Two-dimensional Finite Element Analysis Research Articles

Effectiveness of soil improvement for deep excavation in under-consolidated soil: A case study

The main objective of this article is to investigate the effectiveness of soil improvement methods, such as jet grouting and cement deep mixing, for a deep excavation in under-consolidated soil. A well-documented case history, located in Zhuhai, China, was used for analysis. The analyses were conducted using two-dimensional plane-strain finite element analysis. The studies included an examination of the effect of wall length on lateral wall deformation, the effect between the degree of consolidation and lateral wall deformation, and the influence of soil improvement on lateral deformation and settlement. The deformations induced by under consolidating states are greater than those caused by normally consolidated states. A similar trend was found with or without soil improvement. The greater the degree of consolidation is, the smaller the deflection of the wall. In this case, the retaining wall's length is well designed and stable, but the analysis results showed that the wall length can be shorter than the constructed length. Massive jet grouting was used behind the left wall to successfully reduce wall deflection and ground surface settlement. Finally, deep cement mixing has only a small effect on reducing wall deflection and ground surface settlement.

Electromagnetic Field Analysis of Distributed Winding Permanent Magnet Synchronous Motor Considering Axial Leakage Flux using Two-Dimensional Finite-Element Analysis

This paper proposes a method for the electromagnetic field analysis of permanent magnet synchronous motors (PMSMs) considering the axial leakage flux. To the axial leakage flux while employing two-dimensional (2D) finite-element analysis (FEA), the permeance of the axial leakage path is added into a slot region by increasing the permeability of elements in that region. The increased permeability is calculated based on the permeance relationship of the main magnetic and axial leakage paths, which are calculated using the equivalent magnetic circuit method. The effect of the proposed method is verified by comparing it with the 3-dimensional FEA results. The proposed coupling method uses finite element analysis and is developed from the lumped method proposed in our previous research. The developed method enables the analysis of distributed winding machines, which is not possible with the existing method.

Deformation of Sandy Ground Induced by Tunneling of Super-Large-Diameter Shield—Influence of Buried Depth of Tunnel and Relative Density of Sand

The mechanical properties of sandy soil depend on both the confining pressure and the state of compactness. Therefore, both the buried depth of the tunnel and the relative density of the sand are key factors that affect the ground deformation induced by the tunneling of a super-large-diameter shield. In this study, the parameters of the SANISAND constitutive model are first calibrated based on triaxial test data for Foshan silty fine sand. Then, based on the actual project, a two-dimensional finite-element analysis model is established to investigate the ground deformation induced by the tunneling of a super-large-diameter shield. The width and maximum value of the settlement trough, the volume loss ratio, and the deformation characteristics of the soil are summarized and analyzed for 13 cases. The results show that as the ratio of the buried depth to the diameter and the relative density of sand increases, the anti-disturbance ability of the sand layer to the tunnel construction increases and the volume loss ratio of the stratum reduces correspondingly. The denser the sand and the smaller the confining pressure of the soil around the tunnel, the more significant the shear-induced expansion of the sand at the tunnel haunch; this expansion partially makes up the volume loss caused by the tunnel excavation and reduces the loss ratio of the stratum at the arch crown.

Effects of strength and weight of pre-ground improvement on seismic behavior of shallow overburden tunnel

