Three-dimensional Finite Element Method Research Articles

Finite Element Analysis of Electromagnetic Characteristics of a Single-Phase Permanent Magnet Linear Oscillation Actuator

The electromagnetic characteristics of a single-phase permanent magnet linear oscillation actuator are analyzed by the finite element method. Firstly, the basic structure and operation principle of the linear oscillation actuator are introduced. The internal stator slot and arc tooth are used to reduce the detent force. According to the principle of electromagnetic fields, the electromagnetic field equation is listed and the function of the motor is deduced. At the same time, the eight-node hexahedral element is used to calculate the listed universal functions, and the inductance, flux linkage, induced electromotive force and electromagnetic force of the motor are deduced. The electromagnetic field of the motor is simulated by two-dimensional and three-dimensional finite element methods, and the accuracy of the calculation results of the electromagnetic characteristics of the cylindrical linear oscillation motor by the two methods is compared and analyzed. Finally, an experimental prototype was developed and the no-load characteristics of the motor were tested using the existing linear motor towing method. By comparing the experimental and simulation results, the accuracy of the theoretical analysis and the rationality of the motor design are verified.

Reliability of Proposed Three-Dimensional Finite Element Method Prestressing Analysis

Reliability of Proposed Three-Dimensional Finite Element Method Prestressing Analysis

Study on the Influence and Deformation Control of Rich Water Foundation Excavation on Adjacent Buildings

Taking the foundation pit of the Suzhou Chunshenhu Road Expressway Reconstruction Project as an example, the excavation process of the foundation pit was numerically simulated using a three-dimensional finite element method. The measured data and simulated data of the lateral deformation of the enclosure structure, surface settlement deformation of the ground outside the pit, and settlement deformation of the building were compared to analyze the impact of foundation pit construction on adjacent buildings. The influence of foundation pit floor and diaphragm wall thickness on wall displacement, building settlement, and foundation pit uplift was also discussed. The results showed the following: (1) Adding a foundation pit floor has a significant effect on reducing the lateral displacement of the diaphragm wall, settlement of the building, and uplift of the foundation pit. Increasing the thickness of the foundation pit floor has a limited effect on reducing the displacement, while increasing the thickness of the diaphragm wall has a small effect. (2) The displacement curve of the underground diaphragm wall increases with depth. It reaches a maximum at the excavation surface and then decreases gradually. (3) The surface settlement increases first and then decreases with distance from the foundation pit, showing a concave shape. As the depth of excavation increases, the settlement value increases. (4) Through analysis of the monitoring data of vertical displacement of buildings, it can be seen that during foundation pit excavation, buildings undergo five stages: initial slow descent, steep descent, mid-term slow descent, late steep descent, and stable deformation. The buildings are dominated by settlement deformation.

Full Life Cycle Evaluation of Stability Pile in High Slope with Multi-Layer Weak Interlayers

High slopes with multi-layer weak interlayers are a type of special slope that tends to fail due to the unfavorable mechanical properties of interlayers. In this study, the influence of the position, length, diameter, and ratio of on-center spacing to the pile diameter on the stability of such slopes is investigated using the three-dimensional strength reduction elastoplastic finite element method. Based on a high slope with multi-layer weak interlayers, two models were created, and three states (an initial state, a state with a safety factor of 1.35, and a limit equilibrium state) were considered. The pile can improve slope stability when the it is located at the lower to lower-middle part of a high slope. The resistance effect no longer has a strengthening property if it exceeds a critical pile length (28 m and 30 m in the two models); 30 m was found to be the optimal pile length for the high slope. As the diameter increased, the safety factor increased from 1.38 (1.37) to 1.41 (1.40) in Model 1 (or in Model 2), while the maximum compressive stress, the maximum shear stress of the pile, and the maximum displacement of the pile head decreased in the two models from 20.84 (81.24) MPa to 16.15 (18.8) MPa, 11.19 (42.02) MPa to 7.77 (10.43) MPa, and 714.1 (4585.00) mm to 396.3 (1272.00) mm, respectively. The pile diameter should be >1.4 m in such cases. When stress and displacement increased, the arching effect and the pile group effect weakened, and the safety factor decreased as the ratio of on-center spacing to diameter increased. The ratio should be <3 to ensure slope ability.

