Two-dimensional Finite Element Analysis Research Articles

Hydraulic Fracture Propagation in Layered Heterogeneous Rocks with Spatially Non-Gaussian Random Hydromechanical Features

AbstractThis study proposes a stochastic method to analyse the propagation of hydraulic fractures affected by layered heterogeneity in rocks in a toughness-dominated regime. The study utilises the phase-field method in the context of two-dimensional finite element analysis to model the hydraulic fracture (HF) propagation in rock materials in laboratory scale. Field data on hydrogeologic properties of some rocks reveal that material heterogeneity may appear in the form of leptokurtic marginal distributions. Generalised sub-Gaussian (GSG) model is capable of capturing physical characteristics of such rocks, and it is employed to stochastically model rocks with layered lithologic heterogeneity by generating a large number of auto- and cross-correlated random fields for hydro-geomechanical properties. To investigate the sensitivity of the cracking response to the inherent characteristics of material heterogeneity, various GSG distribution forms are considered in Monte Carlo (MC) analyses. The HF’s deviation from the theoretically predicted direction, which is perpendicular to the direction of the minimum in situ stress, is correlated with the distribution of hydro-geomechanical properties, showing a Gaussian-type distribution. This study concludes that the differential stress and the bedding orientation are the main factors affecting the HF deviation and the required breakdown pressure for initiating the HF propagation from a borehole. In the application of directional hydraulic fracturing (DHF), the effect of bedding layers becomes dominant when the bedding orientation is aligned with the direction of perforations in the boreholes.

Compact-tension-shear specimen for orthotropic materials in fracture toughness testing

Conducting Compact-Tension-Shear (CTS) tests emerges as a promising research methodology to determine the fracture toughness of orthotropic materials in mixed-mode I&II. However, the absence of pertinent fracture parameter solutions incorporating material orthotropy impedes the further application and standardization of CTS testing. Therefore, this study performed a systematic two-dimensional finite element analysis (FEA) on orthotropic CTS specimens to evaluate critical fracture parameters, including the normalized stress intensity factors (YI, YII) and compliance (u). First, the impacts of three commonly cited boundary conditions (BCs) of CTS models were investigated, revealing that the simplified or equivalent methods developed for isotropic CTS models are no longer applicable. Subsequently, the suitable CTS models were used to analysis the coupling effects of material orthotropy (λ, ρ), crack length ratios (a/W), and loading angles (β). Findings indicated that YI or u no longer exhibit a monotonic relationship with respect to a/W or β under strong orthotropy. The impact of λ and ρ on fracture parameters is equally significant across different geometries and loading conditions. Further, the impact of orthotropy on YII is relatively small, while the more affected YI may have a difference compared to isotropic results of over 80%. Finally, CTS tests were carried out on the unidirectional carbon fiber-reinforced epoxy resin composite measuring the fracture toughness in mixed-modes I&II. The obtained fracture parameter solutions were applied and validated during the process. The acquired results are poised to contribute to the advancement of fracture toughness testing standardization for orthotropic materials under mixed-mode loading.

Indenting a thick gel with a solid spherical inclusion

A spherical inclusion is embedded in a soft gel block. A vertical force is applied on the gel surface by means of a spherical indenter. The loading axis is not aligned with the inclusion but placed at a horizontal offset displacement from the inclusion. The measurement of indentation force and inclusion trajectory are compared to the computational results from two-dimensional (2D) Finite Element Analysis (FEA) simulations. A discernible instability emerges when the indentation reaches a critical depth, in accordance with the Southwell instability theory. The three-dimensional (3D) trajectory shows distinct features that were previously not captured by the 2D FEA simulations.

