Two-dimensional Finite Element Method Research Articles

Simulation of the 2016 Kumamoto Earthquakes Using the Finite Element Method with Concentrated Friction

In this paper, the process of simulating the occurrence of an earthquake on the fault plane for the 2016 Kumamoto, Japan earthquake is investigated dynamically using finite element methods. The two-dimensional finite element method is used by concentrating friction at the finite points. The used element is the elastic element, whose properties are determined based on the shear wave velocity and longitudinal wave. In order to verify the proposed method, the acceleration and velocity response spectra, Fourier spectrum, and other main parameters of the record obtained from the simulation were compared with the Kik-net data. From the obtained results, the role of displacement and velocity of its application to the fault plate in PGA can be pointed out, so that with a faster displacement of the fault plane, a larger PGA is expected. Friction and shear stiffness between the two fault planes and the dependence of friction on velocity are the main and influential factors in the characteristics of the produced earthquake. In high-frequency earthquakes, friction is dependent on velocity, and when friction is not dependent on velocity, static plays a major role, and no drastic changes in the response spectrum are observed.

The Method of Optical Paths for the Numerical Solution of Integrated Photonics Problems

A number of topical problems of integrated photonics are reduced to oblique incidence of radiation on a plane-parallel scatterer. For such problems, a method for integrating Maxwell’s equations along the direction of beam propagation is proposed. As a result, the original two-dimensional problem is reduced to a one-dimensional problem, and it is solved using recently proposed one-dimensional bicompact schemes. This significantly reduces the computational cost compared with the conventional two-dimensional finite difference and finite element methods. The proposed method is verified by solving test problems for which exact solutions are known.

A modified sonic black hole structure for improving and broadening sound absorption

In order to improve and broaden the absorption performance of Sonic Black Hole (SBH), we propose a modified SBH structure with micro-perforated panels which is embedded the multiple resonator cavities, and investigate the sound absorption effect of the structure. Characteristics of acoustic streaming effects are embodied in sound pressure and flow velocity distribution. Further, proposed SBH structure can achieve high sound absorption under 6.0 kHz. Based on the symmetry of the structure, the Two-dimensional axisymmetric Finite Element Method (FEM) model is proposed to study the sound absorption mechanism, which shows that the change of flow velocity gradient of acoustic medium leads to the loss of acoustic energy inside the structure. By discussion on acoustic streaming effects of different frequencies, the resonator cavity and micro-perforated panels contributes more to the sound absorption performance at low frequencies, and SBH produces a sound absorption advantage at high frequencies.The theoretical calculation and simulation result match and prove the correctness of the sound streaming effect. Sound absorption tests by acoustic impedance tube confirm that the proposed structure can maintain a sound absorption coefficient of over 0.5 in the range of 0.05–6.0 kHz. The combination of micro-perforated panels and SBH structure is widely applicable to muffler design and has good application prospects.

Nanoindentation test of a DLC coated high-speed steel substrate using a two-dimensional axisymmetric finite element method

Diamond-Like Carbon is a thin coating that has high hardness, chemical inertia and low coefficient of friction characteristics that can improve the performance of cutting tools and mechanical components. To identify the characteristics of this film it is important to carry out mechanical tests, such as nanoindentation, which can provide important information in understanding and improving coating techniques and, when combined with the finite element method, leads to more detailed results of material behavior during testing. Considering this, the present work aimed to study and apply a nanoindentation test simulation of a Diamond-Like Carbon coated high-speed steel specimen. The results of the indenter penetration versus load were compared with experimental data seeking correlation of the model. A great proximity was observed between the experimental results and the results obtained in the simulation. When comparing the final indentation force, a proximity of 93.9 % and 95.5 % was found for the model with only one indentation and with partial indentations, respectively, thus validating the created model. The impact of modifying the indenter tip radius for the partial indentation method was also evaluated. The tip radius variation did not have a significant impact on the results of final indentation force and material hardness. The material hardness was also obtained in the simulation, which was equal to the experimental: 9.25 GPa.