Pre-ground improvement is an auxiliary method for shallow overburden tunnels in which the tunnel excavation is performed after improving the ground on top of the tunnel with/without sides by the replacement method and/or the cement mixing method. Although it has been confirmed in previous studies that pre-ground improvement enhances the tunnel face stability and reduces the settlement of the ground surface during the tunnel excavation, the seismic behavior of tunnels with pre-ground improvement has not been fully investigated. Therefore, the authors conducted a shaking table experiment under the centrifugal acceleration of 50 g in order to understand the effect of the ground-improvement pattern on the seismic behavior of a shallow overburden tunnel. Furthermore, the authors performed a two-dimensional elasto-plastic finite element analysis of the centrifuge model experiment to verify the applicability of the numerical method and to examine the influence of the stress release associated with the tunnel excavation, which cannot be considered in the centrifuge model experiment. In this study, the effects of the strength and weight of the improved ground on the seismic behavior of a shallow overburden tunnel are investigated using the same numerical method. The results confirm that, for a Level 1 earthquake, the increments in bending moment are almost the same regardless of the strength of the improved ground in both ground-improvement patterns. On the other hand, for a Level 2 earthquake, the seismic behavior of a tunnel has different tendencies depending on the ground-improvement pattern because of the expansion of the plastic area in the improved ground and the difference in stiffness between the improved ground and the surrounding ground. Therefore, the optimum strength of the improved ground differs depending on the ground-improvement pattern. It is also found that, although the translational motion of the tunnel with the improved ground is slightly greater when the weight of the improved ground is larger, the increase in weight due to the ground improvement has only a small effect on the seismic behavior of the tunnel because the behavior of the tunnel during an earthquake is dominated by the surrounding ground.

A Study on Reduction of Cogging Torque and Magnet Usage through Intersect Magnet Consequent Pole Structure

Owing to the shortage of rare-earth magnetic materials, various methods are being examined to reduce the use of magnets. One of these is a consequent pole. The consequent pole model can reduce the use of magnets by 50% using only one pole of the magnet and replacing the other pole with iron. However, the consequent pole has the disadvantage of generating back EMF asymmetry and a high cogging torque. In this study, an intersect magnet consequent pole structure is proposed to overcome the disadvantages of the existing consequent pole. Two methods have been proposed to improve axial leakage magnetic flux caused by the intersect magnet consequent pole structure. Finally, we propose a method to reduce the cogging torque and minimize the use of magnets with the same performance standard. For motor design, two-dimensional and three-dimensional finite element analysis was used, and comparative analysis was performed via simulations for several models. The existing model and the final model were compared and verified.

Principle and Performance of a New Brushless Doubly Fed Reluctance Machine With Asymmetrical Composite Modulator

For the brushless doubly fed reluctance machine (BDFRM), a composite rotor featuring salient pole reluctance and short-circuited coils (SCC) is applied to efficiently improve the cross-coupling capability and magnetic field modulation effects, where the SCCs induce symmetrical multiphase current and then establish the corresponding additional magnetizing magnetomotive force to modulate the source one. This article investigates the modulation behavior and evaluates the modulation capability of the composite modulator from the perspective of the magnetic field conversion mechanism. The modulated airgap harmonic phase-shift phenomenon in space caused by the SCC modulator is first observed, resulting in the reduction on the effective magnetic field conversion factors in the BDFRM with conventional symmetrical composite rotor. The phase-shift mechanism is revealed for the first time, then an asymmetrical composite modulator configuration is proposed to eliminate the phase shift so as to enhance the rotor cross-coupling capability and improve torque performance. A BDFRM prototype with the asymmetrical composite modulator is designed and manufactured for experimentation. Theoretical predictions are verified by two-dimensional finite-element analysis together with experiments.

Influence of end-effect and end-winding on the electromagnetic losses and efficiency in high speed permanent magnet machines

<span>Permanent-magnet excitation machines (SPMMs) having mounted magnet on the outer surface of their rotor are preferred for high speed applications such as turbochargers, mechanical turbo-compounding systems, racing engines and fuel pumps, over other types of machines including induction and switched-reluctance machines, since the SPMMs integrate the features of high torque density, compact rotor structure, high reliability and simple structure. However, in the SPMMs, due to the need for a retaining sleeve for the rotor, a large magnetic airgap results and consequently a large magnet thickness is required, hence the magnetic end-effect is relatively high. On the other hand, the use of an overlapping distributed winding leads to a significantly large end-winding length. Hence, the end-effect and the end-winding influences on the performances of a high-speed SPMM is considered in this paper. With a view to get the impact of the end-effect, a comparison between three-dimensional (3D-FEA) results and counterparts two-dimensional finite element analyses (2D-FEA) have been conducted. Results show that, higher efficiency at low torque and low speed due to the low electromagnetic losses and at high speeds due to the high flux-weakening capability are seen when the influences of end-effect as well as end-winding are taken into account.</span>

