Coupling Finite Element Method Research Articles

Coupled mechanical and electrochemical modeling and simulations for electrochemical hydrogen compressors (EHC)

A three-dimensional (3-D) model of an electrochemical hydrogen compressor (EHC) cell was developed by rigorously accounting for the hydrogen oxidation and evolution reactions and resulting species and charge transport through various EHC components. Particular emphasis was placed on coupling computational fluid dynamics (CFD) and finite element method (FEM) methodology to predict EHC performance numerically under the deformed cell geometries, i.e., induced by the cell assembly and the hydrogen pressure difference between the anode and cathode sides. First, the EHC model was validated experimentally against polarization curves and impedance spectra measured under different hydrogen compression ratios and operating temperatures. In general, the simulation results compared well with the measured data and further revealed the operating characteristics of the EHC cells. In particular, the most irreversible voltage rise comes from the ohmic overpotential because of the proton transport through the membrane, clearly indicating dehydration of the electrolyte due mainly to the electro-osmotic drag effect is one of the most critical issues for efficient EHC operations. While the dehydration issue tends to be mitigated under higher hydrogen discharge pressure or higher operating temperatures, the cell deformation toward the low-pressure side (anode) is visible even with the low hydrogen compression ratio of 10, clearly requiring improvement in the mechanical properties of EHC components and cell structure for a higher compression of hydrogen gas.

Coupling finite element method with meshless finite difference method by means of approximation constraints

Coupling finite element method with meshless finite difference method by means of approximation constraints

A numerical framework coupling finite element and meshless methods in sequential and parallel simulations

A numerical framework coupling finite element and meshless methods in sequential and parallel simulations

Coupled mixed finite element and finite volume methods for a solid velocity-based model of multidimensional sedimentation

In this paper we introduce and analyze a model of sedimentation based on a solid velocity formulation. A particular feature of the governing equations is given by the fact that the velocity field is non-divergence free. We introduce extra variables such as the pseudostress tensor relating the velocity gradient with the pressure, thus leading to a mixed variational formulation consisting of two systems of equations coupled through their source terms. A result of existence and uniqueness of solutions is shown by means of a fixed-point strategy and the help of the Babuška–Brezzi theory and Banach theorem. Additionally, we employ suitable finite dimensional subspaces to approximate both systems of equations via associated mixed finite element methods. The well-posedness of the resulting coupled scheme is also treated via a fixed-point approach, and hence the discrete version of the existence and uniqueness result is derived analogously to the continuous case. The above is then combined with a finite volume method for the transport equation. Finally, several numerical results illustrating the performance of the proposed model and the full numerical scheme, and confirming the theoretical rates of convergence, are presented.

Transfer Learning-Based Coupling of Smoothed Finite Element Method and Physics-Informed Neural Network for Solving Elastoplastic Inverse Problems

In practical engineering applications, there is a high demand for inverting parameters for various materials, and obtaining monitoring data can be costly. Traditional inverse methods often involve tedious computational processes, require significant computational effort, and exhibit slow convergence speeds. The recently proposed Physics-Informed Neural Network (PINN) has shown great potential in solving inverse problems. Therefore, in this paper, we propose a transfer learning-based coupling of the Smoothed Finite Element Method (S-FEM) and PINN methods for the inversion of parameters in elastic-plasticity problems. The aim is to improve the accuracy and efficiency of parameter inversion for different elastic-plastic materials with limited data. High-quality small datasets were synthesized using S-FEM and subsequently combined with PINN for pre-training purposes. The parameters of the pre-trained model were saved and used as the initial state for the PINN model in the inversion of new material parameters. The inversion performance of the coupling of S-FEM and PINN is compared with the coupling of the conventional Finite Element Method (FEM) and PINN on a small data set. Additionally, we compared the efficiency and accuracy of both the transfer learning-based and non-transfer learning-based methods of the coupling of S-FEM and PINN in the inversion of different material parameters. The results show that: (1) our method performs well on small datasets, with an inversion error of essentially less than 2%; (2) our approach outperforms the coupling of conventional FEM and PINN in terms of both computational accuracy and computational efficiency; and (3) our approach is at least twice as efficient as the coupling of S-FEM and PINN without transfer learning, while still maintaining accuracy. Our method is well-suited for the inversion of different material parameters using only small datasets. The use of transfer learning greatly improves computational efficiency, making our method an efficient and accurate solution for reducing computational cost and complexity in practical engineering applications.

