Edge Elements Research Articles

Mortar contact discretisation methods incorporating interface models based on Hypoplasticity and Sanisand: Application to vibratory pile driving

A segment-based mortar contact discretisation technique for the analysis of hydro-mechanically coupled dynamic processes with quadratically interpolated finite elements and incorporating advanced interface models is presented. The proposed mortar technique divides the surface pair into finite segments with arbitrary order of integration, allowing, opposite to simpler contact discretisation techniques, for an exact integration of contact stress. The performance of the segment-based in comparison to a (simpler) element-based mortar technique is evaluated by means of simulations of vibratory pile driving model tests in water-saturated sand. For the mechanical modelling of the soil–pile interface either a simple Coulomb friction model, the hypoplastic model with intergranular strain extension, or the elastoplastic Sanisand model is utilised. It is concluded that the segment-based mortar method is superior to the element-based technique in terms of numerical stability if the number of integration points per segment is larger than the number of integration points per element edge for the element-based technique. However, the techniques are found to perform similarly when a comparable number of integration points is used. While the implementation of the segment-based method is found to be more complex in general, the implementation of parallelisation is simpler compared to the element-based mortar method.

Electric circuit element boundary conditions in the finite element method for full-wave passive electromagnetic devices

A natural coupling of a circuit with an electromagnetic device is possible if special boundary conditions, called Electric Circuit Element (ECE), are used for the electromagnetic field formulation. This contribution shows how these ECE boundary conditions can be implemented into the 3D-finite element method for solving coupled full-wave electromagnetic (EM) field-circuit problems in the frequency domain. The frequency response allows the extraction of a reduced order model of the analyzed device, accounting for all the EM field effects. The implementation is based on a weak formulation that uses the electric field strength E strictly inside the domain and a scalar potential V defined solely at the boundary. Edge elements for E are used inside the three-dimensional domain and nodal elements for V are used on its two-dimensional boundary. The weak formulation is described and implemented in the free environment Open Numerical Engineering LABoratory (onelab). The validation is carried out on 3D examples.

A class of finite element methods with averaging techniques for solving the three-dimensional drift-diffusion model in semiconductor device simulations

Obtaining a satisfactory numerical solution of the classical three-dimensional drift-diffusion (DD) model, widely used in semiconductor device simulations, is still challenging nowadays, especially when the convection dominates the diffusion. In this work, we propose a series of finite element schemes with different types of averaging techniques to discretize the three-dimensional continuity equations. Our methods are based on the classical finite element framework, quite different from those mixed finite element/volume methods that also employ inverse averaging techniques. At first, the Slotboom variables are employed to transform the continuity equations into self-adjoint second-order elliptic equations with exponentially behaved coefficients. Then four averaging techniques, denoted with A1-A4, are introduced to approximate the exponential coefficient with its average on every tetrahedral element of the grid. The first scheme calculates the harmonic average of the exponential coefficient on a whole tetrahedron, and the other three schemes calculate the average of the exponential coefficient on each edge of a tetrahedral element. Our methods can avoid the spurious non-physical numerical oscillations and guarantee the conservation of the computed terminal currents with a terminal current evaluation approach. In fact, these methods not only maintain numerical stability but also overcome the disadvantages of some stabilization methods that cannot guarantee the conservation of the terminal currents, such as the streamline-upwind Petrov-Galerkin (SUPG) method. Moreover, the derivation of these discretization methods does not need the dual Voronoi grid as that of the finite volume Scharfetter-Gummel (FVSG) method or other mixed finite element/volume methods with inverse averaging techniques, which greatly reduces the complexity of parallel implementations of our methods. Simulations on two realistic three-dimensional semiconductor devices are carried out to test the accuracy and stability of our methods. According to numerical results, we conclude that scheme A4 can produce more accurate numerical solutions than the other three schemes, especially when the bias applied on the electrode is high. Numerical results also show that the scheme A4 is more robust than the Zlámal finite element method [1] in high-bias cases, and it also performs better than the FVSG method and a tetrahedral mixed finite element method [2] on poor-quality grids. Scheme A4 is also employed to study rich physical properties of the n-channel MOSFET.

Microstructural examination of carbonated 3D-printed concrete.

