Numerical Boundary Element Method Research Articles

A new insight into the analysis of plane elasticity with coupling of numerical manifold and boundary element methods

In this research, a combination of the numerical manifold method (NMM) and boundary element method (BEM) is presented for solving plane elasticity problems to benefit from the advantages of both methods. For this goal, the domain of the problems is divided into two regions, each region is analyzed separately, and finally, equilibrium and compatibility conditions are controlled in the interface by the iteration method. 1D quadratic boundary elements and 2D quadratic, cubic and quartic ones in the form of triangular shapes are utilized in the boundary element and manifold methods, respectively. The proposed method is verified by calculating the displacements and stresses resulting from the application of static loads in five different numerical problems. Comparison of the numerical results shows that the suggested method is very efficient and accurate.

Surface Gravity Wave Interaction With a Submerged Composite Wavy Porous Plate Attached to a Vertical Wall

Abstract The hydrodynamic performance of composite wavy submerged porous plate attached to a wall is investigated using numerical method multi-domain boundary element method in the linearized water wave theory in which wave past the porous barriers are modeled using Darcy’s law. Effect of the presence of wall on the hydrodynamic parameters like reflection coefficient, dimensionless wave height, wave force and moment acting on the composite wavy porous structure, and horizontal force on the vertical rigid wall is analyzed for various physical parameters like the number of ripple wavelength, structural porosity, submergence depth, and relative amplitude of composite wavy porous plate. The study demonstrates that the efficiency of hydrodynamic characteristics of the composite wavy porous plate attached to the wall is better compared to a horizontal porous plate attached to the wall of the same applicability conditions (around 27% reduction in wave reflection). Moreover, optimum performance of this kind of breakwater system is increased by considering the lower submergence, higher relative ripple amplitude, appropriate relative amplitude, and suitable moderate porosity of the structure in the range of wavenumber 1 < k0h < 5. Dimensionless wave height, horizontal load on the impermeable wall are reduced to zero, while substantial minimization of vertical load on the structure with suitable consideration of the other influencing parameters of porosity Gp = 0.3, relative amplitude Ds/h = 0.1, relative ripple wavelength m > 3, and submergence depth h1/h = 0.3. The present structural arrangement will be useful for attenuating wave effects on the sea wall.

A Numerical Framework for Geometrically Nonlinear Deformation of Flexoelectric Solids Immersed in an Electrostatic Medium

Abstract A numerical formulation coupling finite and boundary element methods is developed to analyze the mechanical deformation and electric polarization of flexoelectric solids experiencing geometrically nonlinear deformation. The proposed method considers the electrical interactions among flexoelectric solids, electric charges, and their surrounding medium. First, a higher-order gradient theory is proposed based on the skew-symmetric couple-stress model to analyze the geometrically nonlinear deformation of flexoelectric solids. This theory includes a total Lagrangian weak form that satisfies linear momentum conservation, angular momentum conservation, and Gauss’s law. Based on the proposed theory, a finite element is developed using basis functions that satisfy C1 continuity. Second, a coupled formulation is developed to consider the electrical interactions among solids, electric charges, and their surrounding medium. In this formulation, conventional boundary elements are adopted to account for the electrostatic surroundings. Besides, electric boundary conditions are naturally imposed on solid boundaries according to the electrical interactions between solids and their electrostatic surroundings. Finally, the proposed method is validated via the comparisons of the numerical results with closed-form solutions.

Modelling wide perforated breakwater with horizontal slits using Hybrid-BEM method

A hybrid boundary element method has been developed to efficiently solve the hydrodynamic response of a wide perforated breakwater with arbitrary hull geometry and multiple horizontal slits. The fluid subdomains inside the slits were considered as rectangular and analytical eigenfunctions of the slit area were applied to derive the boundary condition at the interface. The involvement of analytical solutions in the numerical boundary element method (BEM) is the novelty of the present approach. The 2D numerical solution was verified with analytical solution of perforated rectangular breakwater to show the validity of the proposed hybrid BEM. Parametric studies have been performed to study the effect of porosity, position and layout of the slits. It has been found that the slits generally reduce the diffracted and radiation potentials, and would be most effective when placed near the free surface. The approach was also extended to 3D channel flow and the results were calibrated against an experimental study performed in the wave flume.

