Two-dimensional Finite Element Method Research Articles

Numerical and Experimental Demonstration of a Silicon Nitride-Based Ring Resonator Structure for Refractive Index Sensing

In optical communication and sensing, silicon nitride (SiN) photonics plays a crucial role. By adeptly guiding and manipulating light on a silicon-based platform, it facilitates the creation of compact and highly efficient photonic devices. This, in turn, propels advancements in high-speed communication systems and enhances the sensitivity of optical sensors. This study presents a comprehensive exploration wherein we both numerically and experimentally display the efficacy of a SiN-based ring resonator designed for refractive index sensing applications. The device’s sensitivity, numerically estimated at approximately 110 nm/RIU, closely aligns with the experimental value of around 112.5 nm/RIU. The RR sensor’s Q factor and limit of detection (LOD) are 1.7154 × 104 and 7.99 × 10−4 RIU, respectively. These congruent results underscore the reliability of the two-dimensional finite element method (2D-FEM) as a valuable tool for accurately predicting and assessing the device’s performance before fabrication.

Multiple Fano Resonance Modes based Plasmonic Refractive Index Sensor for Edible Oil Adulteration Detection

Surface plasmon polariton (SPP)-based plasmonic sensors are increasingly replacing traditional bulky sensors in refractive index sensing, biosensing, food adulteration detection, and other applications due to their unique optical features and different Metal-Insulator-Metal (MIM) topologies. The present research introduces a new design for a highly sensitive MIM waveguide-based refractive index sensor. This design incorporates an innovative combination of an inverted U-shaped rectangular split-ring resonator (RSRR), a semi-circle-split-ring resonator (SCSRR), and a stub. The sensor’s wave-guiding capabilities, such as electromagnetic wave transmission, field profile distribution, and sensitivity, are meticulously analyzed using a two-dimensional finite-element method. The key objective of this device is to identify slight differences in the refractive index by observing shifts in resonant wavelength through the light’s interaction with the plasmonic structure. Moreover, optimizing the geometric parameters significantly enhances the sensor’s performance. The optimized sensor achieves a maximum refractive index sensitivity of 2400 nm/RIU, a figure of merit (FOM) of 45.28, and a Q-factor of 39.86, as demonstrated by simulation results. Further investigations reveal the MIM structure’s capacity to detect adulteration in edible oils, underscoring the sensor’s adaptability and its potential for widespread biosensing applications.

The study of the influence of the geometry of a lateral electric field resonator on its resonant characteristics

An experimental study of the dependence of the electrical impedance of a lateral electric field resonator on its thickness and the size of the gap between the electrodes was carried out. The resonator was made of PZT-19 piezoceramics in the form of a rectangular parallelepiped with the shear dimensions of 18 × 20 mm2. Two rectangular electrodes with a gap that varied in the range from 4 to 14 mm were applied on one side of the resonator. For each gap width, the frequency dependences of the real and imaginary parts of the electrical impedance were measured using an impedance analyzer. It has been found that increasing the gap width leads to an increase in the resonant frequency and to an increase in the maximum value of the real part of the impedance. Three series of such experiments were carried out for three values of the resonator thickness: 3.02, 2.38 and 1.9 mm. The resonant characteristics of the resonator were also theoretically analyzed by finite element analysis using two models. One resonator model was based on a two-dimensional finite element method. In this case, the vibration modes that existed due to the finite size of the plate in the direction parallel to the gap between the electrodes were not taken into account. The second model of the resonator used a three-dimensional finite element method, which correctly took into account all vibration modes existing in the resonator. Comparison of theory with experiment has shown that the three-dimensional model provides a better agreement between theoretical and experimental results.