The recent interest in 3D printing with concrete has generated great interest on how inhomogeneities arise and affect performance parameters, in particular strength and durability. With respect to durability, of particular interest is how 3D‐printed layer interfaces can impact transport of species of interest, such as moisture, chlorides or carbon dioxide in carbonation processes. This is of particular interest considering that the primary use case of 3D‐printed concrete has been as a lost formwork for a cast structural concrete, and thus it is of interest to determine the carbonation resistance. This study consists of a preliminary look at the microstructure after accelerated carbonation of a 3D‐printed concrete used as a lost formwork. Preferential carbonation is observed in the layer interfaces compared to the bulk of the printed filaments, possibly related to porosity from air voids or a locally high capillary porosity corresponding to the lubrication layer.

A Sequentially- Hybridized Locally Conservative Non-conforming Finite Element Scheme for Two-phase Flow Simulation through Heterogeneous Porous Media

Accurate two-phase flow modeling has a crucial role in detecting pollution in aquifers and/or in the simulating immiscible flow through porous media. In this research, a new hybrid numerical method based on the lower order non-conforming finite element method (NCFEM) and interior penalty discontinuous Galerkin (DG) method is proposed to simulate two-phase incompressible flow in heterogeneous porous media. The pressure and transport saturation equations are discretized by using the non-conforming Crouzeix-Raviart (CR) finite element and the symmetric weighed interior penalty discontinuous Galerkin (SWIPM). As a result of determining the degrees of freedom at the midpoint of neighboring element edges, a consistent set of pressure and velocity fields is obtained via the NCFEM. An H(div) projection based on the Raviart-Thomas (RT) element is implemented to improve the results resolution and preserve the continuity of the normal component of the velocity field. Besides, the spurious numerical oscillations of the saturation solution at the end of each time step are removed by using a novel vertex-based slope limiter, named the modified Chavent-Jaffre limiter. The accuracy and performance of the proposed numerical method are assessed by solving the Buckley-Leverett and McWhorter-Sunada benchmark problems, along with two test problems associated with highly heterogeneous porous media. The numerical results indicate that the proposed scheme has a remarkable potential to accurately capture the shock front and sharp interface zone of immiscible phases in the heterogeneous aquifers and other porous media.

High-Resolution Table-Top NEXAFS Spectroscopy.

A table-top near-edge X-ray absorption fine structure (NEXAFS) spectroscopy system consisting of a soft X-ray source and an integrated spectrometer with a significantly improved resolution is presented. The soft X-ray source is based on a long-term stable and nearly debris-free picosecond laser-induced plasma generated in a pulsed krypton gas jet target. Photon energies ranging from 250 to 1000 eV can be used for the absorption spectroscopy of thin samples. The newly designed spectrometer accomplishes a spectral resolution of E/ΔE = 1535 at 430 eV, being close to typical synchrotron setups. Moreover, a simultaneous multi-edge analysis is possible. The performance of the new system is demonstrated by investigating the fine structure of the K- and L-absorption edges of various elements (carbon, calcium, oxygen, iron, nickel, and copper) for different types of samples. An excellent agreement with synchrotron spectra is achieved.

Investigation of electromagnetic wave propagation in the bicomplex 3D-FEM using a wavenumber Whitney Hodge operator

PurposeThe purpose of this paper is to show the applicability of a discrete Hodge operator in the context of the De Rham cohomology to bicomplex-valued electromagnetic wave propagation problems. It was applied in the finite element method (FEM) to get a higher accuracy through conformal discretization. Therewith, merely the primal mesh is needed to discretize the full system of Maxwell equations.Design/methodology/approachAt the beginning, the theoretical background is presented. The bicomplex number system is used as a geometrical algebra to describe three-dimensional electromagnetic problems. Because we treat rotational field problems, Whitney edge elements are chosen in the FEM to realize a conformal discretization. Next, numerical simulations regarding practical wave propagation problems are performed and compared with the common FEM approach using the Helmholtz equation.FindingsDifferent field problems of three-dimensional electromagnetic wave propagation are treated to present the merits and shortcomings of the method, which calculates the electric and magnetic field at the same spatial location on a primal mesh. A significant improvement in accuracy is achieved, whereas fewer essential boundary conditions are necessary. Furthermore, no numerical dispersion is observed.Originality/valueA novel Hodge operator, which acts on bicomplex-valued cotangential spaces, is constructed and discretized as an edge-based finite element matrix. The interpretation of the proposed geometrical algebra in the language of the De Rham cohomology leads to a more comprehensive viewpoint than the classical treatment in FEM. The presented paper may motivate researchers to interpret the form of number system as a degree of freedom when modeling physical effects. Several relationships between physical quantities might be inherently implemented in such an algebra.

