Numerical Boundary Element Method Research Articles

SIF determination with digital image correlation

Purpose – Hybrid methods, wherefore numerical and experimental data are used to calculate a critical parameter, have been used for several years with great success in Experimental Mechanics and, in particular, in fracture mechanics. The purpose of this paper is to report on the comparison of the strain field from numerical modelling forecasts against the experimental data obtained with the digital image correlation method under Mode II loading in fatigue testing. The numerical dual boundary element method has been established in the past as a very reliable method near singular regions where stresses tend to grow abruptly. The results obtained from the strain data near the crack tip were used in Williams expansion and agree fairly well with both the numerical results and the analytical solution proposed for pure Mode II testing. Design/methodology/approach – The work presented in this note is experimental. The proposed methodology is of an hybrid experimental/numerical nature in that a numerical stress intensity factor calculation hinges upon a stress field obtained with an image method. Findings – The obtained results are an important step towards the development of a practical tool for crack behaviour prediction in fatigue dominated events. Research limitations/implications – The results also stress the necessity of improving the experimental techniques to a point where the methods can be applied in real-life solicitations outside of laboratory premises. Originality/value – Although several research teams around the globe are presently working in this field, the present research topic is original and the proposed methodology has been presented initially by the research team years ago.

Numerical and analytical verifications of the electrostatic attraction between two like-charged conducting spheres

We calculate the capacitance coefficients for the problem of two conducting spheres using a numerical (boundary element) method as well as two analytical approaches. The consistency of the results serves as an independent verification of the counter-intuitive analytical result that like-charged spheres almost always attract at close approach. We further support this claim by reproducing the analytical surface charge density with the numerical method. Practical implementations are given in the Supporting Information.

Swimming efficiency of spherical squirmers: beyond the Lighthill theory.

Nonreciprocal shape deformations can drive inertialess cellular swimming, as first explored by Taylor and Lighthill in the 1950s, for the small-amplitude squirming of a planar and a spherical surface, respectively. Lighthill's squirmer, in particular, has been extensively studied for large wave numbers in the context of ciliated microbes. The maximal power efficiency for small-amplitude planar squirming motility is well characterized and degenerate, with nonunique optimal swimming strokes. We explicitly show that this degeneracy is retained at high wave numbers for the small-amplitude spherical squirmer such as a ciliated microbe but is broken for low wave numbers. Hence further complexity emerges in parameter regimes outside that of ciliate swimming even at small amplitudes. Large-amplitude squirming also characterizes more recent observations of large-amplitude/low-wave-number membrane deformations driving the motility of Euglena, neutrophils, and Dictyostelium discoideum. Thus boundary element numerical methods are used to explore swimming with increased deformation amplitudes, especially in the context of power efficiency and swimming performance. As radial squirming amplitudes are increased, small-amplitude linearized theories can be unreliable even for nominally low deformation amplitudes. Furthermore, even for a simple single-mode metachronal wave, a highly motile and efficient large-deformation/small-wave-number swimming modality arises, which can surpass theoretical limitations of purely tangential squirming given a constrained surface deformation velocity.

The Stability and the Computed Speed of Boundary Element Numerical Method for Electric Field Intensity Generated by Oblique Hundred-Needle Electrodes

According to the electric field intensity of oblique hundred-needle electrodes (OHNE), the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE) The non-uniform distribution of the current flowing from hundred-needle electrodes was imaged by solving a set of linear equations. Then, the electric field intensity generated by OHNE at any point can be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced significance for computing the potential generated by OHNE, which is a fast, effective and accurate computing method.

Deformation and breakup of a leaky dielectric drop in a quadrupole electric field

AbstractThe deformation and breakup of a leaky dielectric drop suspended in a leaky dielectric medium subjected to a quadrupole electric field are studied. Analytical (linear and nonlinear asymptotic expansions in the electric capillary number, $C{a}_{Q} $, a ratio of electric to capillary stress) and numerical (boundary element) methods are used. A complete phase diagram for the drop deformation in the $R$–$Q$ plane is presented, where $R$ and $Q$ are the non-dimensional ratios of the resistivities and dielectric constants, respectively, of the drop and the medium phase. The prolate and oblate deformations are mapped in the phase diagram, and the flow contours are also shown. The large deformation and breakup of a drop at higher $C{a}_{Q} $ are analysed using the boundary element method. Several non-trivial shapes are observed at the onset of breakup of a drop. A prolate drop always breaks above a certain critical value of $C{a}_{Q} $. In the oblate deformation cases, breakup as well as steady shapes are observed at a higher value of $C{a}_{Q} $. A detailed study of prolate and oblate deformation tendencies due to the normal and tangential electric stresses and the countervailing role of viscous stresses is presented. The circulation inside a drop is found to be more intense for a quadrupole field as compared with a uniform electric field. More intense internal circulations can lead to enhanced mixing characteristics and will have implications in microfluidic devices.