МЕТОДИКА РОЗРАХУНКУ ФУНДАМЕНТІВ В ЩІЛЬНОМУ КОТЛОВАНІ МЕТОДОМ ГРАНИЧНИХ ЕЛЕМЕНТІВ

The main mission of civil engineer is to ensure he reliability of the structure with maximum efficiency of time, materials and energy. In construction, everything must be provided in the design workshop - both strength and economic feasibility. Balancing on the "edge of the abyss" requires a precise mathematical apparatus. The modern mathematical apparatus of soil mechanics is based on the solutions of the theory of elasticity and the theory of limit equilibrium. In this case, the calculation of the bases is carried out from the conditions of purely elastic connection and the ultimate loads are determined without connection with deformations. Most of the elastic-plastic deformation - from the end of the elastic stage to the loss of stability is not covered by the calculation models. At the same time, the reserves of the elastic-plastic zone allow to increase the load on the foundation, provided that the subsidence of the elastic stage does not yet reach the maximum allowable value for this structure. The boundary element method (BEM) allows to solve problems of this kind. The main disadvantage of foundations on a natural basis is the complexity of its manufacture and high material consumption. These shortcomings can be eliminated by building foundations in cavities of a predetermined shape, which are formed in the soil. These include foundations in compacted ditches, which are arranged in wells with expansion at the bottom. The soil retains its full-fledged composition, so that the work includes a side surface that receives part of the vertical load and provides significant resistance to horizontal forces. The paper presents a method of integration of a mathematical model of behavior under load of foundations in a compacted pit with a numerical BEM. A theoretical study presents the effect of the addition of sand-gravel mixture on the bottom of the compacted pit on the bearing capacity of pyramidal piles.

Efisiensi Model Mesh Kasus Deteksi Simulasi Korosi Beton Bertulang Menggunakan Metode Axisymmetric Mesh Problem

In this study, a computational numerical modelling for corrosion simulation in reinforcing steel is developed. The corrosion simulation using Boundary element Method (BEM) and focusing for cylindrical reinforced concrete (RC). The main problem is high performance computer was required for the reinforced concrete corrosion simulation. Therefore, main purpose of this study is to reduce the needs of high-performance computer during the corrosion simulation. For the purpose, axisymmetric computational problem was integrated to the numerical BEM that considered able to reduce the computational effort. On the analysis process, the whole axial RC structures column was modeled by Laplace equation. The boundary condition for the corroded and non-corroded areas on the reinforcing steel (rebar) were represented by their established polarization curve. The Laplace equation was solved by BEM, thereby the potential on the structure can be analyzed. The simulation results show the similar potential distribution between BEM computational modelling by triangle element mesh and improvement BEM using axisymmetric element mesh problem. The simulation shows a significant differences, thereby the corrosion simulation using axisymmetric element mesh problem significantly reduces the computer effort in term of time-consuming and computer effort for the simulation. Thus, the improvement of the axisymmetric modelling for BEM becomes a powerful method for reducing the computational effort in term of cylindrical reinforcing steel corrosion simulation. Keywords— corrosion modelling, axisymmetric, BEM, cylindrical column, reinforced concrete

Wave energy dissipation of a submerged horizontal flexible porous membrane under oblique wave interaction

An analytical model associated with oblique wave interaction with a submerged horizontal flexible porous membrane is presented under the assumption of linearized small amplitude and structural response in finite water depth. The expansion formula associated with Green's functions using fundamental source potentials based on reduced wave equation is derived. Further, a physical problem of oblique wave interaction with a moored finite horizontal submerged flexible porous membrane on wave energy dissipation is illustrated to analyse the different design parameter based on matched eigenfunction expansion method. The roots of the complex dispersion relation are obtained by applying a perturbation scheme and the accuracy of the numerical computation is demonstrated by analysing the convergence of reflection, transmission, and dissipation coefficients for different spring stiffness and porous-effect parameters. Further, the correctness of the present solution is checked by validating against analytical, numerical boundary element method, and experimental data available in the literature. The effects of spring stiffness, porous-effect parameter, submergence depth, structural length, angle of incidence, and flow pattern on reflection, transmission, dissipation coefficients, membrane deflection, vertical force, and contour plots are analysed. The present analysis on different design parameters will be helpful for better understanding for engineers to design as an effective breakwater/wave absorber.