Free vibration analysis of perforated composite cylindrical shell and panel using multi-domain generalized differential quadrature (GDQ) method

Free vibration behavior of a composite shell/panel with and without a central square cutout has been studied using Multi-domain Generalized Differential Quadrature (GDQ) method. A physical domain is decomposed into several elements in such a way that all the elements have uniform thickness and material properties, as well as continuous loading and boundary conditions at their edges. The governing equations are derived based on the first-order shear deformation theory. They are formulated in a general form and can be converted to Donnell’s, Love’s, and Sanders’ theories. In addition, compatibility conditions are considered at the interface boundaries of adjacent elements as well as proper boundary conditions on other elements edges. The GDQ method is employed to discretize these equations in both longitudinal and circumferential directions. By assembling these discretized relations, a system of algebraic equations will be generated. These equations can be solved throughan eigenvalue solution to compute the natural frequencies of the whole shell/panel. Numerical results obtained by the presented method are compared with ABAQUS results and those available in the literature. After verifying the accuracy and precision of the proposed method, it is employed to study the effect of an opening on the vibrational behavior of composite shells and panels through a parametric study. The influence of the presence of a cutout and its size is investigated on shells/panels with various material properties, layup orientations, thicknesses, dimensions, and boundary conditions. The obtained results can be used as a benchmark for further researches.

BAM: Block attention mechanism for OCT image classification

Diabetic retinopathy attracts considerable research interest due to the number of diabetic patients increasing rapidly in recent years. Diabetic retinopathy is a common symptom of retinopathy, which damages the patient's eyesight and even causes the patient to lose sight. The authors propose a novel attention mechanism named block attention mechanism to actively explore the role of attention mechanisms in recognizing retinopathy features. Specifically, the block attention mechanism contributions are as follows: (1) The relationship between the blocks in the entire feature map is explored, and the corresponding coefficients are assigned to different blocks to highlight the importance of blocks. (2) Furthermore, the relationship between the edge elements of the feature map and the edge elements is explored, and corresponding coefficients are assigned to the elements at different positions on the feature map to highlight the importance of the elements in the feature map. Experimental results show that the proposed framework outperforms the existing popular attention-based baselines on two public retina datasets, OCT2017 and SD-OCT, achieving a 99.64% and 96.54% accuracy rate, respectively.

Sliding Stability Assessment of Concrete Dams Using a 3D Discontinuum Hydromechanical Model Following a Discrete Crack Approach

Evaluation of the sliding stability of concrete dams requires the use of numerical tools not only able to simulate the coupled hydromechanical behavior but also able to adequately represent the foundation discontinuities and the specific features of dam foundations. The formulation of a three-dimensional (3D) small displacement finite element model based on interface elements to simulate the discontinuities is presented. In this model, the hydraulic behavior is simulated assuming that the water flow occurs only along channels located at the edges of the triangular interface elements that simulate the discontinuities. The model is used to perform coupled hydromechanical analysis of a large arch-gravity dam and to assess safety against dam base sliding, assuming different constitutive models at the dam/foundation interface and two different approaches: (i) strength reduction method and (ii) amplification of the hydrostatic pressure, assuming an increase in the reservoir level. The present study shows that consistent results are obtained with the proposed numerical model and that stability analysis should preferably be carried out using the method of increasing the hydrostatic pressure and the corresponding uplift pressures, as this methodology leads to significantly lower safety factors.

Edge Location and Identification Method for Electronic Components based on Improved Canny Algorithm

The position identification of SMD electronic components mainly uses Canny edge detection algorithm to detect the edges of specific elements, benefited from its computational simplicity. The traditional Canny algorithm lacks the adaptability in gradient calculation and double thresholds selection, which may affect the location and identification accuracy of specific elements in electronic components. In this paper, an improved canny edge detection algorithm is proposed. The gradient magnitude is calculated in four directions, i.e., horizontal, vertical, and diagonal. Both the high and low thresholds can be adaptively determined based on the grayscale distribution information, to increase the adaptability of edge identification. The experimental results show that the proposed method can better locate the true edges of specific elements in electronic components with a reasonable processing speed, compared with the traditional Canny algorithm, and has been successfully applied on practical real-time vision inspection on SMD electronic components.

