Coupling Finite Element Method Research Articles

Analysis of r - Adaptive coupling adaptive time integration strategy in FEM of seismic liquefaction

In seismic finite element analysis of saturated soils, the challenges primarily reside in liquefaction and the large deformation of soil induced by strong earthquakes. Traditional updated Lagrangian methods may result in severe mesh distortion after updating the spatial configuration of nodes. To address this issue, this study develops an r - adaptive approach based on a solid - fluid coupling finite element method (FEM) platform to mitigate mesh distortion problems. This technique optimizes mesh nodes without altering the overall topology, thereby maintaining mesh integrity. However, enhancing mesh accuracy comes at the expense of increased computational costs. To alleviate high computational expenses, this study couples two types of adaptive time stepping techniques, based on mixed error and displacement history curvature, with mesh adaptation. Through verification on two typical dynamic liquefaction models of saturated soil on embankment and subway station, this technique effectively balances the relationship between computational accuracy and costs.

Broadband topology optimization of three-dimensional structural-acoustic interaction with reduced order isogeometric FEM/BEM

This paper presents a model order reduction method to accelerate broadband topology optimization of structural-acoustic interaction systems by coupling Finite Element Methods and Boundary Element Methods. The finite element method is used for simulating thin-shell vibration and the boundary element method for exterior acoustic fields. Moreover, the finite element and boundary element methods are implemented in the context of isogeometric analysis, whereby the geometric accuracy and high order continuity of Kirchhoff-Love shells can be guaranteed and meantime no meshing is necessary. The topology optimization method takes continuous material interpolation functions in the density and bulk modulus, and adopts adjoint variable methods for sensitivity analysis. The reduced order model is constructed based on second-order Arnoldi algorithm combined with Taylor's expansions which eliminate the frequency dependence of the system matrices. Numerical results show that the proposed algorithm can significantly improve the efficiency of broadband topology optimization analysis.

Influence of deposition path strategy on residual stress and deformation in weaving wire-arc additive manufacturing of disc parts

Deposition pattern and path-planning deposition strategy have significant impacts on the deformation and residual stress of components during a wire-arc additive manufacturing (WAAM) process. This work comparatively addressed the influence of weaving and non-weaving deposition patterns on the distributions of residual stress and warping deformation during a single-bead-on-plate WAAM process. Further, four path strategies with different deposition sequences (in-out and out-in) and deposition directions (alternate and consistent) were designed for a weaving WAAM process of disc part, and their impacts on temperature history, warping deformation, and residual stress were comparatively analyzed through thermal-mechanical coupling finite element (FE) method. Simulation and experiment results manifest that, compared to the non-weaving pattern, the weaving deposition pattern results in more uniform deformation and lower residual stress on the deposited plate due to wider and shallower molten pool. Comparison results for the four deposition path strategies in the weaving WAAM process of disc part suggest that the out-in deposition sequence exhibits faster heat dissipation and uniform temperature field during the cooling stage, resulting in reduced warping deformation and residual stress on the workpiece. Moreover, uniform deformation is observed across path strategies employing alternate deposition direction. The out-in alternate deposition path strategy was identified as the optimal choice for the weaving WAAM process of disc part. Finally, physical experiments validated the simulated warping deformation of disc parts under different deposition path strategies. This work contributes to the design and optimization of weaving WAAM process for disc-shaped components.

Research on Structural Collapse of a Containership under Combined Bending–Torsion by Oblique Waves

Large waves cause a great number of collapsed-ship accidents, resulting in the loss of many lives and properties. It has been found that most of these collapses are caused by encountering oblique waves. As a result, the ship structure experiences a complex collapse under combined bending and torsion. This paper utilizes a numerical hydroelasto-plastic approach, coupling CFD (Computational Fluid Dynamics) with the nonlinear FEM (Finite-Element Method), to study the structural collapse of a containership in oblique waves. First, a 4600 TEU containership was selected to study its collapse mechanism under oblique waves. Second, a hydroelasto-plastic numerical coupling of CFD and nonlinear FEM is used to co-calculate the wave loads and structural collapse of containership. The hydrodynamic model is constructed and used to solve wave loads in the CFD solver, and a nonlinear FEM model of containership with finer meshes is also modeled to solve the structural collapses, including plasticity and buckling. Third, several oblique-wave cases involving heading angles of 120°, 135°, 150°, and 180° are determined and calculated. Typical cases are discussed for time-domain stress histories and collapsed courses. Finally, the influence of oblique-wave parameters on structural collapse is discussed, and the collapse mechanism of containerships under the action of oblique waves is obtained, which provides a new understanding of ship structure design.