Stator current identification in generator among single and composite faults composed by static air‐gap eccentricity and rotor inter‐turn short circuit

In this study, a fault diagnosis model based on magnetic density is proposed to analyse the current characteristics of synchronous generator rotor inter-turn short circuit and air gap eccentric single fault and composite fault. The model considers the influence of rotor inter-turn short circuit and air gap eccentricity on air gap magnetic density. According to two main factors, the short circuit turns and eccentric distance, are used to reflect the short circuit and eccentricity of the generator. The detailed parameter input model of the generator can easily and quickly predict the development trend of these current parameters based on the air gap magnetic density. And the phase current is selected as the current parameter. The validity of the proposed model is verified by two-dimensional finite element analysis and experimental research.

A new explicit solution for the mode I stress fields in notched orthotropic solids

This paper deals with the stress distributions in orthotropic solids weakened by hyperbolic-shaped notches and loaded under in-plane tension. A complex potential function and proper boundary conditions are proposed from which, thanks to an optimization algorithm, a new solution is derived that can account for the geometrical features of the notch, such as the notch radius and opening angle, as well as the elastic material properties.A large bulk of results from two-dimensional finite element analyses are then compared with the derived solution, documenting its high accuracy, and showing the improvements with respect to the previous existing solution for the same problem.

Analysis and Mitigation of AC Losses in High Performance Propulsion Motors

In this paper, the AC copper losses in classical random windings are investigated and mitigated using several techniques across a range of permanent magnet synchronous motor designs. At high operating frequencies, AC copper losses can represent a substantial share of the total loss in electrical machines, thus, reducing the machine’s overall performance, and increasing the thermal loading. Recently, different approaches for modelling AC copper losses have been proposed. This paper utilises simulation software to quantify the expected AC losses in six different propulsion motor designs. The motor designs are then modified to reduce the AC winding losses through the implementation of five different methods. Using two-dimensional finite element analysis, the magnetisation direction, magnet to airgap ratio, copper stranding, magnetic wedges and the motor slot openings are modified to reduce AC losses. The paper considers distributed, fractional, slot and concentrated windings, and the results show promising reductions across these different winding configurations.

Linear Permanent Magnet Vernier Generators for Wave Energy Applications: Analysis, Challenges, and Opportunities

Harvesting energy from waves as a substantial resource of renewable energy has attracted much attention in recent years. Linear permanent magnet vernier generators (LPMVGs) have been widely adopted in wave energy applications to extract clean energy from oceans. Linear PM vernier machines perform based on the magnetic gearing effect, allowing them to offer high power/force density at low speeds. The outstanding feature of providing high power capability makes linear vernier generators more advantageous compared to linear PM synchronous counterparts used in wave energy conversion systems. Nevertheless, they inherently suffer from a poor power factor arising from their considerable leakage flux. Various structures and methods have been introduced to enhance their performance and improve their low power factor. In this work, a comparative study of different structures, distinguishable concepts, and operation principles of linear PM vernier machines is presented. Furthermore, recent advancements and innovative improvements have been investigated. They are categorized and evaluated to provide a comprehensive insight into the exploitation of linear vernier generators in wave energy extracting systems. Finally, some significant structures of linear PM vernier generators are modeled using two-dimensional finite element analysis (2D-FEA) to compare their electromagnetic characteristics and survey their performance.