Dual interpolation boundary face method for 3-D potential problem based on binary tree grids

This paper presents the dual interpolation boundary face method (DiBFM) based on a binary tree grid for solving the 3-D potential problems. The subdivision method based on binary tree algorithm is capable to generate both continuous and discontinuous grids, and to achieve the grids​ generation for arbitrary complex model much easier and automatically. By adding virtual nodes on the vertices and edges of traditional discontinuous element, the dual interpolation elements are introduced while the order is increased by two. The values of physical variables are approximated by Lagrange interpolation polynomial in the first-layer interpolation, and meshless interpolation is used to condense the degree of freedom of virtual nodes in the second-layer interpolation. Since no requirement is needed for the continuity of grids in the DiBFM, the dilemma of discontinuous grids are avoidable. In this paper, the DiBFM is implemented based on the binary tree grids to solve general problems with thin-wall structures and “geometrical construction noise”.

New hybrid approaches for SLL reduction and size miniaturization of planar antenna arrays based on 2D convolution and genetic algorithm

In this paper, a new hybrid beamforming approach based on the 2D convolution and genetic algorithm (GA), denoted as C/GA, is proposed for side lobe level (SLL) reduction and size miniaturization of planar antenna arrays (PAA). The convolution algorithm determines the elements excitations, whereas the GA optimizes the element spacing to adjust the half power beamwidth (HPBW). Two beamforming approaches are derived from the C/GA approach. The first one is the single-stage C/GA that is denoted as (SC/GA), where the convolution of the excitation matrix by itself is performed just once. The SC/GA yields a twofold decrease in the SLL. The second is the double-stage C/GA, (DC/GA), which is developed for further SLL reduction, where the convolution of the excitation matrix by itself is performed twice successively, resulting in a fourfold decrease in the SLL. However, both SC/GA and DC/GA approaches provide high dynamic range ratios (DRR). This issue is addressed either by taking the middle excitations of the estimated excitation matrices or by performing array thinning by turning off the edge elements of the synthesized PAAs, which indeed minimizes the array size. The practical validation of the proposed approaches is realized using the computer simulation technology (CST) microwave package.

The comparative study of resolving parameters for a family of ladder networks

<abstract><p>For a simple connected graph $ G = (V, E) $, a vertex $ x\in V $ distinguishes two elements (vertices or edges) $ x_1\in V, y_1 \in E $ if $ d(x, x_1)\neq d(x, y_1). $ A subset $ Q_m\subset V $ is a mixed metric generator for $ G, $ if every two distinct elements (vertices or edges) of $ G $ are distinguished by some vertex of $ Q_m. $ The minimum cardinality of a mixed metric generator for $ G $ is called the mixed metric dimension and denoted by $ dim_m(G). $ In this paper, we investigate the mixed metric dimension for different families of ladder networks. Among these families, we consider Möbius ladder, hexagonal Möbius ladder, triangular Möbius ladder network and conclude that all these families have constant-metric, edge metric and mixed metric dimension.</p></abstract>

Стимулированная эмиссия в сильно легированных Al-=SUB=-0.68-=/SUB=-Ga-=SUB=-0.32-=/SUB=-N : Si-структурах с поперечной оптической накачкой при комнатной температуре

The broadband stimulated emission in the spectral range λ = 380−700 nm with the inhomogeneous broadening has been experimentally obtined in the heavily doped Al0.68Ga0.32N : Si structures grown by molecular beam epitaxy. The behavior of the intensities and spectra of stimulated emission from the edge of the active element with transverse pulsed pumping by radiation with λ = 266 nm, measured at room temperature, demonstrate the threshold behavior and optical gain. For stimulated emission with a maximum at λ = 500 nm, the minimum threshold pump power density was 6.5 kW/cm2 for excited region length of 1.5 mm. The parameters and contributions of the two main processes e − A and D − A of radiative recombination in the excited structures for stimulated emission and optical gain are studied.