Calculation of band structures of a phononic crystal within a waveguide in 3D with cubic inclusions using a Periodic Green’s Function Method

The Phononic Crystals have generated a growing scientific interest as a means to control the dispersion of waves in various technological applications such as telecommunications. In particular, Phononic Crystal Waveguides are composed of periodic distributions of dispersers immersed in a propagation medium and, designed by an arrangement with dimensions and periods comparable to the wavelength. These crystals have properties that give them the ability to guide acoustic waves efficiently. In this paper, we present a numerical Boundary Element Method, which requires the use of a Periodic Green’s Function. This method allows to calculate the band structure of phononic crystals in two- and three-dimensions. In particular, the band structure is calculated for a waveguide formed by two flat, and parallel plates that involve a two-dimensional periodic arrangement of cubic inclusions. All surfaces involved are considered acoustic hard surfaces. The system considered, in addition to being a waveguide is in itself a phononic crystal, so that this type of systems present an alternative to manufacture to phononic crystal that can act as a phononic crystal and as an acoustic waveguide. These properties present some interest from a technological point of view.

Fracture Analysis for Torsion Problems of a Deep Sea Spar Platform Main Body

Attention should be paid to variations of crack effects on the stability of offshore structure during building and using. The body of the deep-water Spar platform is the important support of the whole structure, once produced edge cracks in certain parts, the overall structure of the platform would be severely affected. By using boundary integral equations which applied to the edge cracks of the cylinder, this paper discussed singularity of the crack tip; then used the boundary element numerical calculation method to divide the crack boundary into many units, used different interpolation functions to calculate the stress intensity factor of crack tip; Finally, calculated torsional fracture of spar platform with edge cracks under different wind loads, got the allowed maximum crack length of Spar’s body with cracks under different wind scale. It was concluded that used the boundary element calculation method was practical in ocean engineering.

Numerical modelling to predict fracturing rock (Thanet chalk) due to naturally occurring faults and fluid pressure

Outcrop mapping of a chalk cliff and wavecut platform in Thanet, Southeast England show a complex fracture pattern that seems to be controlled by meso-scale strike-slip faults within the chalk. The response of these faults to changes to in situ stress and fluid pressure is thought to control the nucleation and propagation of fractures in the chalk. In this study the DEM (Discrete Element Method) technique has been employed as a follow up to previous field and numerical (boundary and finite element method) investigations to ascertain the role of the faults in the initiation and nucleation of fractures The role of fluid pressure, in-situ stress, and fault geometry are recognised as focal factors. The generation of localised areas of tensile stresses due to fluid pressure and stress perturbations have been shown to cause the initiation of fractures around the fault bends. For releasing bends, localised tensile stresses tend to occur along the central segment of the fault bend, whereas for restraining bends, tensile stresses are more likely to develop on the outer edges of the fault bend. The dissimilarity in the fracturing process due to differences in the geometry of pre-existing faults demonstrates the significance of both fault geometry and fluid behaviour in controlling fracturing.

Characterization and modeling of the acoustic field generated by a curved ultrasound transducer for non-contact structural excitation

Conventional excitation techniques typically use an impact hammer, piezoelectric actuator, or mechanical shaker excitation for experimental modal testing. However, the use of these devices may be challenging if accurate high-frequency dynamic measurements on small or lightweight structural parts have to be performed. To overcome these problems, the high-frequency radiation force generated by focused ultrasonic transducers (FUTs) can be used. This approach has shown potential to be used as a non-contact method for modal excitation of small-sized or flexible structures such as MEMS devices, small turbine blades, integral blade rotors (IBR), and biological structures. However, the sound radiation in the air of these ultrasonic transducers and the resulting radiation force imparted onto a structure is not well understood and critically crucial for performing accurate modal analysis and system identification. In this research, the technical development of ultrasound radiation pressure mapping and simulation is presented. Starting from the calibrated sound pressure fields generated by the spherically FUT, driven by amplitude modulated signals, the dynamic focused ultrasound radiation force is modeled and estimated. The acoustic pressure field of a FUT operating in the air is measured and used for validating the accuracy of a new numerical boundary element method (BEM) model in predicting the direct acoustic force generated in the high-frequency range (i.e., 300–400 kHz). The results show that an excellent agreement is found regarding both the pressure profile and amplitude. Pressure fields up to 1200 Pa can be generated as the transducer is driven at 400 kHz. Experiments also prove that the FUT is capable of creating a focal spot size of nearly 3 mm in diameter. To finish, the FUT's dynamic focused ultrasound radiation force is quantified and could be used to quantify a force-response relationship for experimental modal analysis purposes.