Design and Optimization of Linear Permanent Magnet Vernier Generator for Direct Drive Wave Energy Converter

A novel linear permanent magnet vernier generator (LPMVG) for small-power off-grid wave power generation systems is proposed in this paper. Firstly, in order to reduce the cogging force and the inherent edge effect of the linear generator, a staggered tooth modular structure is proposed. Secondly, in order to improve the output power and efficiency of the LPMVG and reduce the fluctuation coefficient of electromagnetic force, the relationship between the parameters of the generator is studied, and a method combining multi-objective optimization and single parameter scanning based on the response surface model and particle swarm optimization algorithm is proposed to obtain the optimal structural parameters of the generator. Thirdly, the output power and efficiency of the optimized generator are calculated and analyzed based on the two-dimensional finite element method, and the effectiveness of the multi-objective optimization design method based on the response surface model and particle swarm optimization algorithm is verified. Finally, a prototype is developed, and the calculated results and the measured results are shown to be in good agreement.

Shear capacity of reinforced concrete beams strengthened with web bonded steel bars or steel plates

This paper presents the report of two groups of experimental works to study the shear capacity and strain distribution of reinforced concrete beams strengthened on beam sides with the near-surface mounted (NSM) method. One group was strengthened with steel bars, and the other was strengthened with steel plates. Each group consisted of three control beams and six strengthened beams. Steel bars or plates were installed vertically or diagonally at an angle of 45°. The total number of reinforced concrete beam specimens tested in this study was 18. All beams tested were simply supported and monotonically loaded with two concentrated loads. The longitudinal reinforcement ratio was used as a test variable to attain differences in the required shear demand. An analytical study using the two-dimensional finite element method was carried out to observe the strain distribution along the length of the beams. In the finite element model strengthening on the beam side for either steel bars or plates was modeled with line segments as transversal reinforcement, and the bond between concrete and strengthening materials is assumed to be perfect. The complete flexural response of the cross-section due to bending was also analyzed using the fiber element method. The test results show that some of the specimens strengthened with steel bars or plates achieved flexural capacity, and others experienced a sudden failure due to shear. The analysis results using the finite element method predict well the test results for beams that fail in the flexural mode and on beams with shear failure mode before the failure occurs. The analysis results also show significant differences in the strain distribution between beams without and with strengthening. The orientation of the angle of installation of steel bars or plates and the ratio of longitudinal reinforcement also affect the strain distribution along the beam length. In addition, the fiber element method can satisfactorily predict the tested beams' flexural behavior.

Inclination and heterogeneity of layered geological sequences influence dike-induced ground deformation

Abstract Constraints on the amount and pattern of ground deformation induced by dike emplacement are important for assessing potential eruptions. The vast majority of ground deformation inversions made for volcano monitoring during volcanic unrest assume that dikes are emplaced in either an elastic half-space (a homogeneous crust) or a crust made of horizontal layers with different mechanical properties. We extend these models by designing a novel set of two-dimensional finite-element method numerical simulations that consider dike-induced surface deformation related to a mechanically heterogeneous crust with inclined layers, thus modeling a common geometry in stratovolcanoes and crustal segments that have been folded by tectonic forces. Our results confirm that layer inclination can produce localized ground deformation that may be as much as 40× higher in terms of deformation magnitude than would be expected in a non-layered model, depending on the angle of inclination and the stiffness of the rock units that host and are adjacent to the dike. Generated asymmetrical deformation patterns produce deformation peaks located as much as 1.4 km away from those expected in non-layered models. These results highlight the necessity of accurately quantifying both the mechanical properties and attitude of the geology underlying active volcanoes.