Two-Dimensional Finite Element Analysis of Piled Raft Coefficient Settlement Ratio on Clays

Nowadays, designing a piled raft foundation is challenging because the behavior is three-dimensional. For some engineers, a three-dimensional analysis might not be affordable due to more costly than a two-dimensional analysis. In this study, 2D Finite element analysis – axisymmetric was used to study the piled raft foundation. The pile diameter and pile length were varied to investigate the relation between piled raft coefficient and load-settlement. In addition, the load transfer mechanism between the raft part and the pile part in clayey soils is also examined. The results show the longer the pile and the larger the diameter, the greater the load carried by the pile and the smaller the settlement. Increase in pile length by 5 m, resulting in a load transfer of 2% to 6% from a raft to pile, and reduced settlement by 2% to 3%. Furthermore, A 0.5 m increase in pile diameter results in an 8% to 25% load transfer from a raft to pile, and a 2% to 7% reduction in a settlement. The soil consistency affects the load distribution and settlement of the pile-raft foundation system. The higher the soil consistency, the smaller the amount transferred to the pile, and the higher the effectiveness of the pile in reducing the settlement that occurs.

Comparison of Temperature Characteristics of Outer Rotor Low-Speed PM Motors Considering Magnetic Load and Current Density

In the electromagnetic design process of the outer rotor of a low-speed permanent magnet motor (LSPMM), due to the different heat dissipation conditions of the stator core and the stator winding, the selection of different magnetic loads and stator current densities will produce different temperature distributions even under the same efficiency. In the existing literature, the effects of magnetic load and current density on temperature distribution are rarely studied, which makes it difficult for designers to select optimal electromagnetic parameters to achieve better temperature performance. Therefore, in this paper, the comparison of temperature characteristics considering magnetic load and current density is conducted based on an outer rotor LSPMM. Firstly, the structure and parameters of an initial scheme of a 200 kW 56 rpm motor is determined, and the electromagnetic and temperature characteristics of the initial scheme are obtained through two-dimensional finite element analysis (2D-FEA) using Ansys Maxwell and Motor-CAD software. Secondly, by comparing the temperature and loss characteristics under different magnetic loads and different current densities, the effect of magnetic load on temperature and the effect of current density on temperature are obtained. Furthermore, four different schemes are proposed, and the loss and temperature characteristics of the four schemes under rated load are also compared to obtain the comprehensive effects of magnetic load and current density on temperature. Next, a final scheme is determined based on the above analysis, and the temperature characteristics of the final scheme and the initial scheme are compared to verify the validity of the conclusions. Finally, a prototype is built and tested to verify the feasibility of the conclusions. For LSPMM design, the results and several measurements provided in this paper can help researchers to choose a better optimization scheme to achieve good temperature performance.

Seismic vulnerability analysis for shallow-buried underground frame structure considering 18 existing subway stations

The variability of structural engineering parameters is not accounted for in available literature on seismic vulnerability of underground frame structures. This study investigates the seismic vulnerability of 18 existing subway stations with different site condition, structural stiffness, reinforcement ratio and buried depth employing two-dimensional (2D) finite element analysis considering soil-structure interaction. The peaks of structure inter-story drift ratio under different earthquake intensity of different ground motion records are obtained from non-linear dynamic time-history analysis. Taking the inter-story drift ratio as the damage measure (DM) and the peak ground acceleration (PGA) as the ground motion intensity measure (IM), the seismic vulnerability curves of 18 subway stations are constructed. The comparison of seismic fragility curves of different subway stations demonstrates that site conditions are critical to the post-earthquake structure probability of failure. Furthermore, representative seismic fragility curves are established based on the data collected form the computed results of 18 subway stations, which can aid in evaluating the seismic performance of existing urban underground frame structures in China. The results of this study can provide reference for the performance-based seismic design of urban underground frame structures.