Multi-physics simulation of mechano-electrochemical bidirectional coupling interaction of galvanic corrosion between Al alloy and 316L SS

Due to the limitations of experimental testing in material size and time scale, this work presents a mechano-electrochemical bidirectional coupling finite element method (FEM) simulation model on account of mechanistic and corrosion kinetics understanding in Al alloy-316L SS galvanic couple. The galvanic corrosion behavior and anodic dissolution deformation of the couple in 3.5 wt.% NaCl solution were analyzed. The effect of external load on galvanic corrosion initiation and propagation was investigated based on Gutman’s theory. The FEM model reveals that the galvanic corrosion is connected with the mechanical damage and the stress concentration coefficient, and highlights the crucial role of corrosion defect in the mechanical behavior of Al alloy. The results show that the external force aggravates the galvanic corrosion at the defects, deteriorating the protection of corrosion products. The thickness of the Al (OH)3 deposition layer reflects the electrochemical reactivity at different positions on the anode surface. The mechanical damage occurs initially at the corrosion defect and then extends to the middle of the anode. The stress concentration coefficient at the center of the anode gradually exceeds the position of the corrosion defect, resulting in mechanical failure at this position.

Stochastic Vibrations of a System of Plates Immersed in Fluid Using a Coupled Boundary Element, Finite Element, and Finite Difference Methods Approach.

The main objective of this work is to investigate the natural vibrations of a system of two thin (Kirchhoff-Love) plates surrounded by liquid in terms of the coupled Stochastic Boundary Element Method (SBEM), Stochastic Finite Element Method (SFEM), and Stochastic Finite Difference Method (SFDM) implemented using three different probabilistic approaches. The BEM, FEM, and FDM were used equally to describe plate deformation, and the BEM was applied to describe the dynamic interaction of water on a plate surface. The plate's inertial forces were expressed using a diagonal or consistent mass matrix. The inertial forces of water were described using the mass matrix, which was fully populated and derived using the theory of double-layer potential. The main aspect of this work is the simultaneous application of the BEM, FEM, and FDM to describe and model the problem of natural vibrations in a coupled problem in solid-liquid mechanics. The second very important novelty of this work is the application of the Bhattacharyya relative entropy apparatus to test the safety of such a system in terms of potential resonance. The presented concept is part of a solution to engineering problems in the field of structure and fluid dynamics and can also be successfully applied to the analysis of the dynamics of the control surfaces of ships or aircraft.

Contact forces and motion behavior of non-Newtonian fluid-solid food by coupled SPH-FEM method.

The non-Newtonian fluid-solid interaction food has complex physical properties and complicated contact force, which brings the greater technical challenge to improving the food fetching rate. In this work, we used the smooth particle hydrodynamics and finite element coupling method for a node-to-surface penalty function contact to characterize the contact forces between non-Newtonian fluid food and solid foods. The shear rheological properties and density of non-Newtonian fluid food, including xanthan gum (XG) and guar gum (GG), were investigated by a viscometer and densitometer, respectively. The results showed that the shear viscosity of non-Newtonian fluid food depends to some extent on the mass ratio of the thickening gums. We investigated the effects of the end-effector with different fetching velocities and different inclination angles, and the nut root powder paste (NRPP) food with different ratios of XG and GG, on the fetching rate, stress-strain, and motion behavior. The results showed that the stress increased with increasing v1 and w; however, the v2 had less effect on the stress. The sparseness of the distribution of solid food was related to the v1 and w, whereas it was less influenced by the v2 . The distribution of solid food became denser in the X-Z plane and sparser in the X-Y plane with increasing inclination angle. The motion behavior of viscoelastic solid foods depended on the mass ratio of XG to GG dissolved in NRPP. The present work can provide a theoretical foundation for meal-assisting robots and robots in the field of food engineering with the task of improving the food fetching rate.