Effects of tool angles and uncut chip thickness on consumption of plastic deformation energy during machining process

Research on the underlying mechanism that controls the chip deformation and energy consumption is a basis to instruct the cutting process planning and improve the machining efficiency. The metal cutting process can be treated as purposeful separation of workpiece material, and the stress state located at the tool tip has great effect on the fracture of material being removed. Through studying the relationship between the stress triaxiality and chip formation process, this paper aims to reveal the effects of tool rake angle, inclination angle and uncut chip thickness on chip deformation behavior and associated energy consumption during machining of 1045 steel based on finite element method (FEM). A two-dimensional FEM model for orthogonal cutting is developed to study the effect of tool rake angle and uncut chip thickness on chip deformation, while a three-dimensional FEM model for oblique cutting is developed to investigate the effect of tool inclination angle. The parameter of chip compression ratio (CCR) is adopted to assess the chip plastic deformation and energy consumption under varied machining conditions. The cutting force component calculated based on CCR is compared with the total cutting force to demonstrate the dominant role of chip plastic deformation in cutting energy consumption. The results indicate that larger rake angle and smaller inclination angle of cutting tools as well as larger uncut chip thickness lead to increase of stress triaxiality near the tool tip, which can reduce the material fracture strain and be beneficial for the separation of material being removed from the bulk workpiece. This paper will be attractive from both practical and fundamental perspectives devoted to instructing the optimization of cutting parameters to improve the processing efficiency and reduce the energy consumption.

Study of magnetoplasmons in graphene rings with two-dimensional finite element method

Graphene plasmons are important collective excitations in graphene, which play a key role in determining the optical properties of graphene. They have quite lots of unique features in comparison with classical plasmons in noble metals. Of them, the active tunability is the most attractive, which is realized by external gating (equivalently electric field). As is well known, graphene also has strong magnetic response (e.g. room temperature quantum Hall effect), so magnetic field can act as another degree of freedom for actively tuning graphene plasmons, with the new quasi particles being so-called graphene magneto-plasmons. Because of the two-dimensional nature of graphene, the numerical studies (or full wave simulations) of graphene magneto-plasmons are usually carried out through a three-dimensional approximation, e.g. treating two-dimensional graphene as a very thin three-dimensional film. Actually, this treatment takes quite some time and requires high memory consumption. Herein, starting from Coulomb law and charge conservation law, we propose an alternative numerical method, namely, two-dimensional finite element method, to solve this problem. All the calculations are now performed in two-dimensional graphene plane, and the usual three-dimensional approximation is not required. To characterize the excitations of graphene magneto-plasmons, the eigenvalue loss spectrum is introduced. Based on this method, graphene magneto-plasmons in graphene rings of four kinds are investigated. The strongest magneto-optic effect is observed in circular ring, which is consistent with its highest rotational symmetry. In all the rings, the lowest dipolar graphene magneto-plasmon always supports symmetric mode splitting, which can be further modified by the interaction between inner edge and outer edge of ring. As the hole size is very small, the edge current confined to the outer edge dominates, and that confined to the inner edge can be ignored; while increasing the hole size, the interaction between these two edges increases, which results in the reduction of the symmetric mode splitting; when the hole size is larger than a critical value, the symmetric mode splitting will disappear.

Numerical modeling of phase prediction and geometry evolution of micro-drilling using single pulse laser

Due to high production capability, long laser pulses are preferred over ultrashort pulses during Laser-based machining. To reduce metallurgical defects, viz. heat-affected zone, recast layer, and micro-cracks, it is essential to analyze the causes of these defects and to derive the remedies. Generally, an extensive experimental investigation is carried out for the same. The experimental analysis is time-consuming, tedious, and requires high capital investment. Therefore, in this work, a two-dimensional axisymmetric transient finite element method (FEM) based numerical model of Laser-material interaction was developed to explore the temperature evolution, phase change, and geometry evolution with the help of coupled heat transfer and deformed mesh. The heat transfer module was implemented by considering the phase change using the apparent heat capacity method. The model was duly validated for the evolution and geometry of the Laser-drilled hole. The model was found in agreement with the experimental results, with a percentage deviation of 12% in the prediction of the responses. The numerical model will help to predict the temperate evolution and hydrodynamic behavior of the material during the laser-material interaction. This, in turn, will help to mitigate the metallurgical defects.