Vibration analysis of rotating pre-twisted composite beams through isogeometric-based dimensional reduction method

The free vibration analysis of rotating pre-twisted composite beams with arbitrary cross-section geometry is investigated using an isogeometric-based dimensional reduction method. The three-dimensional beam problem is decomposed into a two-dimensional cross-sectional analysis and a one-dimensional beam problem, significantly reducing the numerical cost compared to three-dimensional finite element method. The simultaneous influences of pre-twist and rotational speed are carefully studied for various composite beams. This approach benefits from the numerical advantages of isogeometric analysis, with results showing better agreement with three-dimensional finite element method than other studies in the literature.

A Three-Dimensional Finite Element Analysis of A Two-Axially Pre-Loaded Plate Exposed To A Dynamic Force

In this paper, the forced vibration analysis by a harmonically time-dependent force of an elastic plate covered rigidly by a rigid half-plane is given. The plate layer is subjected to bi-axial normal initial force, into lateral sides separately. Here, the preloading state is exactly static and homogeneous. To eliminate the disadvantage of such a nonlinear model, the problem formulation is modeled in terms of the fundamental consideration of the theory of linearized wave in elastic solids under a pre-loaded state (TLWESPS) in a plane-stress case. For this purpose, considering Hamilton’s principles, the system of the partial equations of motion and the boundary-contact conditions are found. Based on the virtual work and the fundamental theorem of the calculus of variation, the three-dimensional finite element method (3D-FEM) is used to understand the dynamic behavior of the plate. A numerical validation process is established based on error norm functions. Next, influences of certain problem parameters such as Young’s modulus, aspect ratio, thickness ratio, pre-loaded parameter, etc. on the frequency mode of the pre-stressed system are given. The numerical investigations show that higher values of Poisson's ratio promote the resonant mode of the plate while increasing the influence of the preloaded parameter on the dynamic response of the plate.

Research on Temperature Control Anti-cracking in the Main River Bed Dam Section of Concrete Gravity Dams in the Cold Area

Abstract Cracks have always been a difficult problem in the construction and operation of water conservancy projects. Once cracks occur in concrete dams, it will have an impact on the appearance, structural bearing capacity, waterproofing, durability and service life of the dams. Taking the 9# typical retaining dam section of SETH Dam in Xinjiang as an example, this paper uses the three-dimensional finite element method to simulate the temperature field and stress field of the typical dam section during construction and operation, considering the actual pouring progress of the dam and various temperature control measures taken during construction. The results show that the thermal insulation measures adopted in this project have good effects. According to the analysis results, some construction suggestions are put forward, such as strengthening downstream thermal insulation and continuous monitoring, pouring upstream and downstream through warehouses, avoiding long interval and multiple empty pouring blocks, and avoiding exposure of overwintering surface.

Workflow for systematic design of electrochemical in operando NMR cells by matching B0 and B1 field simulations with experiments

Abstract. Combining electrochemistry (EC) and nuclear magnetic resonance (NMR) techniques has evolved from a challenging concept to an adaptable and versatile method for battery and electrolysis research. Continuous advancements in NMR hardware have fostered improved homogeneity of the static magnetic field, B0, and the radio frequency field, B1, yet fundamental challenges caused by introducing essential conductive components into the NMR sensitive volume remain. Cell designs in EC–NMR have largely been improved empirically, at times supported by magnetic field simulations. To propel systematic improvements of cell concepts, a workflow for a qualitative and semi-quantitative description of both B0 and B1 distortions is provided in this study. Three-dimensional finite element method (FEM) simulations of both B0 and B1 fields were employed to investigate cell structures with electrodes oriented perpendicular to B0, which allow realistic EC–NMR measurements for battery and electrolysis applications. Particular attention is paid to field distributions in the immediate vicinity of electrodes, which is of prime interest for electrochemical processes. Using a cell with a small void outside the electrochemical active region, the relevance of design details and bubble formation is demonstrated. Moreover, B1 amplifications in coin cells provide an explanation for unexpectedly high sensitivity in previous EC–NMR studies, implying the potential for selective excitation of spins close to electrode surfaces. The correlation of this amplification effect with coin geometry is described by empirical expressions. The simulations were validated experimentally utilising frequency-encoded 1H profile imaging and chemical shift imaging of 1H, 13C, and 23Na resonances of NaHCO3 electrolyte. Finally, the theoretical and experimental results are distilled into design guidelines for EC–NMR cells.