A theoretical procedure for the stress state assessment of hyper-static crankshafts

Crankshafts with many rods and crankpins for mechanical and industrial applications can be designed with first-order-approximation theoretical procedures in the literature. Numerical boundary element method (BEM) or finite element method (FEM) procedures can be used, with the latter models having a 3D tetrahedral, wire beam or hexahedral finite elements. To the best of the author's knowledge, the literature does not contain accurate evaluations of hyper-static reactions at the restraints of a crankshaft with four crankpins and five supports. The principle of virtual work is implemented to allow calculation of the reactions at the bearings of the shaft and to determine the internal actions (bending, torsion, shear and axial force) for each section of the shaft. The developed procedure does not give better results than a numerical BEM or 3D FEM code, but it is less expensive and less time consuming when implemented in a mathematical commercial code. Furthermore, the procedure gives results that have a better approximation with respect to the theoretical literature models. The theoretical model was validated through comparison with the results of a finite-element linear beam model developed using a commercial FEM code.

APPLICATION OF THE METHOD OF BOUNDARY INTEGRAL EQUATIONS FOR NON-STATIONARY PROBLEM OF THERMAL CONDUCTIVITY IN AXIALLY SYMMETRIC DOMAIN

The article considers the non-stationary initial-boundary problem of thermal conductivity in axially symmetric domain in Minkowski space, formulated as equivalent boundary integral equation. Using the representation of the solution in the form of a Fourier series expansion, the problem is reformulated as an infinite system of two-dimensional singular integral equations regarding expansion coefficients. The paper presents and investigates the explicit form for fundamental solutions used in the integral representation of the solution in the domain and on the border. The obtained results can be used in the construction of efficient numerical boundary element method for estimation of structures behavior under the influence of intense thermal loads in real-time.

Perturbation theory for asymmetric deformed microdisk cavities

In an article by Dubertrand et al. [Phys. Rev. A 77, 013804 (2008)] the perturbation theory for slightly deformed optical microcavities with a mirror-reflection symmetry was developed. However, in real experiments such a mirror-reflection symmetry is often not present either intended or unintended via production tolerances. In this paper we therefore extended the perturbation theory to asymmetric boundary deformations. Consequently, we are able to describe interesting non-Hermitian phenomena like copropagation of optical modes in the (counter-)clockwise direction inside the cavity. The derived analytic formulas are demonstrated at two generic boundary shapes, the spiral and the double-notched circle where a good agreement to the numerical boundary element method is observed.

Analysis on the Performance of Deckwetness of Sandglass-type and Cylindrical Floating Bodies

In this paper, the influence of the second-order slowly varying loads on the estimation of deck wetness is studied. A series of experiments related to classic cylindrical and new sandglass-type Floating Production, Storage, and Offloading Unit (FPSO) models are conducted. Due to the distinctive configuration design, the sand glass type FPSO model exhibits more excellent deck wetness performance than the cylindrical one in irregular waves. Based on wave potential theory, the first-order wave loads and the full quadratic transfer functions of second-order slowly varying loads are obtained by the frequency-domain numerical boundary element method. On this basis, the traditional spectral analysis only accounting for the first-order wave loads and time-domain numerical simulation considering both the first-order wave loads and nonlinear second-order slowly varying wave loads are employed to predict the numbers of occurrence of deck wetness per hour of the two floating models, respectively. By comparing the results of the two methods with experimental data, the shortcomings of traditional method based on linear response theory emerge and it is of great significance to consider the second-order slowly drift motion response in the analysis of deck wetness of the new sandglass-type FPSO.

Pitch motion problem induced by dynamic positioning system for new sandglass-type floating body

In this paper, a new concept of sandglass-type floating body, which can overcome the performance limitations of traditional ship-type and cylindrical FDPSO (floating drilling production storage and offloading), is proposed as research subject. In the general design of dynamic positioning systems, it is adequate to deal with a three-degree of freedom problem in the horizontal plane. However, the new floating body with small water-plane area and low metacentric height may cause an unintentional coupling phenomenon between the pitch and surge motions by the thruster system. Therefore, first by numerical boundary element method (BEM) based on wave potential theory and experiments, the pitch motion characteristic of the sandglass-type model is studied and meanwhile the numerical method of this paper is validated. Furthermore, two dynamics models with and without consideration for the additional pitch moment by the thruster systems are introduced and numerically simulated, which can show the problem of pitch motion induced by the positioning thrusters. Then by the mass-spring-damper systems with two-degree of freedom, the influence of additional pitch moment by the thrusters on the pitch and surge motion performances is theoretically analyzed. Finally, based on the essential reason of pitch motion problem, a control law considering pitch inertia effect has been used and proven to be effective to decrease the pitch motion response.