A FEM-DFN model for the interaction and propagation of multi-cluster fractures during variable fluid-viscosity injection in layered shale oil reservoir

To investigate the height growth of multi-cluster fractures during variable fluid-viscosity fracturing in a layered shale oil reservoir, a two-dimensional finite element method (FEM)-discrete fracture network (DFN) model coupled with flow, stress and damage is proposed. A traction-separation law is used to describe the mixed-mode response of the damaged adhesive fractures, and the cubic law is used to describe the fluid flow within the fractures. The rock deformation is controlled by the in-situ stress, fracture cohesion and fluid pressure on the hydraulic fracture surface. The coupled finite element equations are solved by the explicit time difference method. The effects of the fracturing treatment parameters including fluid viscosity, pumping rate and cluster spacing on the geometries of multi-fractures are investigated. The results show that variable fluid-viscosity injection can improve the complexity of the fracture network and height of the main fractures simultaneously. The pumping rate of 15 m 3 /min, variable fluid-viscosity of 3-9-21-36-45 mPa s with a cluster spacing of 7.5 m is the ideal treatment strategy. The field application shows that the peak daily production of the application well with the optimized injection procedure of variable fluid-viscosity fracturing is 171 tons (about 2.85 times that of the adjacent well), which is the highest daily production record of a single shale oil well in China, marking a strategic breakthrough of commercial shale oil production in the Jiyang Depression, Shengli Oilfield. The variable fluid-viscosity fracturing technique is proved to be very effective for improving shale oil production.

Research of the thermoelastic performance of the functionally graded sandwich slabs with convective-radiative boundary conditions based on FVM

<p indent="0mm">In this study, a two-dimensional control volume finite element method (CV-FVM) has been developed for the thermoelastic coupling problem of sandwich structures with functionally graded material core under a convection-radiation heat transfer environment. Based on a four-node quadrilateral element, the discrete process of the governing equation and the nonlinear heat transfer boundary are given in detail. Based on the staggered grid technology, the variables are stored at the node of the element, and the material parameters are defined at the center of the element. To ensure the convergence of the temperature solution, the radiation heat transfer boundary condition is handled by the linearization technique. The numerical method developed in this study is validated for the heat conduction problem of sandwich structures with an exponential core. The results showed that CV-FVM results are consistent with the analytical solution. The influences of the geometric and physical parameters, such as the Biot number, radiation conduction coefficient, environmental temperature ratio, panel thickness, and gradient index of the functionally graded core, on the thermoelastic performance of the structure are investigated. The results showed that the Biot number of the heating surface has only a slight effect on the thermoelastic response of the structure, whereas the Biot number of the cooling surface has a significant effect on the thermoelastic response. The cooling surface is more sensitive to the change in the environmental temperature than the heating surface. For sandwich structures with an exponential core, increasing the thickness of the upper panel can reduce the large gradient change of the stress at the junction between the upper panel and the core. The stress with a linear variation of the properties (<italic>p</italic> = 1) is smoother than that with a nonlinear variation of the properties (<italic>p</italic> = 0.1 and 10), and the large gradient change of the stress of the structure can be reduced significantly (<italic>p</italic> = 1).

Radiation-enhanced acoustically driven magnetoelectric antenna with floating potential architecture

A magnetoelectric (ME) antenna driven by a high-overtone bulk acoustic resonator (HBAR) can play a potentially positive role in the bandwidth enhancement benefit from its narrow harmonic frequency interval, in which radiation characteristics remain to be explored. HBAR ME antennas with floating potential architecture (FPA) and grounded are fabricated and demonstrated separately. The measured far-field radiation characteristics show that the FPA can significantly enhance the gain and radiation efficiency of the HBAR ME antenna by more than 10 dB compared to the grounded setup. Meanwhile, the time domain amplitude sweep demonstrates the high-power tolerance (&amp;gt;23.2 dBm) of the HBAR ME antenna. Two-dimensional finite element method analysis reveals that the FPA-induced electric field excites additional longitudinal-wave resonance, resulting in the coupling of dual longitudinal and shear waves, which is the intrinsic mechanism of its radiation enhancement from the perspective of acoustic excitation. Not only limited to HBAR antennas, the mechanism of FPA described here is also a promising candidate for radiation enhancement in acoustically driven antennas.

Biot Theory-Based Finite Element Modeling of Continuous Ultrasound Propagation Through Microscale Articular Cartilage.