Analysis of residual stress relief for Ti62A alloy welded joints by post weld heat treatment considering creep effect

In this paper, the Arrhenius-type constitutive equation based on strain compensation was developed, and the constants of the constitutive equation were determined by linear fitting to construct the material models of Ti62A alloy. Meanwhile, the creep parameters of Ti62A alloy at high temperature were corrected by existing experiments, and the Norton creep model during post weld heat treatment (PWHT) was established. The sequential coupling finite element method was used to calculate the residual stress distribution in the welding and PWHT processes of Ti62A alloy plates. The effects of PWHT parameters on the residual stress relief of welded joints were revealed, such as creep, heating rate, and heat treatment temperature. The results reveal that the creep has an important influence on residual stress relief during PWHT. Compared with longitudinal residual stress, the effects of heating rate and heat treatment temperature on transverse residual stress are more significant. A lower heating rate or higher heat treatment temperature will be beneficial for releasing residual stress. The results of this paper will contribute to a better understanding of PWHT mechanisms and provide a good theoretical guidance for optimizing process parameters.

Progress in FEM modeling on mechanical and electromechanical properties of carbon nanotube cement-based composites

Abstract Carbon nanotubes (CNTs) reinforced cementitious composite (CNRC) with excellent electrical and self-sensing properties, which enables it to serve as an intrinsic sensor for structural health monitoring (SHM). However, the requirements of modern industry for accurate calculation and performance design of engineering materials are not met by traditional experimental studies alone. The finite element method (FEM) has the advantages of simplicity of operation, accuracy, and cost-effectiveness, and it has been widely used in the property verification and prediction of various composite materials. In this article, the constitutive model, FEM modeling method, and simulation process of CNRC along with existing model types, innate relations, and model parameters are reviewed, and the corresponding mechanical, electrical, and electromechanical coupling properties of CNRC under different parameters are systematically analyzed by FEM method. By combining different uncertainty parameters and model types, the advantages and disadvantages of FEM for mechanical, electromechanical coupling, and SHM applications of CNRC modeling are explored. The results are in good agreement with those in the existing CNRC experiment, which effectively proves the reliability of the FEM method in CNRC research. This work is important to develop a sound theoretical model verification and performance prediction for early applications in SHM of CNRC.

Fracture failure analysis of insulation with initial crack defect for stator end-winding in induction motor by using magnetic-structural coupling model

The insulation mechanic failure in stator end-winding of induction motor is usually an early and serious cause to weaken the residual breakdown electrical field strength and produce the short-circuit fault, especially subjecting to the combination of dynamical electromagnetic forces, mechanical stress and vibration. In this paper, the fracturebehavior of insulation layer with considering the initial crack defects and end-hoop support failures in end-windings were analyzed by using magnetic-structural coupling model and finite element method (FEM). Firstly, the distributions of magnetic flux density and electromagnetic force around the stator end region were determined by injecting three-phase alternating current. Secondly, the dynamic characteristics of deformation, stress and strain in winding insulation were respectively calculated by coupling the transient electromagnetic and structural analysis. Furthermore, the weak points of the concentrated stress and strain were located. Thirdly, the crack model mounted in winding insulation is defined and simulated by employing three-dimensional (3-D) semi-elliptical crack element. To evaluate the fracture mechanism and the degree of crack expansion quantitatively, the stress intensity factor (SIF) was introduced. Finally, the influence of crack location, direction, depth and end-hoop support failure on SIF and crack propagation were investigated. Results show that the concentrated stress at knuckle part of the coil insulation is lager quite larger than that of other parts. The SIF of transverse crack is larger than that of longitudinal cracks. The larger the initial crack depth in the stator end-winding insulation, the more serious the tendency and degree of crack fracture. Local end-hoop support failure also has an important influence on the crack propagation. Results in this study may contribute to the understanding of fracturefailure behaviors in insulation under dynamical electromagnetic vibration and provide necessary theoretical reference for fault diagnosis and prediction of stator winding in induction motors.