Comparative analysis of dual stator machines

Electromagnetic performance of three different types of double stator permanent magnet machine is analyzed and compared in this study. The analyzed machines in this study are Machine 1, Machine 2 and Machine 3. These machines are designated as: M 1, M 2 and M 3, respectively. The studies are implemented using two-dimensional and three-dimensional finite element analysis (2D-FEA and 3D-FEA) methods. The predicted performance indices are: total harmonic distortion of the voltage, torque ripple, cogging torque, winding inductances, output torque and unbalanced magnetic force (UMF). The studies show that the investigated machine types have negligible reluctance torque and thus, similar axes inductance values. Therefore, the machines’ bulk torque components are contributed mainly by the magnets while the armature excitation sources yield lesser torque components. Amongst the compared machines, M 3 type has an outstanding performance in almost all the performance metrics, compared to M 2 and M 1 types. Nevertheless, M 1 machine type has some good attributes, particularly, with respect to its high output torque per applied magnet volume, in addition to its widest operating speed range ability. Low-speed high-torque applications are most suitable for the investigated machines in practice.

Improving force characteristics of linear oscillatory generator with spring permanent magnet for Stirling engines based on subdomain method

In this paper, an electromagnetic analysis method is proposed to improve force characteristics by using spring permanent magnets (PMs) along the axial and circumferential directions of a linear oscillatory generator (LOG). For accurate electromagnetic analysis, a detailed analysis model of the LOG is developed, and the governing equations of each subdomain are derived based on Maxwell’s equations and electromagnetic theory. Analytical solutions of the magnetic vector potential in each subdomain are derived using boundary conditions. The reliability of the proposed method is verified through a comparison with the results of a two-dimensional finite element analysis (FEA). In particular, the force characteristics depending on the spring PM is effectively derived by considering the three-dimensional (3D) circumferential and axial end effects. The proposed analysis method is used to determine the thickness of spring PM that transforms the detent force of the LOG with the spring PM into restoring force. The reliability of the proposed analysis method is verified through comparison with the results of a 3D FEA.

Enhancing efficiency of magnetic energy by implementing square-shaped materials adjacent to induction machine windings

This study provides a worthwhile method for increasing the magnetic field energy and induction machine (IM) effectiveness. The coupling between the transmitter and receiver windings in the IM system can be improved by creating materials with specific electromagnetic properties. This added material has altered the magnetic flow as well as the energy of the magnetic field. Eventually, it is possible to calculate the efficiency of the magnetic field, or the ratio of primary to secondary magnetic energy. With the use of two-dimensional finite element analysis, numerical results on five cases with various configurations of a magnetic substance have been produced. This material, which varies in length or breadth, is positioned close to the windings of the transmitter, receiver, or both. Case 3, in which the transmitter generates a magnetic field on the receiver side with a minimum energy of 0.05 J and a maximum energy of 0.015 J, is the ideal material configuration for DC current. Currently, the system efficiency is 0.29 on average. A 1 kHz transmitter's energy is constant under all conditions, but its counterpart's energy fluctuates significantly, with case 5 receiving the most energy. Therefore, case 5 turns into the optimal structural arrangement. It can be inferred that case 5 similarly dominates the other with an efficiency of 0.0026, which is much greater than that of 1 kHz efficiency, while the windings are operating at 1 MHz. This leads to stronger magnetic field coupling and increased power transfer effectiveness.

Auxetic cementitious composites (ACCs) with excellent compressive ductility: Experiments and modeling

Auxetic cementitious composites (ACCs) with improved mechanical properties are created, by casting 3D printed polymeric auxetic reinforcement structures inside cementitious mortar. Four types of ACCs incorporating reinforcement with different auxetic mechanisms were prepared: “re-entrant” (RE), “rotating-square” (RS), “chiral” (CR) and “missing-rib” (MR). Experiments and finite element models were used to study the compressive behavior of the ACCs. The results indicate that all ACCs have high compressive ductility. Specifically, the RE shows the highest ductility, manifested by 853% and 708% higher energy absorption than the reference mortar and the auxetic structure itself, respectively. In addition, the RE and RS are found to exhibit stronger crack-arresting effect under compression. Therefore, they achieved comparable compressive strength to the reference mortar, which is considerably higher than CR and MR. Furthermore, decreasing the volumetric ratio of the auxetic structure by half, the ductility of the RS reduces by 32.2%, while decreasing the water-to-binder ratio of the cementitious matrix from 0.4 to 0.3 only increases the compressive strength by 18.5%. Moreover, the two-dimensional finite element analyses used herein show a good match with experiments but become less accurate at high strain levels, due to their inability to capture the out-of-plane failure of the ACCs.

