by using the boundary element method (BEM). For this accomplishment, 120 different aspect ratios in a rectangular and elliptical computational domains are designed. The Dirichlet and Neumann boundary conditions are used respectively for a rectangular and elliptical domains. Also, the Gaussian quadrature integral method is applied to solve the influence coefficient matrix in BEM. To assess a different aspect ratio on the potential solution, two different measurement positions are intended. According to our finding, with an increase of the aspect ratio, the potential value is increased for both rectangular and elliptical domains. However, a potential increment with aspect ratio enhancement is more visible in the elliptical domain.
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.
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.
EN
In this paper, we investigate the inverse problem for the electric field so-called copper mine problem. In general, this task assumes detection of all air gaps. Gaps are localised above ceiling in a copper mine. Such task can be considered as application of the electrical impedance tomography. In order to solve forward problem there was used the boundary element method or the finite element method. The inverse problem is based on the level set method. There was considered extension of boundary element method (BEM). For simplicity zero order approximation has been chosen. The BEM has been connected with the infinite boundary elements. Hence, open domain problems with infinite boundary curves can be analysed. For such domain, we have solved the Dirichlet problem for two-dimensional Laplace’s equation. The proposed numerical model has been verified.
PL
W tym artykule przyjrzymy się problemowi odwrotnemu dla pola elektrycznego na tak zwanym problemie kopalni miedzi. Głównym zadaniem w tym zagadnieniu jest wykrycie szczelin powietrznych, które są zlokalizowane w stropie kopalni. Takie zadanie można rozwiązać za pomocą elektrycznej tomografii impedancyjnej. W celu rozwiązania zagadnienia prostego można użyć metody elementów brzegowych (MEB) lub metody elementów skończonych. Zagadnienie odwrotne zostało oparte na metodzie zbiorów poziomicowych. Dla uproszczenia zostały zastosowane elementy zerowego rzędu. Metoda elementów brzegowych została rozszerzona o elementy nieskończone. Stąd problemy otwarte domeny z nieskończonymi brzegami mogą być analizowane. Dla takiej domeny, musimy rozwiązać zagadnienie Dirichleta dla równania dwuwymiarowy Laplace'a. Zaproponowany model numeryczny został zweryfikowany.
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