A general mathematical modeling and finite element analysis of a strain wave gear possessing a double-circular-arc-with-a-common-tangent profile

In this study, the characteristics of a strain wave gear (SWG) with a double-circular-arc with a common tangent (DCACT) profile were simulated using two-dimensional (2D) and three-dimensional (3D) finite element analysis (FEA). First, theoretically generated tooth profiles for the flexible spline (FS) and circular spline (CS) of an SWG were developed according to the theory of gearing. An automated mesh-generating computer program was developed in Visual C++ to establish 2D and 3D finite element models of the SWG based on its derived geometry. An FEA was then performed to explore the meshing characteristics, including the stress distribution, torsional angle, torsional stiffness, and number of engaged teeth, of the SWG. Continuous meshing of multiple tooth pairs between the FS and CS from the 2D FEA verified the conjugation of tooth profiles. The coning effect on the FS during assembly of the SWG was also predicted and discussed from the 3D FEA results. The 3D FEA produced more accurate and practical results than the 2D FEA did. Additionally, 3D FEAs of a modified (with longitudinal crowning) and unmodified (without longitudinal crowning) FS were performed and compared. Finally, a 3D FEA of a modified FS was successfully conducted to predict cyclic contact stress, root stress, and transmission error.

Two-dimensional equivalent mechanical modeling and finite element analysis of normal female pelvic floor system

Objective: To construct the geometric model of the pelvic floor by a two-dimensional equivalent mechanics method, and to explore the effect of the shape and position of pelvic floor organs and tissues on the biomechanical properties of the pelvic floor under different abdominal pressure. Methods: A 28-year-old healthy and symmetrical married infertile female volunteer was included. The pelvic floor tissue was scanned in the supine position using a 3.0T magnetic resonance scanner (Philips Company, Holland). Based on the method of magnetic resonance imaging (MRI) two-dimensional parameter measurement and computer aided design, the geometric model and finite element model of the female pelvic floor were established, and the biomechanical characteristics of the pelvic floor support system under different abdominal pressure were analyzed. Results: In this study, four different working conditions of the pelvic floor force were simulated under 60, 99, 168, and 208 cmH2O (1 cmH2O=0.098 kPa) abdominal pressure loads. The trend was as follows: under the abdominal pressure load, the retrograde flexion of the uterus occurred, the cervical, the middle and upper vaginal segment and the levator anus muscle had the characteristic change of mechanical axial direction pointing to the sacrum and coccyx, and the deformation of the levator anus muscle in the horizontal direction was greater than that in the vertical direction. With the increase of the abdominal pressure, the maximum stress values of the pelvic floor whole system of healthy subjects under four different working conditions were 0.194 3, 0.389 6, 0.557 1, and 0.627 5 MPa, respectively, and the maximum displacement values were 10, 14, 21 and 25 mm, respectively. The maximum stress values of the cervical and vaginal middle and upper segment were 0.111 7, 0.161 8, 0.250 6, and 0.304 1 MPa, respectively, and the maximum displacement values were 3, 6, 9, and 11 mm, respectively. The maximum stress of the perineal body was 0.063 4, 0.119 6, 0.235 2, and 0.288 0 MPa, and the maximum displacement was 1, 2, 4, and 5 mm. The maximum stress values of the levator anus muscle were 0.194 3, 0.389 6, 0.557 1, and 0.627 5 MPa, and the maximum displacement values were 2, 4, 7, and 8 mm, respectively. The maximum stress and maximum displacement of pelvic organs increased with the increase of the abdominal pressure under different working conditions. The stress axial relationship of normal female pelvic floor was that the middle and upper segment of uterus and vagina mainly acted on the sacrococcyx and the levator anus muscle, and the lower vaginal segment acts on the perineal body. Conclusions: The two-dimensional equivalent mechanical modeling and finite element analysis of the female pelvic floor system can accurately reflect the biomechanical characteristics of the female pelvic floor, and the resultant stress direction of the pelvic organs points to the sacrum and coccyx. The sacrum and coccyx, levator anus and perineal body play important stress supporting roles in the pelvic floor system.