Design and testing of a high precision parallel manipulator with hyperbolic–elliptic flexure hinges

A novel six-degree-of-freedom (6-DOF) parallel manipulator (PM) with a 6-PSS configuration is designed as a piston error compensation mechanism in an optical system. To meet the high-precision adjustment requirement, the prismatic hinges are driven by nanometer resolution piezoelectric motors, and hyperbolic–elliptic (H-E) flexure hinges are used as spherical hinges because of their zero clearance and greater precision transmission capability than traditional rigid hinges. The analysis of the closed-loop vector relationship of the kinematic chain of the leg results in the construction of the kinematic equation, which can satisfy the inverse kinematic solution within a certain precision. The Newton–Raphson method is used for the iteration to solve the forward kinematics. A kinematic simulation was performed to verify the accuracy and effectiveness of the kinematic model using the rigid–flexible coupling finite element method. The workspace of the PM was analyzed using inverse kinematics and kinematics simulation. Two test systems were constructed to test the working performance of the PM. The experimental tests demonstrated that the resolution reached the nanometer level and the travel reached the millimeter level.

Vibration isolation characteristics of a novel composite flexible vibration-damping foundation

To address the challenge of low-frequency vibration in ships, we introduce a vibration isolation technique and a composite flexible vibration-damping foundation grounded in the principles of impedance equalization and the off-plane attenuation properties of surface waves. We utilize a fluid-structural coupling finite element method and experimental validation to analyze the effect of various properties of the liquid layer of the base. The results indicate that the composite foundation offers superior vibration isolation compared to traditional foundations across a frequency range of 10–500 Hz. Enhancements in the liquid’s viscosity and an increased layer thickness are found to significantly bolster the foundation’s ability to isolate vibrations. The relationship between liquid density and the vibration isolation performance of the base is not entirely positive. An increase in liquid density does provide some improvement to the vibration isolation performance at higher frequencies. Additionally, the presence of multiple liquid sacs within the foundation has a minimal influence on low-frequency isolation but proves to be increasingly beneficial at higher frequencies. Through this study, we aim to provide fresh perspectives and solutions for the attenuation and management of low-frequency vibrations in ships.

Influence of microwave irradiation and water-based cooling on the fracturing behavior and failure mode transition of CSTBD granite

Utilizing microwave heating in conjunction with water-based cooling technology can effectively reduce the fracture toughness of hard rocks. However, the fracturing characteristics and failure modes of hard rocks following microwave heating and water-based cooling remain undisclosed. Granite, being one of the most common types of hard rocks, was selected for this study, employing Cracked Straight Through Brazilian Disc (CSTBD) specimens for laboratory testing. CSTBD specimens with various crack angles (0, 30, 60, and 90°) underwent treatment with varying microwave durations (30, 60, 180, 300, and 420 s). Subsequently, Brazilian splitting tests were conducted on the damaged specimens. To simulate the entire process of microwave heating and mechanical testing of CSTBD specimens, we developed a coupled Finite Element Method – Distinct Lattice Spring Model (FEM-DLSM) approach. The results indicate that microwave heating with water-based cooling significantly influences the fracture toughness of CSTBD granite. Mode-I fracture toughness decreases with microwave heating temperature at a low crack angle (pure tensile failure and tensile–shear mixed failure) and increases at a high crack angle (compressive–shear failure and compressive failure). Mode II fracture toughness decreases with microwave heating temperature at any crack angle. Microwave heating with water-based cooling causes a decrease in the transition angles from tensile–shear failure to compressive–shear failure and from compressive–shear failure to compressive failure. Thermally induced microcracks in the rock specimen are responsible for changes in fracture toughness and failure mode transitions. After microwave heating and water-based cooling, numerous microcracks are induced in the rock interior. While macroscopic cracks predominantly control failure, growing microcracks, by weakening the rock matrix, shift the initiation position of the failure crack from the tip of the macroscopic crack to other positions, following the principle of the weakest failure path.

Coupling finite and boundary element methods to solve the Poisson-Boltzmann equation for electrostatics in molecular solvation.