Numerical analysis and experimental measurement on segmented ring transducer acoustic fields

In order to overcome the shortcomings of the two traditional methods of finite element method (FEM) and direct coupling of mechanical FEM and acoustic boundary element method (BEM) in the comprehensive simulation of acoustic characteristics of non-two-dimensional axisymmetrical transducers, the acoustic FEM and acoustic BEM coupling method is adopted in this study to model, calculate and analyze the three-dimensional (3D) model of the segmented ring transducer. Firstly, the basic theory of FEM, BEM and FEM-BEM coupling calculation of the transducer is introduced. Secondly, a 1/8 3D model of the segmented ring transducer is built to simulate the underwater electro-acoustic characteristics of the transducer. Finally, a transducer prototype is manufactured according to the numerical model, and the electro-acoustic performance of the transducer is measured in the anechoic tank. The numerical results of transmission voltage response (TVR), admittance and radiation directivity curves are in good agreement with the experimentally measured results, which indicate that the proposed method is correct and effective. Therefore, the method could be used to comprehensively calculate the acoustic characteristics of the segmented ring transducer. In addition, the method could be used not only to study the acoustic problems of other transducers or transducers arrays with complex structures that are non-two-dimensional axisymmetrical, but also to comprehensively analyze and predict the near-field and far-field acoustic characteristics of any transducers including two-dimensional (2D) axisymmetrical transducers.

Coupled finite element-discrete element method (FEM/DEM) for modelling hypervelocity impacts

Coupled finite element-discrete element method (FEM/DEM) for modelling hypervelocity impacts

Failure Mechanisms and Constitutive Model of Composite Rock under Dynamic Loading

Abstract In order to investigate the dynamic response characteristics of composite rock with different joint angles, static compression test and dynamic impact test are carried out using WDW-300E servo pressure-testing machine and split Hopkinson pressure bar (SHPB) test system. The dynamic compressive strength, energy dissipation, and failure modes are compared between rock coal (R-C) and coal rock (C-R). Furthermore, a 3D SHPB simulation system is constructed using coupling finite difference method and discrete element method (FDM-DEM) to reproduce the energy evolution and failure modes of composite rock with different joint angles, and the fabric tensor is obtained based on secondary development. Finally, a constitutive model of composite rock is established considering joint angles. The results of experiment, simulation, and theoretical analysis show that for the case of uniaxial compression test, with the increase of joint angle, the peak stress of composite rock shows obvious U-shaped change, and the elastic modulus increases gradually while the peak strain decreases gradually. For the case of dynamic impact test, the peak stress, strain, and energy dissipation values of composite rock decrease first and then increase with the increase of angle, and the elastic modulus of composite rock increases monotonically after a slight fluctuation of 30°. The stress, energy dissipation and elastic modulus of composite rock R-C are larger than that of composite rock C-R. However, the strain value of composite rock R-C is generally less than of composite rock C-R. The failure mode of composite rock with small and large angle is mainly splitting under dynamic impact, and the fracture fragmentation is relatively small with high energy absorption rate, while the fracture fragmentation is mainly shear and splitting mixed failure with low energy absorption rate. The energy accumulation and transformation process inside the composite rock are analyzed by 3D simulation system, and the damage of the composite rock under impact is mainly concentrated on the coal side, and peak values of contact number and contact force with different joint angles are calculated by using fabric tensor. Based on Weibull distribution, a constitutive model of composite rock is constructed considering initial damage and dynamic failure effect, which is in good agreement with experimental and simulation results, verifying the correctness of the constructed model.