The Stability and the Computed Speed of the Boundary Element Numerical Method for Electric Potential Generated by Oblique Hundred - Needle Electrodes

Abstract:According to the electric potential of oblique hundred -needle electrodes (OHNE), the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE) The non-uniform distribution of the current flowing from hundred -needle electrodes was imaged by solving a set of linear equations. Then, the electric potential generated by OHNE at any point can be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced significance for computing the potential generated by OHNE, which is a fast, effective and accurate computing method.

Boundary Element Numerical Method for Electric Potential Generated by Eleven-Needle Electrodes in Vacuum

Abstract. According to the electric potential on the eleven -needle electrodes in vacuum, the discrete equations based on the indeterminate linear charge density (LCD) are established by the boundary element integral equations. The non-uniform distributions of LCD on the needle electrodes are calculated through solving a set of linear equations. With the help of the LCD, the potential generated by the multi-needle electrodes at any point in vacuum have been obtained. In this paper we have realized the numerical calculation of the static field distributions for multi-needle electrode system by the boundary element approach.

The Stability and the Computed Speed of Application Boundary Element Numerical Method to Compute the Electric Field Intensity Generated of One Hundred and Fifty-Needle Electrodes

According to the electric field intensity of one hundred and fifty-needle electrodes (OONE), the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE) The non-uniform distribution of the current flowing from one hundred and fifty-needle electrodes was imaged by solving a set of linear equations. Then, the electric field intensity generated by OONE at any point can be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced significance for computing the electric field intensity generated by OONE, which is a fast, effective and accurate computing method.

On the numerical solution of some two-dimensional boundary-contact delocalization problems

The elastic equilibrium of a multi-layer confocal elliptic ring is studied. The ring consists of steel, rubber and celluloid layers which differ in thickness and in the order in which they are placed relative to one another. Using the solutions of the considered problems, the following delocalization problem is solved: for a three-layer elliptic body, the external elliptic boundary of which is loaded by normal point force and the internal boundary is stress-free and the layers of which are in rigid or sliding contact with one another, by an appropriate choice of layer thickness and arrangement of the layers relative to one another we can obtain a sufficiently uniform distribution of normal displacements on the internal elliptic boundary. Numerical solutions are obtained by the boundary element method and the related graphs are constructed. For the two-layer ellipse, exact and approximate solutions of the same problem are obtained respectively by the method of separation of variables and by the boundary element method. The results obtained by both methods are compared and the conclusion as to the reliability of the numerical boundary element method is made.

Boundary Element Numerical Method for Electric Field Intensity Generated by Oblique Twelve - Needle Electrodes in Biological Tissue

According to the electric field intensity of oblique twelve -needle electrodes (OTNE) in biological tissue, the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE). The non-uniform distribution of the current flowing from twelve -needle electrodes to conductive biological tissues was imaged by solving a set of linear equations. Then, the electric field intensity generated by OTNE in biological tissues at any point can be determined through the boundary element method (BEM). It means that this method has an important referenced significance for computing the electric field intensity generated by OTNE in bio-tissue.

Boundary Element Numerical Method for Electric Field Intensity Generated by Ten-Needle Electrodes in Vacuum

According to the electric field intensity of ten-needle electrodes (OTNE) in vacuum, the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE). The non-uniform distribution of the current flowing from ten-needle electrodes to conductive in vacuum was imaged by solving a set of linear equations. Then, the electric field intensity generated by OTNE in vacuum at any point can be determined through the boundary element method (BEM). It means that this method has an important referenced significance for computing the electric field intensity generated by OTNE in vacuum

Boundary Element Numerical Method for Electric Potential Generated by Oblique Five-Needle Electrodes

According to the electric potential of oblique five-needle electrodes (OFNE) in biological tissue, the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE). The non-uniform distribution of the current flowing from five-needle electrodes to conductive biological tissues was imaged by solving a set of linear equations. Then, the potential generated by OFNE in biological tissues at any point can be determined through the boundary element method (BEM). It means that this method has an important referenced significance for computing the potential generated by OFNE in bio-tissue.

Meshless EFG Simulation of Linear Elastic Fracture Propagation Under Various Loadings

We used computational mechanics consisting of various numerical methods to analyze different problems under various boundary conditions. The main advantage of the element free Galerkin (EFG) method is that the model meshing stage is not required and the nodal points are distributed throughout the model domain instead of being meshed. Nodal points are distributed within the model domain to capture a stress singularity around the crack tip. In this paper, various 2D problems in the field of linear elastic fracture mechanics were analyzed to validate the accuracy of the EFG code that was developed in a Matlab environment. To simulate the fracturing process based on the maximum hoop stress criterion, stress intensity factors and the angle of crack propagation were calculated under different loading conditions and the crack trajectory was determined. The obtained results of the developed EFG-code were compared with available experimental data and other numerical (boundary element method and finite element method) methods.