Dynamic model of pulse mechanical seal

Double mechanical shafts seals with gas lubrication constructions are widely used in modern machine engineering for sealing the centrifugal machines, pumping aggressive, cryogenic substances and the melts. These constructions mainly use creating and maintaining a stable value for gas-dynamic method and the special microgrooves to draw the barrier gas into sealing gap are shaped to draw the barrier gas into the sealing gap. This article deals with the mathematical model of the pulse gas-barrier mechanical seal dynamics that synchronically use both gas-static and gas-dynamic methods of maintaining the contactless mode of operation, and is out of the disadvantages inherent for seals with microgrooves. The aim of this work is to develop a mathematical model of pulse seal functioning dynamics. The object of the research is the workflow of the seal. Іt is necessary to complement the existing method of pulse seals parameters calculation, and propose a methodology of operation gap pressure distribution calculation for achieve the objectives of the study. This model applies the numerical boundary element method, which allows to determine the pressure distribution in the operation gap due to the Reynolds equation. The model can be used to define the response of the movable face ring for the harmonic changes of external influences as well as for the frequencies risky range identification and for selecting such parameters of the seal where the movable ring oscillation amplitude would not be exceed by the allowable limits

Numerical and experimental study of contact for bodies of complex shape

This work delivers results of experimental studies performed in order to justify the validity of the developed version of the boundary element method that accounts for the compliance of the intermediate layer. Experimental investigation of contact interaction of complex shaped bodies in the presence of local compliance of conjugate surfaces has been conducted on a prototype of a hydrovolumetric drive, for which the contact area and the magnitude of the contact pressure were determined by means of pressure sensitive films. In order to capture the entire domain where contact pressure is applied and their maximal values and therefor for the sake of measurement error reduction each test is made using two types of contact films: MS and HS. It was demonstrated that the increased compliance of the intermediate layer results in contact over a larger area and leveling of the maximal contact pressure pike. With the increase of pressing force both the size of the contact zone and the values of contact pressure grow. Comparison of contact pressure distributions obtained experimentally and from numerical boundary element method solution confirmed full qualitative and quantitative correspondence of the experimental and numerical results. The discrepancy in contact area and maximal contact pressure was less then 10%. The results are summarised in a curve chart that contains correlation between the size of the contact area and the value of the maximal contact pressure for different local compliances of the contact layer.

Numerical and experimental analysis on motion performance of new sandglass-type floating body in waves

In order to solve the performance limitations of traditional ship-type and cylindrical FPSO, this paper presents a new concept of sandglass-type FPSO. For the new sandglass-type floating model, firstly by using classic boundary element method based on wave potential theory, the effects of shape parameters on motion performance of sandglass-type model are studied. Then the wave frequency versus minimum heave motion RAO is selected as the critical design parameter to control heave motion of new floating model, and its convenient engineering estimation expression is theoretically and mathematically deduced. Furthermore, on this basis the design guideline for sandglass shape is analyzed and proposed. Next according to the information of a cylindrical FPSO, a sandglass-type floating model with the same basic function has been designed. Finally, by analyzing the numerical solution and experimental data, the numerical boundary element method and design guideline in this paper can be validated to be effective and accurate. Furthermore, it can be found that the sandglass-type design can obviously improve the hydrodynamic performance of FPSO. Thus this paper can provide an innovative engineering platform and a design proposal for the development of ocean oil and gas exploitation.

Calculating transfer and loss coefficients in bent slab single mode micro-waveguides and micro-rings considering bending and coupling losses

In this work, using boundary element numerical method, monochromatic wave propagation equation was solved in a bent micro-waveguide coupled with two direct waveguides. In the previous works, bent micro-waveguides have been generally considered by themselves without comparison with any direct waveguides; however, in this study, the bent waveguide was assumed to be connected to two direct waveguides at both ends. Transfer matrix was proposed in a multi-mode bent waveguide. Using the components of this matrix, loss coefficients were calculated. Results of modeling for the single-mode waveguide were compared with those from FDM method, which showed that the proposed method had higher accuracy and needed less time for calculation. Finally, by eliminating the effects of coupling, a model was presented for calculating loss coefficient in micro-rings and the behavior of loss coefficient was investigated in terms of radius and wavelength.