Stimulated emission in the heavily doped Al-=SUB=-0.68-=/SUB=-Ga-=SUB=-0.32-=/SUB=-N : Si structures with transverse optical pumping at room temperature

The broadband stimulated emission in the spectral range λ=380-700 nm with the inhomogeneous broadening has been experimentally obtined in the heavily doped Al0.68Ga0.32N : Si structures grown by molecular beam epitaxy. The behavior of the intensities and spectra of stimulated emission from the edge of the active element with transverse pulsed pumping by radiation with λ=266 nm, measured at room temperature, demonstrate the threshold behavior and optical gain. For stimulated emission with a maximum at λ=500 nm, the minimum threshold pump power density was 6.5 kW/cm2 for excited region length of 1.5 mm. The parameters and contributions of the two main processes e-A and D-A of radiative recombination in the excited structures for stimulated emission and optical gain are studied. Keywords: stimulated emission, heavily doped AlxGa1-xN structures, luminescence, optical gain, donor-acceptor recombination.

Simulation Test of the Cutting Process

Cutting is a production process commonly employed used in various industries. The aim of improving its efficiency entails the improvement of the durability of the cutting blade, increasing the accuracy in terms of the resulting item dimensions obtained after cutting, but also the quality of the obtained edge. The material factor for the above is the distribution of forces in the cutting edge and cut element system. Furthermore, the pursuit of minimized interaction of forces in this process is of significance, which has a positive impact both on the durability of the blade as well as the process energy consumption. The paper presents a simulation of the process of cutting a flat bar made of aluminium. The numerical model was built in the ABAQUS system. The model includes a knife-cut element. The purpose of performing simulation tests is to determine the cutting force, changes in its value and the nature of these changes when cutting with knives of different geometry and trajectory.

On non-axisymmetrical buckling modes ofcircular plates under normal pressure

The paper presents the results of a study of the bifurcation of axisymmetric equilibrium forms of round plates under various conditions for fixing the outer edge. It is shown that for the case of sliding edge, the analytical, asymptotic and finite element approaches give close results. When the edge of the plate is hinged, the buckling to a non-axisymmetric state occurs at a much higher load and with the formation of a smaller number of waves than for a sliding boundary conditions. Difficulties in obtaining a numerical solution based on the analytical approach are apparently associated with the need for a more accurate description of the stress-strain subcritical state of the plate.

Magnetic-field-free spin–orbit torque-driven magnetization dynamics in CoFeB/β-W-based nanoelements

A full numerical analysis, which takes into account the effects of the spin Hall effect, interfacial Dzyaloshinskii–Moriya interaction, and thermal fluctuations, is carried out in in-plane magnetized CoFeB/MgO/CoFeB/high-resistivity tungsten (β-W) nanoelements. The analysis is focused on the investigation of the underlying mechanisms of magnetic-field-free spin–orbit torque (SOT)-driven magnetization reversal process on subnanosecond time scales. It is found that the magnetization in the free magnetic layer can be electrically toggled between the parallel and antiparallel alignment with respect to the fixed magnetic layer without the assistance of an external magnetic field, in which the out-of-plane canting of the magnetic moments at the element edges plays a significant role in the nucleation and subsequent expansion of the reversed magnetization. Furthermore, the thermally activated magnetization process combined with the SOT effect is found to significantly reduce the effective energy barrier to the magnetization reversal and alter the details of the SOT-driven magnetization process in nanomagnets.

Diagnostics of the presence of a fatigue crack in the compressor blade using the spectrum of vibration amplitudes at the superharmonic resonance

In this study, the solution of the forced vibration response of a structural element with a fatigue crack was carried out using the finite element method to determine the influence of its presence on the flexural forced vibration behaviour of the compressor blade airfoil at the superharmonic resonance of the order 1/2. The blade airfoil with a low twisted angle was used as an object of investigation to perform the computational analysis. Its vibrations in the plane of minimum stiffness were excited by the kinematic displacement of root edge elements. The fatigue crack was modelled as a mathematical cut. Two locations of the crack were investigated – on the leading edge and convex side of the blade airfoil. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, was taken into account by solving the contact problem. To quantify this kind of nonlinear dynamic behaviour, the vibration diagnostic parameter was defined as the displacement amplitude ratio of the dominant harmonics at the superharmonic resonance of the order 1/2. Based on the results of the calculations it has been found that regardless of the crack location, the ratio nature is the same for all vibration axes. However, with vibrations in the plane of minimum stiffness, the crack on the convex side of the airfoil has an opening mode propagation, which makes it possible to fix its location due to a sharp change in the ratio of the amplitudes of the dominant harmonics along the corresponding axis.