Computational and physical aspects for the occurrence of crease in an elastomer under general loading conditions

We study the occurrence of crease in an elastomer under three loading conditions from both computational and physical points of view. A two-dimensional finite element analysis, including a perturbation force-based approach, is performed to detect the stable creased state, where the crease formation is completed. A mesh convergence study for the energy release and crease depth in the creased state provides a guideline for the finite element mesh requisite for predicting the occurrence of crease. We also visualize the mesh convergence for the critical creasing onset by plotting the set of compressive strain and mesh resolution at the point where the energy release is zero. In addition, the present evaluation method of the surface tension using the energy release and surface area change for an elastomer with a traction-free surface yields a good prediction for the creasing onset delayed by surface tension without additional numerical implementations or adjustment parameters. This facilitates the comprehensive study of the creasing onset delayed by the surface tension under general loading conditions. The results reveal that tensile deformation in the out-of-plane direction encourages the retardation of the creasing onset via the extension of the width and the energy emission. We further demonstrate that energetically preferential crease interval can be used to evaluate the spacing between creases delayed by moderate surface tension.

Numerical Modelling Study of Subsurface Drainage of Permeable Friction Course Considering Road Geometric Designs

This study aimed to evaluate the subsurface drainage of a permeable friction course (PFC) via two-dimensional finite element analysis. To achieve the scope, PFCs with equivalent water flow paths of length values of 10, 15, 20, and 30 m and slope values of 0.5%, 2%, 4%, 6%, and 8% were modelled based on FEniCS and implemented entirely in Python programing language to extract the time for surface ponding according to a range of rainfall intensities. The results show that when the rainfall intensity and the length of equivalent water flow path of the PFC rose, the time for surface ponding decreased. For instance, with a rainfall intensity of 10 mm/h and a slope of 0.5%, when the length of equivalent water flow path increased by 20 m, the time for surface ponding dropped by 21 min. Moreover, when the slope of the equivalent water flow path and the thickness of the PFC increased, the time for surface ponding increased. For instance, with a rainfall intensity of 10 mm/h, and a PFC with an equivalent length of 10 m, when the slope increased by 16 times, the time for surface ponding increased more than two times. The current study highlights that the thickness of the PFC has the most influence on subsurface drainage. The findings of this study indicate that at high rainfall intensities, the subsurface drainage of a PFC is not sensitive to its geometric design. Further experimental investigations are needed to evaluate and validate the subsurface drainage of a PFC considering permeability, rutting, and environmental factors.

Research on seismic fragility of subway station based on incremental dynamic analysis method

Seismic intensity measure is an significant parameter that affects the accuracy of structural seismic risk assessment, and plays an important role in the performance-based earthquake engineering research framework. Taking a two story, three span, and shallow buried subway station as the research object, a two-dimensional finite element analysis model of soil structure underground in a typical engineering site was established using ANSYS. Ten earthquake records were selected from PEER as input, and the structural seismic fragility analysis method based on incremental dynamic analysis (IDA) method was introduced into the subway station structure. The maximum story drift angle was used as the structural damage index, and three typical seismic intensity measures were selected, the exploration is conducted on the seismic intensity measures applicable to shallow buried subway stations and the variation pattern of seismic response of subway stations with increasing seismic amplitude. The seismic fragility curve of shallow buried subway station structures is established to obtain the failure probability of the structure at different seismic intensity levels. The analysis results indicate that for shallow buried subway stations, PGA is the most suitable seismic intensity measure, and the comparison with existing empirical fragility curves shows that the vulnerability analysis method is feasible and can quantitatively provide the failure probability of structures at different performance levels, providing reference for seismic design of underground structures.