Field and Numerical Investigation of Taihu Resort Cut Slope Failure in Suzhou, China

This study aims to determine the cause of a landslide located at Taihu Resort in Suzhou, Jiangsu Province, China. Field monitoring has been conducted, including two-dimensional finite element method (FEM) numerical analyses to examine slope stability under different working conditions. The monitoring data indicated that the slope deformation was triggered in two phases: at a certain period when the slope was cut and moderate rainfall occurred in November; and afterward, when a continuous heavy rainfall intensity hit during the monsoon rainfall, which accelerated sliding of the slope. Numerical simulations show that stress and maximum displacement distributions formed and redistributed during the excavation process, where the shear strain occurred mainly in the front layer of soil. Additionally, the factor of safety of the slope decreases gradually with the increase in the excavation rate. During 15 days of continuous rainfall infiltration, the slope under heavy rainfall indicates a minimum factor of safety (FoS). Specifically, the slope excavation followed by heavy rainfall intensities contributed significantly to the landslide.

Semianalytical modeling of squirrel-cage induction machines with consideration of iron permeability and eddy-currents using elementary subdomain technique

PurposeThis paper aims to propose a semianalytical model of a squirrel-cage induction machine (SCIM), considering local magnetic saturation and eddy-currents induced in the rotor bars.Design/methodology/approachThe regions of the rotor and stator are divided into elementary subdomains (E-SDs) characterized by general solutions at the first harmonic of the magneto-harmonic Maxwell’s equations. These E-SDs are connected in both directions (i.e., along the r- and θ-edges).FindingsThe calculation of the magnetic field has been validated for various values of slip and iron permeability. All electromagnetic quantities were compared with those obtained using a two-dimensional finite-element method. The semianalytical results are satisfactory compared with the numerical results, considering both the amplitude and waveform.Originality/valueExpansion of the recent analytical model (E-SD technique) for the full prediction of the magnetic field in SCIMs, considering the local saturation effect and the eddy-currents induced in the rotor bars.

The Financial Aspects behind Designing a Wind Turbine Generator

This article investigates the construction of a wind power generator requiring the lowest possible cost. The proposed model is an Axial Flux Permanent Magnet (AFPM) Synchronous Machine, which contains two iron rotors and a coreless stator between them, constructed from resin. The scientific contribution relates to the coupling of economic and technical parameters, which will clarify the feasibility, i.e., a wind turbine construction capable of producing approximately 3.5 KW, using a simple mill and a generator of nominal rotor speed 100 rpm. Such studies are few in international literature and mainly concern low levels of rotor speed in relation to the produced output power. For the generator dimensioning, analytical equations are used, while the type and the dimensions of the magnets are determined, before the start of dimensioning. The authors carried out research in the international market, ending up with specific cost-effective magnets, while trying to adjust the remaining dimensions and materials of the machine based on these cost-effective magnets and the aforementioned nominal values of the generator. The machine, whose dimensions are derived by analytical equations, was simulated and analyzed using the Two-Dimensional Finite Element Method (2D-FEM) and the Three-Dimensional Finite Element Method (3D-FEM), for comparison purposes. Moreover, an economic analysis of the generator and its individual parts was conducted. Finally, a novel idea for reducing the total generator cost is proposed, by replacing the rotor disks with rings. The investigation revealed that analytical equations can predict with satisfactory accuracy the generator’s parameters. In addition, as permanent magnets are the most expensive materials in the construction, their predetermination using low-cost magnets can reduce the construction cost. Finally, the proposed concept of a ring-shaped rotor instead of a disk rotor, provides a cost reduction of up to 20%.

Analysis of low-speed blade coating flows

From industrial-scale production to small-scale fabrication of functional films, the blade coating method is used widely to apply a uniform thin liquid film on a moving substrate. However, conventional hydrodynamic models are inadequate for laboratory-scale low-speed blade coating, where capillary forces dominate. In this study, the low-speed blade coating of non-evaporative Newtonian fluids was investigated in experimental, computational and analytical approaches. The transient free boundary problem was solved utilizing a two-dimensional finite element method, and a simple viscocapillary model was developed to describe the viscous stress and capillary forces within the puddle, and predict the thickness of the wet film as a function of the speed of the substrate. Comparing the predicted film thickness with the computational results, and a flow visualization experiment of blade coating with silicone oil, respectively, confirmed the model's validity. The study indicates that the proposed model may be a useful tool for optimizing laboratory coating processes, as it provides a greater understanding of the low-speed blade coating system on a laboratory scale.