Three-dimensional finite element analysis of occlusal stress on maxillary first molars with different marginal morphologies restored with occlusal veneers

BackgroundThere are differences in the research results regarding which edge design of occlusal veneers can achieve the best long-term success rate as a relatively new fixed prosthesis restoration method. Further research is needed. The three-dimensional finite element method was used to conduct stress analysis on occlusal veneers of maxillary first permanent molars with different thicknesses and margin preparation designs. The aim of this study was to provide mechanical research evidence and a reference for exploring standardized clinical protocols for the design of occlusal veneer restorations of maxillary first molars.MethodA 3Shape (Intraoral Scanner) was used to scan the maxillary first molar teeth in vitro, after which 3D printing was carried out. Three different edge designs were applied to identical teeth: straight-beveled finishing line(SFL), chamfer finishing line(CFL), and standard cuspal inclination(SCI). Preparation was carried out with a thickness of 0.5 mm. Using the surface deformation feature, the occlusal veneer was thickened to 0.5 mm and 1.0 mm, and periodontal ligaments were added. They were then placed into the upper and lower jaws and dental arches. Finite element analysis was performed after applying bite force dispersion to the loading area on the mandible following dynamic contact.Results(1) As the thickness increased, the maximum Von Mises stress in the occlusal veneers SFL and CFL also increased, while the SCI exhibited the opposite trend. (2). The trend of the maximum Von Mises stress in the adhesive layer decrease gradually with increasing thickness of the occlusal veneer. The stresses of the SFL and CFL is concentrated primarily at the edge position below the functional cusp, resulting in relatively low adhesive stress. However, in the SCI group, the maximum stress at the edge of the adhesive layer exceeds the maximum shear strength of commonly used adhesives.ConclusionsUnder the experimental conditions, the mechanical properties of the maximum Von Mises stress in the SFL, CFL, and SCI occlusal veneers meet clinical needs. Incorporating the minimally invasive concept of tooth preservation, a thickness of 1.0 mm are optimal for glass ceramic occlusal veneers on maxillary first molars.

Static solid cooling (SSC) method for directional solidification and single crystal production: A CAFE Simulation Approach

This article presents a novel directional solidification (DS) technique called static solid cooling (SSC), which has been characterized and compared to the conventional high rate solidification (HRS) method using finite element simulation and a coupled three-dimensional (3D) cellular automaton finite element (CAFE) method. The SSC technique uses alternative heat conductor and insulation layers to provide DS conditions. Simulation results show that the SSC method provides a higher cooling rate, temperature gradient, and velocity of the solidification front compared to the HRS method. Moreover, due to its higher heat dissipation ability, the SSC method produces a convex shape in the solidification front, which is crucial for the production of defect-free single crystal blades. According to the simulation model, the HRS method can produce a defect-free single crystal structure up to a withdrawal rate of 3 mm/min, whereas, the SSC method can maintain a single crystal structure without any stray grain defects up to a withdrawal rate of 6 mm/min. These findings demonstrate the effectiveness of the novel SSC technique over the conventional HRS method in producing high-quality single crystal structures. The proposed method could have significant implications for industries such as aerospace and energy that require high-performance materials with superior mechanical properties at elevated temperatures.

Synergistic densification mechanism of irregular Ti powder during CIP: 3D MPFEM simulation with real-shape particles

Achieving high green density is essential for ensuring the mechanical properties of powder metallurgy workpieces. However, the densification behavior of irregular ductile powders remains unclear due to oversimplification in current numerical simulations. To address this, a three-dimensional multi-particle finite element method model incorporating realistic powder morphology, size distribution, and stacking structure is constructed. It is found that a pivotal motion-deformation synergistic stage exists between the conventional particle rearrangement and elastic–plastic deformation stages. In this stage, plastic deformation is driven by the spheroidization of coarse powders, whereas the resulting vacancies in the stacking structure facilitate slight particle motion. Thereafter, plastic deformation is dominated by the flattening of fine particles, and the pore-filling capacity decreases due to the reduction in non-contact surface area. This synergistic and complementary interaction between the spheroidization of coarse powders and the flattening of fine powders enhances mechanical interlocking and promotes micropore closure. As a result, the micropores exhibit a tendency of downsizing and homogenization, substantially boosting the potential for achieving full densification during sintering. Based on these findings, a method for determining the optimal forming pressure is proposed, considering the manufacturing costs of powder compacts and the characteristics of the micropores in both green and sintered bodies.