Seismic Fragility Curves of Combined Multiple Tunnel Complexes in Soft Soils

Seismic fragility assessment is the probability of damage exceeding a certain design limit. The dynamic performance of a combined multiple tunnel complex is less explored and requires thorough study. This research is based on the numerical approach to evaluate the damage caused to the two new types of tunnel complexes, i.e. twin and triple tunnel complexes in a soft soil profile. A two-dimensional (2D) finite element analysis is performed to determine the induced bending moments for each of the tunnel complexes and develop the seismic fragility curves. A set of full acceleration-time histories are applied to the soil–tunnel complex system by varying embedment depths in different soft soil profiles. From the results, it is concluded that increasing the embedment ratio results in an increased probability of tunnel damage. The developed fragility curves are also inter-compared for both the tunnel complexes to evaluate the better performer during a seismic event. This study serves as an initial step toward the guidelines to determine the percentage of incurred damage and design the combined multiple tunnel complex in a seismic-prone area.

Disparate Contact Stress Behavior of Thermoplastic Gears against Steel Gear using 2D and 3D FEA

Based on the applications, the polymer gears are paired with different gear pair combinations such as Polymer – Polymer, Polymer – Steel, and Steel – Polymer. Finite Element Analysis is one of the effective techniques utilized to investigate the contact stress behavior of those gear pairs. Depending upon the selected conditions, such as two-dimensional finite element analysis with plane stress, plane strain conditions, and 3D FEA, the surface and subsurface contact stress occurrence between the gear pairs were observed. And, no proper explanations have arrived on such behaviors till date. Thus, the present study aimed to do a detailed 2D and 3D FE analysis for various thermoplastic gears with different gear pair combinations (S – P, P – S, and P – P) and investigated the occurrence of surface-subsurface stresses among the selected gear pairs. A comparison was done between the 2D and 3D FE analysis and validated with the assumed condition with regard to the face width. A gear with face widths of 5 and 20 mm has opted to reproduce the 2D plane stress and plane strain conditions, and their results were compared with 3D FEA. The contact stress data were extracted at 10 subsequent face width planes along the face width of a gear tooth. Higher directional stresses were noticed at the gear tooth mid-surface and reduced stress on the edges of the gear tooth for all the thermoplastic materials paired with all gear pairs. Surface stress for 2D FEA and subsurface stress for 3D FEA were detected for all the gear pair combinations. The maximum stress occurrence of 5 mm face width Steel – PP, Steel – ABS, Steel – DELRIN, ABS – Steel, DELRIN – Steel gear pairs exhibit a minimum depth value of 0.135 mm whereas 20 mm face width PC – Steel gear pair exhibits a maximum depth value of 0.3 mm. The maximum contact stress increases as a function of depth according to the proportional limit to elastic modulus dimensionless ratio.

Enhancing the Sealing Performance of Bolted Ball Joints by Gaskets: Numerical Simulation and Experiment

With the increasing utilization of bolted ball joint steel mesh structures in offshore floating platforms and deep-sea fish cages, the issue of seawater infiltrating the joints and members through the installation gaps of the bolted ball joint, leading to subsequent corrosion, has become increasingly prominent. This article presents an innovative method to improve the sealing performance of bolted ball joints. The approach involves creating sealed surfaces within the contact gaps between the sleeve and connecting components by adding circular grooves and sealing washers to both ends of the sleeve. Subsequently, a two-dimensional finite element analysis model of the bolted ball joint with the sealing structure was created using SOLIDWORKS 2021 and ANSYS Workbench 2022 R1. The study analyzes the sealing gasket’s contact pressure at various compression levels and evaluates its performance with bubble tests for air tightness. Research results show a linear relationship between the contact pressure and compression rate, achieving sealing pressures of 2.91 MPa, 4.22 MPa, and 5.95 MPa at compression levels of 8%, 11%, and 14%, respectively. Experimental testing demonstrates that the improved bolted ball joint exhibits excellent sealing performance.