Coupled Eulerian-Lagrangian Debris Flow Model with Flexible Barrier

Natural hazards such as large debris flow events can have catastrophic effects on the environment and critical infrastructure, posing a significant threat to human life. Debris flows often exhibit high velocity, high-pressure discharges due to their bulk volume, and the capacity to transport considerable volumes of large rocks, boulders, and woody debris. Although debris flow run-out simulations are commonly performed using hydraulic modelling software, these environments are seldom capable of assessing the interaction between the debris fluid, transported material, and protective structures. In this research, large deformation numerical models are calibrated using input parameters from hydraulic modelling software. Due to the computational cost of the large deformation models involving fluid-solid-structure simulation with flexible net barriers, an equivalent stiffness method is implemented to provide comparable performance through a membrane structure. The Coupled Eulerian-Lagrangian Finite Element method is used to model the impact forces of rocky boulders on the membrane, exhibiting damage characteristics consistent with flexible ring-net protective structures. The Coupled Eulerian-Lagrangian model results highlight the performance of the simplified membrane, as shown through a benchmark simulation of debris flow with boulders.

Central defects control of Ti-6Al-4V alloy with heavy section reduction during flat cross wedge rolling

Cross wedge rolling (CWR) process is expected as an efficient and innovative preforming process for the forged aero-engine blades. But it is still a grand challenge to control the process defects and the performance of the rolled parts. According to the requirements of an aero-engine Ti-6Al-4V (TC4) blade billet with heavy section reduction up to 83%, flat CWR tools were designed and optimized by the thermal-mechanical coupling finite element (FE) method. The metal flow, damage evolution, and the distribution of stress and strain during the forming process were analysed. Then, the CWR experiments were carried out on IM500 flat CWR mill under different technological conditions. The obtained rolled parts were subjected to non-destructive testing (NDT), tension tests and microstructure analysis. The results showed that the central defects, such as micropores and voids, which seriously reduce mechanical properties, occurred in some of the rolled parts more or less. The volume of central defects was closely related to the initial rolling temperature of the billets. When the heated temperature of the TC4 billet was higher than 850°C, the target rolled part without central defects can be obtained. This research work can be a reference for the single-wedge CWR forming of titanium alloy with heavy section reduction, promoting the application of CWR in the aero-engine blade preforming process.

A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions

The boundary element method (BEM) has proven to be an efficient approach for crack analysis in fracture mechanics, while its versatility in application to crack problems of complex structures with irregular boundaries deserves further attention. In this study, to improve the applicability to complex crack analysis, a cracked superelement is first established with BEM to model the near-crack region, and the crack problem is then solved within the frame of finite element method (FEM). The stiffness matrix of the cracked superelement is formulated using the spline fictitious boundary element method (SFBEM) based on the Erdogan fundamental solutions for an infinite plane with a single crack. The proposed superelement is further incorporated into a finite element mesh to simulate the behaviour of the crack zone, and the governing equation of the crack problem is finally established and solved using the typical procedure of FEM. After obtaining the nodal displacements of the superelement, the stress intensity factors (SIFs) of crack tips can be obtained by a backward analysis with SFBEM. The accuracy and efficiency of the proposed SFBEM–FEM coupling method are demonstrated by two numerical examples involving a rectangular plate with a central crack and a square plate with 100 horizontal cracks. The present approach is further applied to the analysis of the SIFs of multiple cracks exposed in a steel anchorage box for a hanger of a suspension bridge, which indicates the merging of the cracked superelements to the commercial FEM software is computationally efficient for the analysis of complex structures with multiple cracks.

Hydrogenated Boron Phosphide THz-Metamaterial-Based Biosensor for Diagnosing COVID-19: A DFT Coupled FEM Study.