A comprehensive numerical procedure for high-intensity focused ultrasound ablation of breast tumour on an anatomically realistic breast phantom.

High-Intensity Focused Ultrasound (HIFU) as a promising and impactful modality for breast tumor ablation, entails the precise focalization of high-intensity ultrasonic waves onto the tumor site, culminating in the generation of extreme heat, thus ablation of malignant tissues. In this paper, a comprehensive three-dimensional (3D) Finite Element Method (FEM)-based numerical procedure is introduced, which provides exceptional capacity for simulating the intricate multiphysics phenomena associated with HIFU. Furthermore, the application of numerical procedures to an anatomically realistic breast phantom (ARBP) has not been explored before. The integrity of the present numerical procedure has been established through rigorous validation, incorporating comparative assessments with previous two-dimensional (2D) simulations and empirical data. For ARBP ablation, the administration of a 0.1 MPa pressure input pulse at a frequency of 1.5 MHz, sustained at the focal point for 10 seconds, manifests an ensuing temperature elevation to 80°C. It is noteworthy that, in contrast, the prior 2D simulation using a 2D phantom geometry reached just 72°C temperature under the identical treatment regimen, underscoring the insufficiency of 2D models, ascribed to their inherent limitations in spatially representing acoustic energy, which compromises their overall effectiveness. To underscore the versatility of this numerical platform, a simulation of a more clinically relevant HIFU therapy procedure has been conducted. This scenario involves the repositioning of the ultrasound focal point to three separate lesions, each spaced at 3 mm intervals, with ultrasound exposure durations of 6 seconds each and a 5-second interval for movement between focal points. This approach resulted in a more uniform high-temperature distribution at different areas of the tumour, leading to the ablation of almost all parts of the tumour, including its verges. In the end, the effects of different abnormal tissue shapes are investigated briefly as well. For solid mass tumors, 67.67% was successfully ablated with one lesion, while rim-enhancing tumors showed only 34.48% ablation and non-mass enhancement tumors exhibited 20.32% ablation, underscoring the need for multiple lesions and tailored treatment plans for more complex cases.

Discrete differential geometry-based model for nonlinear analysis of axisymmetric shells

In this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical model leverages differential geometry principles to accurately capture the complex nonlinear deformation patterns exhibited by axisymmetric shells. By discretizing the axisymmetric shell into interconnected 1D elements along the meridional direction, the in-plane stretching and out-of-bending potentials are formulated based on the geometric principles of 1D nodes and edges under the Kirchhoff–Love hypothesis, and elastic force vector and associated Hessian matrix required by equations of motion are later derived based on symbolic calculation. Through extensive validation with available theoretical solutions and finite element method (FEM) simulations in literature, our model demonstrates high accuracy in predicting the nonlinear behavior of axisymmetric shells. Importantly, compared to the classical theoretical model and three-dimensional (3D) FEM simulation, our model is highly computationally efficient, making it suitable for large-scale real-time simulations of nonlinear problems of shell structures such as instability and snap-through phenomena. Moreover, our framework can easily incorporate complex loading conditions, e.g., boundary nonlinear contact and multi-physics actuation, which play an essential role in the use of engineering applications, such as soft robots and flexible devices. This study demonstrates that the simplicity and effectiveness of the 1D discrete differential geometry-based approach render it a powerful tool for engineers and researchers interested in nonlinear mechanics analysis of axisymmetric shells, with potential applications in various engineering fields.