Comparative analysis of a mining truck motor with permanent magnets in a rotor and a synchronous homopolar motor without magnets in a drive

The relevance. Increasing need for using mining trucks with a diesel-electric (hybrid) drive for development of minerals. Improving operational and cost characteristics of the electric drive of mining trucks helps to reduce costs in the development of minerals. The main aim. To compare theoretically the performance of synchronous traction motors of various designs (a conventional design with permanent magnets inside a rotor and a homopolar design without permanent magnets with an excitation winding on a stator), optimized by the same method, in the drive of a mining truck. To optimize the motor design to reduce power loss and required inverter power, as well as to limit torque ripple and reduce the risk of permanent magnet demagnetization. Objects. Design of twelve-pole nine-phase synchronous AC motors with a rated power of 370 kW of various designs: a homopolar motor without permanent magnets with an excitation winding on the stator and a motor of a traditional design with permanent magnets in the rotor. Methods. Derivative-free optimization method; equivalent circuit method; mathematical modeling; two-dimensional finite element method. Results. Based on the analysis, the advantages and disadvantages of the considered motors were revealed. The advantage of the motor with permanent magnets in the rotor is reduction in active part length by 30 %. The advantage of the homopolar motor with an excitation winding on the stator are 4.6 times lower cost of active materials. In addition, the homopolar motor has a more reliable design, without the risk of overheating, demagnetization or deterioration of the properties of permanent magnets over time

Rate-dependent constitutive modelling blasting crack initiation and propagation in rock masses

This study examines the fracture mechanism of cracks and the final blasting effects on defective rock masses under blasting loads. The failure processes of jointed rock with two prefabricated joints are investigated through numerical simulations using a two-dimensional finite element method. Subsequently, simulations are performed to analyze the blasting of granite specimens with various joint arrangements, focusing on the influence of front joint length, inclination angle, and blast hole distance on failure patterns, displacement, velocity, and stress at the joint ends. The numerical results provide a comprehensive summary of various typical failure modes near blast holes and joints for the first time. Specifically, the simulation successfully captures the characteristics of the ring crack zone, wing cracks, and main crack deflection affected by the front joint. Moreover, the results highlight the shielding effect of the front joint, which enhances damage in the medium between the borehole and the joint while exhibiting the opposite effect behind the joint in terms of stress wave propagation. Overall, this study offers objective insights into the mechanics and failure characteristics of jointed rock masses under blasting loads and serves as a valuable reference for the design and optimization of blasting operations.

3D numerical analysis of soil nailing in sedimentary soil with vertical inclusions

In this case study of a soil nail retaining wall, the measured horizontal displacement is of the order of 0.023% H, where H is the excavation depth, while the two-dimensional Finite Element Method (FEM) analysis suggests horizontal displacements of the order of at least 0.5% H. This study aims to understand which parameters influence such displacements through a Sensitivity Analysis. In addition, the study compares results obtained through two-dimensional and three-dimensional FEM analyses for this case. It concludes that Young’s Modulus (E) and the in-situ earth pressure coefficient (K0) are the two parameters that most influence such displacements. This study shows that Mohr Coulomb’s perfectly plastic Elastic Constitutive Model is unsuitable for simulating this structure, which had minimal displacements in situ, suggesting the Hardening Soil model (Schanz et al., 1999) as a viable alternative. Compared to 3D analysis, 2D analysis showed significantly larger horizontal displacements. This led to the conclusion that 2D analysis in MEF is unsuitable for predicting lateral displacements unless a Reduction Factor (FR) ranging from 0.4 to 1.0 was applied.