The Poisson-Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to the accurate representation of the molecular surface and partial charges, and exact enforcement of the boundary conditions at infinity. However, the boundary element method is limited to linear equations and piecewise constant variations of the material properties. In this work, we present a scheme that couples finite and boundary elements for the linearised Poisson-Boltzmann equation, where the finite element method is applied in a confined solute region and the boundary element method in the external solvent region. As a proof-of-concept exercise, we use the simplest methods available: Johnson-Nédélec coupling with mass matrix and diagonal preconditioning, implemented using the Bempp-cl and FEniCSx libraries via their Python interfaces. We showcase our implementation by computing the polar component of the solvation free energy of a set of molecules using a constant and a Gaussian-varying permittivity. As validation, we compare against well-established finite difference solvers for an extensive binding energy data set, and with the finite difference code APBS (to 0.5%) for Gaussian permittivities. We also show scaling results from protein G B1 (955 atoms) up to immunoglobulin G (20,148 atoms). For small problems, the coupled method was efficient, outperforming a purely boundary integral approach. For Gaussian-varying permittivities, which are beyond the applicability of boundary elements alone, we were able to run medium to large-sized problems on a single workstation. The development of better preconditioning techniques and the use of distributed memory parallelism for larger systems remains an area for future work. We hope this work will serve as inspiration for future developments that consider space-varying field parameters, and mixed linear-nonlinear schemes for molecular electrostatics with implicit solvent models.

Coupled thermo-mechanical field-enriched finite element method for simulating the thermal failure process of quasi-brittle solids

Thermal loads and temperature changes significantly impact the deformation and fracture of quasi-brittle solids, and the computational simulation of such a process is challenging. In this paper, a coupled thermo-mechanical field-enriched finite element method (TM-FE-FEM) is proposed to simulate the thermal fracture process of quasi-brittle solids. The accuracy and correctness of the proposed coupled TM-FE-FEM are validated by four benchmark examples, and the ability to simulate thermal induced crack is validated by the plate containing single edge flaw under coupled thermo-mechanical loading. Finally, the thermal fracture process of the Lac du Bonnet (LdB) granite specimen is reproduced by the proposed method. It can be concluded from the numerical results that the proposed coupled TM-FE-FEM has the ability to simulate the processes of heat conduction, thermal deformation and thermal fracture in quasi-brittle solids.

Experiment and numerical simulation study of thermal fatigue of an aluminum alloy piston

AbstractIn this study, a magneto‐thermo‐structural coupling finite element method was proposed to calculate the electromagnetic field, temperature field, stress field, and strain field of an aluminum alloy piston during thermal shock process. The computed temperature results at the measurement points of T3 and T4 agree well with the measured data. The concept of tensile strain energy density was proposed as a thermal fatigue damage parameter, and the thermal fatigue life of the piston was predicted on the basis of the calculated results by magneto‐thermo‐structural coupling analysis and tensile strain energy density‐life equation; the discrepancy between the predicted life and the experimental one is 16%. The thermal fatigue failure mechanism of the piston was also clarified. High cyclic stresses occur on the edge of Si due to the difference in thermal expansion coefficient of Al and Si; micro cracks first originate on the edge of Si, then grow through combining other micro cracks, and eventually form macro cracks.

Ferrite Pads Gap Thermal-Magnetic Evaluation and Mitigation for 11.1 kW Wireless Power Transfer

Local overheating and airgap magnetic leakage is severe due to the distribution of inter-tile airgap in wireless power transfer (WPT) ferrite pads. In this paper, a thermal-magnetic multi-objective optimization function (MOF) is proposed to evaluate and mitigate the thermal-magnetic deterioration caused by the distributing airgap. The effects of the airgap on temperature and leakage distribution are analyzed based on the magnetic-thermal coupling finite element method (FEM) simulation. It is found that the trend of the local temperature is opposite to that of the magnetic leakage following the increase of the airgap width. An interesting range can also be found by using the proposed MOF strategy. When the airgap width is within the range, the gap thermal-magnetic problems can be mitigated effectively. Subsequently, a full-scale prototype with 11.1kW at 85kHz is fabricated to validate the effectiveness of MOF strategy and the accuracy of evaluation. The pads with optimized airgap achieve greater comprehensive performance than that without the optimization.