Recent reports focus on the hydrogenation engineering of monolayer boron phosphide and simultaneously explore its promising applications in nanoelectronics. Coupling density functional theory and finite element method, we investigate the bowtie triangle ring microstructure composed of boron phosphide with hydrogenation based on structural and performance analysis. We determine the carrier mobility of hydrogenated boron phosphide, reveal the effect of structural and material parameters on resonance frequencies, and discuss the variation of the electric field at the two tips. The results suggest that the mobilities of electrons for hydrogenated BP monolayer in the armchair and zigzag directions are 0.51 and 94.4 cm2·V-1·s-1, whereas for holes, the values are 136.8 and 175.15 cm2·V-1·s-1. Meanwhile, the transmission spectra of the bowtie triangle ring microstructure can be controlled by adjusting the length of the bowtie triangle ring microstructure and carrier density of hydrogenated BP. With the increasing length, the transmission spectrum has a red-shift and the electric field at the tips of equilateral triangle rings is significantly weakened. Furthermore, the theoretical sensitivity of the BTR structure reaches 100 GHz/RIU, which is sufficient to determine healthy and COVID-19-infected individuals. Our findings may open up new avenues for promising applications in the rapid diagnosis of COVID-19.

Numerical investigation of dry bulk cargo load during ship vertical motion

The accurate estimation of cargo load is important for designing double bottom structures. However, dry bulk cargo load due to ship acceleration has rarely been investigated in detail. In this study, DEM (Discrete Element Method)-FEM (Finite Element Method) coupling analyses with simplified vessel models were used to evaluate the dry bulk cargo load acting on the bottom plate; the dry bulk cargo and deformation of the bottom plate were expressed by discrete and finite elements, respectively. The analyses for the first time showed the occurrence of a large force near the edge of the bottom plate and small force around the center when the bottom plate was elastic. These forces resulted in the reduction of the bending stress on the bottom plate compared to a condition assuming uniform distribution of the dry bulk cargo load. This result firstly explained that the reduction of the bottom plate bending stress in previous measurements of double bottom strain of a bulk carrier during ocean going. Above non-uniformity of the force distribution was not observed when the bottom plate was rigid. This change in the distribution was caused by the arching effect, which occurred due to interlocking between discrete elements. The amplitude of force redistribution depended on the ratio of the width of the vessels to the height of the aggregate of the discrete elements. The DEM-FEM coupling analyses also showed that an appropriate design of the hopper plate can support the inertia of the discrete element aggregate located above the flat bottom plate, and thereby reduce the force acting on the flat bottom plate.

Bearing Behavior of Axially Compressed High-Strength Steel Columns in Precipitator Casing Considering the Stressed-Skin Effect of Wallboard

To explore the application feasibility of high-strength steel in skeleton columns of precipitator casing structures, the bearing behavior of axially compressed H-section high-strength steel columns was investigated by the nonlinear finite element method by considering the stressed-skin effect of wallboard. When the column yield strength does not exceed 460 MPa, the column undergoes elasto-plastic interactive buckling, which means the steel strength can be fully utilized. For the column strength of 550 MPa or 690 MPa, the wallboard yield failure occurs, owing to excessive loading of the relatively weak wallboard, and column stress magnitude is usually in the elastic range without the full utilization of steel strength, whereas if the wallboard is stiff enough, columns will still undergo buckling failure. A welding residual stress measuring test was conducted to validate the residual stress generation simulation via the thermal-mechanical coupling finite element method. Concerning the geometrical imperfections and residual stresses, it was found that their influence becomes less severe when the column steel strength increases. The bearing capacity can be improved by increasing the wallboard thickness and stiffener stiffness, or reducing the wallboard width, the stiffener spacing, the width-to-thickness ratio of column flange, the height-to-thickness ratio of column web, and column torsional slenderness ratio. Column material can be fully utilized when column steel strength does not exceed 460 MPa. Hence, employing high-strength steel is reasonable. When the column steel strength is equal to or higher than 550 MPa, wallboard strength should be sufficient to ensure that the column failure occurs before wallboard failure. In such cases, high-strength steel should be used carefully.