Thermally conductive polymer composites for thermal management of electric machines: A modeling and experimental study

With ever-increasing drive to improve the power output of electric machines and reduce heat accumulation based insulation failure, efficient thermal management is highly desirable. Increasing thermal conductivity of impregnation resin is critically important for thermal dissipation in electric machines. In this work, we investigated how the improvement in thermal conductivity of impregnation resins could benefit the heat dissipation of electric machines. To this end, a two-dimensional (2D) finite element analysis (FEA) was conducted, which revealed that increasing the thermal conductivity of impregnation resins to 0.6–0.8 W·m−1·K−1 could significantly decrease the winding temperature. Meanwhile, epoxy-based composites with different thermally conductive fillers were synthesized. The effect of filler type/loading on thermal conductivity and viscosity were investigated. After systematically measuring the thermal conductivity and viscoelastic properties of these composites, a “viscosity-thermal conductivity” correlation was plotted to sort out candidate resin for impregnation trials. In addition, impregnated prototypes comprising enamel wires and both neat epoxy resin and thermally conductive composite impregnation resins were fabricated. Under both natural and forced convection, the epoxy/BN composite resin was shown to be effective in reducing the core temperature of prototype by 9.1–18.6 °C compared with neat epoxy-impregnated prototype. The results indicated that thermally conductive polymer composites had the potential to greatly improve thermal management of electric machines. The findings in this work provide insights and guidelines for future development of thermally conductive impregnation resins.

A Novel Universal Model Considering SAGE for MFD-Based Faulty Property Analysis Under RISC in Synchronous Generators

This article proposes a new rotor interturn short circuit (RISC) fault analysis model for the electromechanical property study in synchronous generators. The specific novelty of this model lies in two aspects: First, It considers that most generators exist static air-gap eccentricity (SAGE), so it analyzes the RISC fault under normal and SAGE, making the model more versatile, and second, it takes into account not only the short circuit degree, but also the short circuit position, consequently it is more universal. By feeding the number of short circuit turns (denotes the short circuit degree), the angle between the two slots, where the short circuit takes place (denotes the short circuit position) and the detailed parameters of the generator into the model, the developing tendency of the key magnetic flux density (MFD)-based parameters can be conveniently predicted. The advantages of the proposed model primarily lie in the universality and the calculation speed. It can quickly evaluate the generator operating conditions. The phase current and the electromagnetic torque are selected in this article as the representatives of the electrical parameter and the mechanical parameter, respectively. Two-dimensional finite element analysis and experimental studies validate the proposed model.

Damage assessment of a cement plant partially collapsed depending on various causes

This study aims at examining the possible causes of the brittle collapse of a tertiary air duct system under vertical loads. Problems related to the design and construction stages were examined. The entire process was illustrated using a tertiary air duct case study in a cement plant. In the plant, the tertiary air duct collapsed without any earthquake, blast, or impact effects. The current study includes a field study, examination of an original/revised design project, and numerical simulation. In the first stage of the study, the existing state of the collapsed system and its compliance with static and mechanical projects were examined. Secondly, a two-dimensional finite element analysis was performed to determine project eligibility. The causes of the system were determined based on the data obtained in the former stages. The results showed that the causes of partial collapse included project errors, construction faults, and project incompatibilities.

Brushless Wound Rotor Synchronous Machine Based on a Consequent-Pole Rotor Structure with Better Torque Attributes

This paper presents a subharmonic-based brushless wound rotor synchronous machine (BL-WRSM) topology with permanent magnet-assisted (PMA) and consequent-pole (CP) rotor structures to achieve better torque characteristics as compared to the conventional subharmonic-based brushless WRSM. The proposed topologies use the conventional high-efficient subharmonic field excitation technique to achieve a brushless operation and a lower volume of permanent magnet (PM) to achieve better average, starting, maximum, and minimum torques and lower torque ripple. A four-pole, twenty-four-slot (4-pole/24-slot) machine with conventional, PM-assisted (PMA), and consequent-pole (CP) rotor structures are developed in a JMAG-Designer 20.1 environment to carry out two-dimensional finite element analysis (2D-FEA). The developed machines are used to validate the operation and achieve electromagnetic and electromechanical performances of the proposed subharmonic-based BL-WRSM topologies with better torque attributes.