Low-intensity ultrasound has shown promise in promoting the healing and regeneration of articular cartilage degraded by osteoarthritis. In this study, a two-dimensional finite element method (FEM) model was developed for solving the Biot theory equations governing the propagation of continuous ultrasound through the cartilage. Specifically, we computed the ultrasound-induced dilatations and displacements in the microscale cartilage that is represented as consisting of four zones, namely, the chondrocyte cell and its nucleus, the pericellular matrix (PCM) that forms a layer around the chondrocyte, and the extracellular matrix (ECM). The chondrocyte-PCM complex, referred to as the chondron, is embedded in the ECM. We model multiple cartilage configurations where in the ECM layer contains chondrons along the depth, as well as laterally. The top surface of the ECM layer is subjected to specified amplitude and frequency of continuous ultrasound. The resulting wave propagation is modeled by numerically solving the two-dimensional Biot equations for seven frequencies in the 0.5 MHz-5 MHz range. It is seen that ultrasound is attenuated in the ECM and the attenuation increases monotonically with frequency. In contrast, manyfold augmentation of the ultrasound amplitude is observed inside the cytoplasm and the nucleus of the chondrocyte. Chondrocytes act as a major sink of ultrasound energy, thereby reducing the depthwise propagation of ultrasound fluctuations. Regions of high dilatations and displacements were found at the ECM-PCM interface, PCM-chondrocyte interface, as well as in the cytoplasm and nucleus of the chondrocyte. We observe that the ultrasound field around a chondron interacts with that around a neighboring chondron located at the same depth in the ECM layer. The qualitative and quantitative insights gained from our study may be relevant to designing ultrasound-based therapies for osteoarthritis.

Topology Optimal Design of NRD Guide Devices Using Function Expansion Method and Evolutionary Approaches

In order to increase communication capacity, the use of millimeter-wave and terahertz-wave bands are being actively explored. Non-radiative dielectric waveguide known as NRD guide is one of promising platform of millimeter-wave integrated circuits thanks to its non-radiative and low loss nature. In order to develop millimeter wave circuits with various functions, various circuit components have to be efficiently designed to meet requirements from application side. In this paper, for efficient design of NRD guide devices, we develop a topology optimal design technique based on function-expansion-method which can express arbitrary structure with arbitrary geometric topology. In the present approach, recently developed two-dimensional full-vectorial finite element method (2D-FVFEM) for NRD guide devices is employed to improve computational efficiency and several evolutionary approaches, which do not require appropriate initial structure depending on a given design problem, are used to optimize design variables, thus, NRD guide devices having desired functions are efficiently obtained without requiring designer's special knowledge.

Effect of Slot Opening on Permanent Magnet Power Loss of a Permanent Magnet Synchronous Machine Driven by PWM

In this study, the influence of slot opening on the leakage reactance, power factors, winding current, and air gap flux density, as well as other parameters of the surface-mounted permanent magnet synchronous motor driven by an inverter is analyzed using the two-dimensional time-step finite element method. Thus, the law of permanent magnet power loss caused by slot opening under PWM qa obtained. The results show that the leakage reactance of the motor increased when the slot opening decreased from 7 mm to 2 mm. Then, the armature ripple current caused by the inverter was found to be suppressed well, and the high harmonic current was filtered well. This reduced the amplitude of the high-order harmonic of the air gap flux density, and the permanent magnet power loss was reduced by nearly 75%. Finally, two prototypes with different slot openings were tested for permanent magnet temperature rise, which verified the analysis method and calculation results proven in this paper.

Tunable Multi-Channels Bandpass InGaAsP Plasmonic Filter Using Coupled Arrow Shape Cavities

A new design for a tunable multi-channel plasmonic bandpass filter was numerically investigated using the two-dimensional finite element method (2D-FEM). The proposed multi-channel plasmonic bandpass filter consists of a metal-insulator-metal waveguide (MIM-WG) and double-sided arrow-shaped cavities. Silver (Ag) and a non-linear optical medium (InGaAsP) are used in the designed filter. InGaAsP fills the bus waveguide and arrow-shaped cavities. The refractive index of InGaAsP is sensitive to the incident light intensity, therefore the resonance wavelengths can be controlled. Utilizing different incident light intensities (such as 1017 v2/m2 and 2 × 1017 v2/m2) on the InGaAsP, the filter wavelengths can be tuned over a range from 600 nm to 1200 nm. The proposed filter with a confinement area of 0.5 μm2 can be used in wavelength division multiplexing (WDM), photonic systems, coloring filters, sensing, and 5G+ communication.