Deformation Characteristics and Stability Prediction of Mala Landslide at Miaowei Hydropower Station under Hydrodynamic Action

In recent years, with the completion of the construction of large-scale hydropower projects in China, a series of engineering geological problems that occurred during the operation of the hydropower station have become an important issue affecting the normal operation of hydropower stations. Landslides on reservoir slopes triggered especially by water storage and other factors related to the construction of hydropower stations seriously affect the normal operation of the hydropower station and lead to other geological disasters. Research indicates that many reservoir-area landslides are triggered by hydrodynamic forces resulting from water level fluctuations in hydroelectric power stations. The Mala landslide of Miaowei Hydropower Station in the Lancang River Basin of China is taken as the engineering example to study the influence of hydrodynamic forces on the deformation characteristics and stability trends of the landslide. This paper explores the formation mechanism and influencing factors of the Mala landslide by conducting a field investigation of the Mala landslide and analyzing the monitoring data. Additionally, this paper also discusses the impacts of water storage, rainfall, and engineering construction on landslide induction. It is considered that the evolution of the Mala landslide from the initial stage of water storage to the current state mainly includes four stages: small-scale bank collapse stage, creep deformation stage, accelerated sliding stage, and uniform sliding stage. Moreover, the changes in the trend of landslide stability are analyzed using the two-dimensional finite element method. The research results provide a valuable reference for understanding the formation mechanism and predicting the deformation of reservoir landslides, which has considerable engineering practical significance.

The geoelectric field coast effect: Results from two dimensional finite element method and analytic solutions

The geoelectric fields induced during geomagnetic disturbances (GMD) may affect the normal operation of technological systems at the Earth’s surface. The non-uniform Earth conductivity structure, especially large lateral conductivity contrasts, can lead to the enhancement of geoelectric fields near boundaries such as a coastline. In this paper, we give an overview of the applicability of a two-dimensional finite element method (2D-FEM) for studying lateral variations of the Earth’s conductivity, which can be considered as one of magnetotelluric sounding forward modelling methods, including both the E and the H polarization cases. Then the spatial distribution of the geoelectric field near a continent-ocean boundary is calculated with different models. This is compared with analytic solutions for simple models to verify the accuracy of the FEM modelling, which is calculated by using the ANSOFT software. More realistic scenarios are then developed to emphasize the advantages of FEM. The factors influencing the coast effect are discussed. Results show that frequency, the shape of seafloor boundaries, and the depth of ocean have a significant impact on the geoelectric fields. Therefore, these factors should attract more attention when assessing risk for man-made conducting systems located within the coastal influence range.

Quintuple grids plasmonic refractive index sensor for organic gas sensing application

In this article, an optical refractive index (RI) nanosensor has been presented. The layout is arranged in a metal–insulator-metal (MIM) waveguide configuration with gold being the plasmonic metal. The waveguides are coupled with quintuple grids resonant cavity where the grids are uneven in length. The transmission spectral profile of the schematic is numerically analyzed employing the two-dimensional Finite Element Method (FEM) within the mid-infrared region (MIR). Moreover, the key structural parameters are optimized individually to realize the maximum performance of the schematic. The most optimal structure displays a high sensitivity of 4737.87 nm/RIU and a FOM of 9.37. Furthermore, the structure can be suitably used in applications such as sensing organic gas vapors and temperature. Due to the practicality of the applications and the simplicity of the schematic along with the higher longevity provided by gold, this device can replace complex structures effectively.

Quantitative detection of crack depth in V-groove weld using laser-generated surface acoustic waves

Thick-walled structures are widely used in kinds of high-end equipment. As the most conventional method adopted to manufacture large-scale structures, multi-pass butt-welds are one of the most critical areas prone to defects. In this paper, we focus on the quantitative detection of crack depth in a V-groove weld using laser-generated surface acoustic waves. A two-dimensional finite-element method with Q345 steel is adopted to reveal the complicated propagation characteristics of laser-generated surface acoustic waves with surface cracks. The displacement fields are discussed to show the wave transmission, reflection, and mode-conversion phenomena. The main propagating wave modes—P, R, R′, R′r, and R′t waved—are distinguished with the help of the out-of-plane displacement under different crack depths in the time domain. It is found that R′r can be used to locate the cracks and R′t can be used to quantify the depth of the cracks.

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.