An investigation into the influence of variable amplitude creep-fatigue loading on plasticity-induced crack closure

Finite element simulations of fatigue crack growth (FCG) and creep-fatigue crack growth (CFCG) under constant amplitude (CA) and variable amplitude (VA) loading waveforms are performed to investigate the mechanics of crack opening and closing, which has implications on crack growth rate. The material of study is the ferritic-martensitic steel 9Cr-1Mo (modified 9Cr-1Mo) at 625 °C. Two-dimensional finite element analyses of compact tension (CT) specimens are performed to simulate crack growth under several VA loading scenarios, considering elastic–plastic and creep deformations of the material at the crack tip. In this study, the relevant variable influencing crack growth rate is the crack opening load, caused by the phenomenon of plasticity-induced crack closure. A series of loading conditions were simulated using the finite element method, i.e., fatigue overload (OL) in either CA FCG or CFCG waveforms, creep-fatigue OL in CFCG waveforms, and underload (UL) in CFCG waveforms. The crack opening loads obtained from this study for CA loading in both FCG and CFCG, agree with data from published studies. This study also found that a significant reduction in crack opening loads is experienced by the growing crack when an OL or UL cycle was introduced. Immediately after the OL or UL cycle is applied, the crack opening load increases during both fatigue OL and creep-fatigue OL to values larger than those recorded during CA FCG and CFCG loading, whereas UL waveforms result in consistently lower crack opening loads. The increase in crack opening loads is proportional to both the extent of OL and the duration of hold time in the OL cycle. However, following the application of a UL, the crack opening loads in the subsequent cycles were not influenced by the magnitude of the UL or the duration of hold time in the UL cycle.

Proposal of Torque-Correct-by-Construction Optimization Method for Axial Flux Machines

We propose an innovative optimization method for axial flux machine that keeps the output torque constant in the process of weight reduction. A concept of framework is introduced that provides guidance for optimization design on how to choose and redesign the relevant parameters. Unlike the conventional algorithms that search candidates in sample space, new designs with reduced weight are directly determined by following the developed optimization strategy using two-dimensional finite element analysis (FEA). The torque error is restricted by a maximum allowable error introduced in the framework. A single-sided axial flux permanent magnet synchronous machine is used as a starting design. A total of 29 new designs are derived with gradually varying optimization variables. The optimization trend and limit are investigated with respect to the redesigned parameters as well as the resulting weights, which provide an overview for selecting optimal design. At last, the torque of every design is verified by both two-dimensional and three-dimensional FEA. The effectiveness of proposed method is demonstrated by the result that the weight is significantly and continuously reduced as the independent optimization variable increases while the torque error remains in a small extent.

Experimental and numerical study for seismic response of strip footing on slopes

The present study investigates the free-field response of slopes as well as the seismic response of strip footing on slopes. The small-scaled physical model tests (PMT) have been performed under one-directional excitation. The sinusoidal waves of different amplitudes and frequencies are applied at the base of the model. To examine the kinematic interaction between the footing and slope, a rigid strip footing is placed at the center of the slope. The free-field response of the slope as well as the seismic response of the footing on the slope from PMT is determined using digital image correlation (DIC). Two-dimensional finite element analysis (FEA) has been carried out to simulate the PMT results. No study has been reported in the literature considering both experimental and numerical work. Further, the effects of increasing load on the footing on slopes have not been examined yet. Results from PMT and FEA are found in good agreement. The maximum amplification is observed near the crest for free-field response of slope. For both horizontal ground surface and sloping ground, the maximum amplification occurs at the frequency of excitation. However, some small peaks at other frequencies are also observed for the sloping ground due to the reflection of waves from the sloping surface. The seismic settlement of strip footing is increased with the increase of slope angle, amplitude and frequency of the excitation. However, the seismic settlement decreases with the increase in footing width and edge distance of footing from the slope. For footing on slope, the maximum amplification is observed at the center of the slope. A large settlement of footing is observed when the footing is heavily loaded (e.g., 80% of the ultimate bearing capacity of footing).