Measurement of Permittivity of Ferroelectrics Using Coaxial Resonator

This paper presents a coaxial resonator technique applied for the measurement of the permittivity of ferroelectric thick film. A 1/4-wavelength coaxial resonator with appropriate dimensions were designed and made for measurements so that there is only TEM fundamental resonance in the interest frequency range. The permittivity may be extracted from the measured TEM fundamental resonant frequency in the resonator. The equivalent capacitance to the part between sample and open end of coaxial line is discussed, in which the boundary element numerical method was used for modeling the capacitance. The resonant frequency was measured using network analyzer and good experimental results were obtained.

Performance of Traffic Noise Barriers with Varying Cross-Section

The efficiency of noise barriers largely depends on their geometry. In this paper, the performance of noise barriers was simulated using the numerical Boundary Element Method (BEM). Traffic noise was particularly considered with its standardized noise spectrum adapted to human hearing. The cross-section of the barriers was varied with the goal of finding the optimum shape in comparison to classical rectangular barriers. The barrier performance was calculated at different receiver points for a fixed barrier height and source position. The magnitude of the insertion loss parameter was used to evaluate the performance change, both in one-third octave bands and as the broadband mean insertion loss value. The proposed barriers of varying cross-section were also compared with a typical T-shape barrier of the same height.

The Added Mass Coefficient computation of sphere, ellipsoid and marine propellers using Boundary Element Method

The Added Mass Coefficient computation of sphere, ellipsoid and marine propellers using Boundary Element MethodAdded mass is an important and effective dynamic coefficient in accelerating, non uniform motion as a result of fluid accelerating around a body. It plays an important role, especially in vessel roll motion, control parameters as well as in analyzing the local and global vibration of a vessel and its parts like propellers and rudders. In this article, calculating the Added Mass Coefficient has been examined for a sphere, ellipsoid, marine propeller and hydrofoil; using numerical Boundary Element Method. Since an Ellipsoid and a sphere have simple geometric shapes and the Analytical values of their added mass coefficients are available, so that the results of added mass matrix are obtained and evaluated, using the boundary element method. Then the added mass matrix is computed in a given geometrical and flow specifications for a specific propeller and its results are studied versus experimental results, which it's current numerical data In comparison with other numerical methods has a good conformity with experimental results. The most important advantage of the method in determining the added mass matrix coefficients for the surface and underwater vessels and the marine propellers is extracting all the added mass coefficients with very good Accuracy, while in other numerical methods it is impossible to extract all the coefficients with the Desired Accuracy.

Boundary element numerical method for the electric field generated by oblique multi-needle electrodes

According to the electric potential of oblique multi-needle electrodes (OMNE) in biological tissue, the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE). The non-uniform distribution of the current flowing from multi-needle electrodes to conductive biological tissues was imaged by solving a set of linear equations. Then, the electric field and potential generated by OMNE in biological tissues at any point may be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced significance for computing the field and the potential generated by OMNE in bio-tissue, which is a fast, effective and accurate computing method.

A matrix of fundamental solutions in the theory of plate oscillations

A matrix of fundamental solutions is constructed for the operator governing the high-frequency oscillations of a plate with transverse shear deformation. Important properties of the corresponding wave functions and layer potentials are discussed, as an essential step in the development of numerical boundary element methods.

Calculation of the optical force on an infinite cylinder with arbitrary cross section by the boundary element method

We have developed and implemented a numerical scheme to compute optical forces in two-dimensional (2D) structures based on the boundary integral equations, which are solved by the numerical boundary element method. We demonstrate the efficiency of this method by calculating the optical scattering and radiation pressures exerted on 2D objects under the illumination of both plane wave and cylindrical Gaussian beams. The results are validated by comparing to analytical Mie scattering results on circular cylinders. In the framework of this approach the object can be of arbitrary shape with dimensions either far larger, comparable, or much less than the wavelength concerned, and the constituent components can be either dielectric or metallic. We applied the method to study the resonance enhancement of optical forces and the effect of surface roughness on such enhancement. Surprisingly, we found that a cylinder with “controlled roughness” can give a stronger optical force than a smooth surface at resonance.

Light intensity and its fluctuations on a layered microsphere: Effects of shell thickness acting as a quantum well

Abstract The present study is an extension of the former research where a double-layer microsphere is irradiated by monochromatic unpolarized plane light. One can realize intensity fluctuations on the particle surface by the numerical boundary element method. The effect of the shell thickness is primarily investigated in the present study. A refractive index reflects its potential energy photons experience in a domain. The potential energies in the air, shell, and core are different from one another with the smallest in the shell. As the shell thickness reduces, the shell layer behaves like a quantum well after a critical thickness. The resultant light intensities on the particle surface show noise-like fluctuations depending on such parameters as the shell thickness, the light wavelength, the particle size, etc. Noticeable fluctuations appeared with the shell thicknesses less than around 5 nm. The thinner the shell, the stronger the intensity fluctuations, suggesting the more light absorbing ability. More efficient photon energy absorption observed with quantum well optoelectronic devices should be explained by stronger intensity fluctuations, not by higher intensities ensuing from photon confinement in quantum wells.