Flexural wave propagation in periodic Micropolar-Cosserat panels: Spectral Element Formulation

In this research, a perspective of the dispersion relation of flexural waves on periodic structures is proposed. The rotational theory of micro-elements is stem to explore the favorable impact of size effect on structures through the localization of the strain energy. The panels are modelled as a one-dimensional (1-D) Micropolar–Cosserat (MC) continuum to explore the effect of length-scale or micro-rotational waves of solids. The spectral element formulation of a panel and the transfer matrix of the unit cell is presented within the framework of the state-space method. The propagation constant in the eigenvalue domain is established based on the Bloch–Floquet theorem to account for the periodicity of the panel. The MC theory in analyzing the band-gap (stop-band) and pass-band characteristics of the unit cell panels is validated by a commercial finite element software package-COMSOL Multiphysics. The mode shape of unit cell for the start and end point of band-gap is further analyzed within the realms of finite element method (FEM) analysis. The appropriate limiting condition reverts MC spectral element into Timoshenko (TM) beam model. The comparison of Timoshenko beam model with the spectral element of 1-D plane-stress (PS) analysis is also investigated. It is observed that the shear wave of the MC model is coupled with a micro-rotational wave of micro-elements, unlike the classical continuum framework. The response of the finite structure subjected to various frequencies is presented too. Presence of vibration attenuation in the specified band-gap (BG) is justified through the elemental dynamic stiffness (DS) matrix of unit cells. This reduced the level of vibration at the specific frequency range within the attenuation band or disintegrates it into two bands. The attenuation bandwidth and its location is significantly affected by the modulation of both geometry and material properties of the beam. Investigation of flexural wave propagation based on the proposed 1-D MC beam theory shows good agreement with the two-dimensional (2-D) plane-stress FEM analysis.

The chamfered bend two, four and eight-way SIW power dividers analysis for millimeter wave applications using the quick finite element method

In this paper, we propose three kinds of substrate-integrated waveguide (SIWs) based chamfered bend power divider junctions provide equal power distribution to all output ports while maintaining high isolation and operating in the 54 GHz to 60 GHz frequency band. The advantages of the SIW technology are ease of design, fabrication and low form and full integration with planar printed circuits. In this case, the concept of the SIW H-plane power divider is implemented using a rigorous two-dimensional quick finite element method (2D-QFEM) programmed by MATLAB software. The numerical performance of this method is the Quick simulation time for using the mesh with Delaunay regularization in two dimensions, if we increase the mesh the FEM gives better results. This paper presents the transmission coefficient, return loss and the electric field distribution. The results obtained from QFEM were compared with those provided by HFSS for validation. When using the discretization with the Delaunay procedure only in two dimensions, we notice that the calculated simulation time decreases with good precision.

Magnetic Field Distribution and Ripple Loss Analysis of an Optimized Self-Shielding DC HTS Cable

Compared with AC HTS cable, DC high-temperature superconducting (HTS) cable has prominent advantages of low transmission loss, large current capacity and high controllability. The current directions in adjacent layers of “sandwich” cable with self-shielding characteristic are opposite, which can greatly reduce the magnetic field influence and the critical current degradation. In order to homogenize the magnetic field distribution of the cable, an optimized self-shielding DC HTS cable is proposed. Compared with the previous structure, the optimized self-shielding DC HTS cable has a larger critical current and smaller ripple loss. In this paper, the magnetic field distribution and the ripple loss of three different DC HTS cables with ripple current are studied by a two-dimensional (2D) finite element method (FEM) based on T-A formulation. The 2D simulation model offers a valuable reference for the design and operation of DC HTS cable with low voltage and large current.