Novel Double Mode Dual-Stator Wound Rotor Synchronous Machine for Variable Speed Applications

This paper offers a novel dual-mode double stator wound rotor synchronous machine for variable speed applications. The proposed motor integrates the benefits of both the traditional wound rotor synchronous machine (WRSM) and brushless wound rotor synchronous machine (BL-WRSM). A constant torque can be attained in the maximum torque per ampere region by operating the proposed machine as a traditional WRSM in Mode I, and a constant power can be attained in the field-weakening region by operating it as a BL-WRSM in Mode II. Moreover, due to the dual-stator structure, the proposed machine exhibits improved performance in terms of high torque density as compared to the existing single stator BL-WRSM. By using a special stator winding arrangement to achieve the sub-harmonic component of the stator magnetomotive force, the brushless operation of the proposed machine is achieved. The additional sub-harmonic component induces a voltage in the harmonic winding placed on the rotor, which is then rectified and provided a DC current to field winding for brushless excitation. In order to validate the effectiveness of the proposed machine, a two-dimensional finite element analysis (FEA) is carried out.

Method for estimating three-dimensional effects on braced excavation in clay

The maximum lateral wall movements are usually estimated by two-dimensional finite element analysis. However, three-dimensional effects due to the higher stiffness at the corner will result in smaller wall movements than that under plane strain conditions. This paper proposed a method to quantize the three-dimensional effects. The limitations of quantifying the three-dimensional effects by the current method were presented by analyzing an excavation case. A comprehensive parametric study was carried out to explore the effects of soil condition, support system stiffness, and the excavation geometry on the three-dimensional effects of excavation. The finite-element simulation results were represented by the plane strain ratio (PSR), and an empirical equation for PSR prediction was proposed considering soil condition, support system stiffness, excavation geometry, and distance from the excavation corner. The proposed equation was verified against case data reported in the literature, and the overall agreement was satisfactory. This equation offers a more reliable way to quantify the three-dimensional effects of rectangular excavation with internal struts in clay.

Optimization design of Tubular Permanent Magnet Linear Generator based on entropy model for wave energy conversion

—The effective use of wave energy which has huge reserves is one of the ways to solve the climate problem and energy crisis. In this paper, a Tubular Permanent Magnet Linear Generator (TPMLG) is optimized by the combination of comprehensive sensitive parameters method and particle swarm optimization based on entropy model (EPSO). By introducing the information entropy model, the aggregation characteristics in the process of particle swarm search are accurately analyzed, which can effectively reduce the invalid iteration of particle swarm. Firstly, the main design parameters of TPMLG are designed using the basic initial principle of permanent magnet linear machines. Then, the two-dimensional parametric finite element analysis model of the TPMLG is established, and a comprehensive sensitivity index Sc is defined to calculate the sensitivity indices according to power density and thrust fluctuation. The strong sensitivity parameters are optimized Particle Swarm Optimization based on entropy model, and the Non-sensitivity parameters maintain the initial design values. Finally, an experimental prototype TPMLG was manufactured according to the optimized results. The speed of TPMLG was simulated by the universal testing machine MTS100kN, the experimental results show that the designed TPMLG can be effectively applied to the direct drive power take-off system.

Investigation of Rotor Topologies for Reducing Torque Ripple in Double-Layer IPMSMs for Automotive Applications

Interior permanent magnet synchronous motors (IPMSMs) are currently widely used for traction applications. However, the torque ripple in these motors needs to be reduced because it causes vibration and acoustic noise. Accordingly, this study first determined the guidelines for reducing the torque ripple of multilayer IPMSMs and then proposed a double-layer IPMSM with holes drilled in the rotor core. The torque ripple reduction for the proposed rotor structure was examined using two-dimensional finite element analysis and experiments with prototypes. The analytical results showed that, under maximum torque-per-ampere control, the torque ripple using the proposed model was suppressed by 54.8% compared with the reference model while limiting the average torque reduction to 3.6%. Moreover, multi-objective optimization based on the guidelines was performed. With the proposed structure, the torque characteristics at high and low currents were highly correlated, and a similar torque ripple reduction effect was obtained even at low current, which is frequently used in traction motors for automotive applications. Finally, optimization was performed for an IPMSM with other topologies, resulting in verification of the generalizability of the proposed method.