Analysis of the Magneto-Thermal Bidirectional Coupling Strength of Macro and Micro Integration for Self-Starting Permanent Magnet Hysteresis Synchronous Motors

High-speed permanent magnet synchronous motors (PMSMs) are usually started with the hybrid low-speed open-loop and high-speed closed-loop control mode. However, low-speed open-loop control produces large starting current, or even current overload, resulting in demagnetization and motor damage. Therefore, there is an urgent need to develop a high-speed permanent magnet synchronous motor with self-starting ability at low speed, that is, a permanent magnet hysteresis motor (PMHM). This paper takes the permanent magnet ring hysteresis column rotor structure as the research object. Firstly, the performance of this type of rotor is improved using the micro level of effective layer material AlNiCo, and the mechanical properties of AlNiCo are calculated. Secondly, based on the thick-walled cylinder theory, the analytical model for calculating the strength of the composite rotor considering the temperature effect is deduced, and the tangential and radial stress distribution for each part of the rotor under no-load and load conditions are obtained. Then, the electromagnetic losses and temperature field distribution of the rotor are obtained using the magneto-thermal bidirectional coupling finite element method. Finally, strength of the thermal rotor is analyzed by substituting the temperature rise curve function and AlNiCo parameters at the operating temperature. The comparison of the stress calculation results of the semi-analytical solution and the finite element method showed that the error between both of them is less than 5%, which verified that the semi-analytical solution can accurately analyze the thermal stress distribution of the rotor during high-speed rotation.

Research on the Distribution of Overlying Rock Fractures Caused by Mining in Ultra-Thick Coal Seams and Its Impact on the Near-Surface Aquifer

Near-surface water is the foundation for maintaining the ecological environment, and coal remains an important energy source in today’s world as we face a shortage of green energy. Achieving near-surface-water protection while safely mining coal is an important way to ensure social and ecological health and sustainability. The key lies in whether the fracture height of the mining overlying strata affects the aquifer. This article compiles the coupling finite element and discrete element method (CFE-DEM) and established mechanical constitutive models such as the interaction between rock blocks on both sides of the penetrated fracture, rock mass fracture process, and the plastic deformation law of rocks based on the results of mining-induced overlying rock failure. On this basis, a numerical calculation model is established based on the engineering geological conditions of the Beixinyao Coal Mine. The numerical simulation results indicate that the theory and the CFE-DEM method can numerically simulate the distribution and evolution of mining-induced overlying rock fractures. The water-conducting fractures in the overlying strata of extra-thick coal seams extend to the front of the working face in a trapezoidal shape, and the angle formed between them and the advancing direction ranges from 62° to 75°. Combined with the in situ measurement results, the height of the water-conducting fracture zone of the extra-thick coal seam is between 209 m and 230 m; the fractures were not found to have affected the aquifer at a vertical distance of 252 m from the coal seam. This means that the impact of ultra-thick coal seam mining on the aquifer is very limited. The research is of great significance for ensuring coal mining and surface ecological sustainability in ultra-thick coal seam areas.

Research on vibration suppression of satellite bearing cylinder based on particle damping

During the launch and separation phases, the satellite will be subjected to massive random loads and impact loads, which will quickly cause broad frequency vibrations in the thin-walled skin structure of the satellite bearing cylinder, leading to resonance in severe cases and causing fatigue and damage to the equipment and structure. A vibration suppression method of satellite-bearing cylinder based on PD (particle damping) technology is proposed to overcome the problem of abnormal vibration of satellite-bearing cylinder structure at resonance frequency excitation. Firstly, the DEM-FEM coupling model of the force-bearing cylinder and particle damper is established using the DEM-FEM coupling (discrete element method and finite element method coupling) theory. Secondly, the acceleration value response of the bearing cylinder's upper-end surface is used to evaluate the vibration-dampening effect. The particle dampers' particle diameter, particle material, particle filling ratio, and installation site parameters are then optimized for design. Finally, the ground vibration damping test of the satellite bearing cylinder was designed. According to the experimental results, after installing the best damping scheme, the vibration attenuation of the satellite bearing cylinder may achieve 32%. The peak acceleration at the first and second-order intrinsic frequencies is lowered by 78.46% and 94.3%, respectively. This result also verifies the correctness of the theoretical model and simulation model.

Finite element modeling of programmable liquid crystal elastomer plates and its application in text display

AbstractLiquid crystal elastomers (LCEs) have wide and potential applications in artificial muscles, soft robots, biomedical devices, and so on. On the application of LCE plate in text display, different from others' work where specially shaped ultraviolet (UV) lighting is used, in this paper, the programmable deformation of LCE plates with arbitrary liquid crystal orientation subjected to uniform light illumination is investigated. A photomechanical coupling finite element method (FEM) is developed, in which the impact of the shear strains induced by light is taken into account. Inspired by the FEM, the LCE plate is divided into finite small regions. By altering the liquid crystal orientation of each region in the LCE plate, the ability to generate 24 letters and 10 numbers through light‐induced deformations is demonstrated. Matrixes of the liquid crystal orientation corresponding to each letter and number are provided. This work indicates that it is possible for blind people to read text information by touching the deformed LCE plate.

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.