Analyzing the effect of undermining on suture forces during simulated skin flap surgeries with a three-dimensional finite element method

Skin flaps are common procedures used by surgeons to cover an excised area during the reconstruction of a defect. It is often a challenging task for a surgeon to come up with the most optimal design for a patient. In this paper, we set up a simulation system based on the finite element method for one of the most common flap types — the rhomboid flap. Instead of using the standard 2D planar patch, we constructed a 3D patch with multiple layers. This allowed us to investigate the impact of different undermining areas and depths. We compared the suture forces for each case and identified vertices with the largest suture force. The shape of the final suture line is also visualized for each case, which is an important clue when deciding on the most optimal skin flap orientation according to medical textbooks. We found that under the optimal undermining setup, the maximum suture force is around 0.7 N for top of the undermined layer and 1.0 N for bottom of the undermined layer. When measuring difference in final suture line shape, the maximum normalized Hausdorff distance is 0.099, which suggests that different undermining region can have significant impact on the shape of the suture line, especially in the tail region. After analyzing the suture force plots, we provided recommendations on the most optimal undermining region for rhomboid flaps.

Three-dimensional simulation on phase change heat transfer of moving spherical particle

Investigating the motion process of paraffin particle under a mesoscopic scale is very helpful to master the heat transfer mechanism of the mushy zone in solid–liquid phase change. Prior researches predominantly focused on either particle motion or phase change, without accounting for their coupling. In this study, the three-dimensional finite element method is used to solve the motion and heat transfer of the particle, taking into account the coupling of motion and phase change. The moving grid is employed to trace the interface of moving particles and liquid using the Arbitrary Lagrangian-Euler method, which is able to calculate flow and heat transfer in fluid region and allow grid deformation in solid region. The results indicate that uneven fluid velocity around the particles results in non-uniform temperature gradients on particle’s surface. In areas with larger temperature gradient, it melts more quickly and its deformation is obvious. The maximum is located at particle orientation angle 30°. Changing the size and direction of fluid velocity will reinforce or inhibit the movement of particle. The changing time of motion direction when fluid velocity is −0.03 m/s shorten 2.7 times than when fluid velocity is −0.01 m/s. The initial temperature of the surrounding fluid has a positive relationship with the particle melting rate. The channel width affects significantly the motion and melting of particle. The initial position of particle has an important effect on it’s falling movement, and the closer is close to the wall of channel, the greater the displacement of left and right movement.

Integrating parametric HFGMC and isogeometric RZT[formula omitted] for multiscale damage modeling of composite structures: A numerical and experimental study

In this research effort, a novel multiscale analysis scheme is proposed for damage modeling of composite laminates, sandwich structures, and stiffened plates relying on capabilities of the parametric HFGMC and isogeometric RZT{3,2} formulations. The Ramberg Osgood (RO) model is incorporated into the micromechanics model to reflect polymer matrix material nonlinearities on the overall homogenized composite behavior. Carbon fibers are assumed to behave in a linear transversely isotropic manner. The higher order RZT{3,2} theory employed at the macro level facilitates efficient applicability of the model to thick composite laminates and soft core sandwiches. On the other hand, it generates all three-dimensional stress components and thus ensures dimensional consistency between micro and macro levels. Numerical discretization and prediction of RZT{3,2} kinematic variables are enabled by performing NURBS based isogeometric analysis (IGA) thereby enhancing modeling efficacy to a significant degree. Soft core plasticity and failure in the composite are evaluated at the macro level through the RO model and Hashin criteria, respectively. Applicability of the method is presented for thin and thick flat composite and sandwich laminates; and further extended to stiffened plates via developing a multipatch formulation. A comprehensive validation of our analysis is conducted by comparing the results with established benchmarks from the literature, experimental data, and three-dimensional finite element method (3D-FEM) simulations. Initially, a moderately thick, simply supported square laminate under transverse loading is examined, a common verification benchmark. Then, results from standard mechanical tests, including tensile, shear, and four-point bending tests on thin laminates, followed by experiments on moderately thick sandwich structures subjected to four-point bending, are presented. Finally, the analysis is extended to a stiffened plate under uniform pressure, demonstrating the method’s accuracy and applicability across diverse structural configurations.

Application of a Modified First-Order Plate Theory to Structural Analysis of Sensitive Elements in a Pyroelectric Detector.

Pyroelectric materials, with piezoelectricity and pyroelectricity, have been widely used in infrared thermal detectors. In this paper, a modified first-order plate theory is extended to analyze a pyroelectric sensitive element structure. The displacement, temperature, and electric potential expand along the thickness direction. The governing equation of the pyroelectric plate is built up. The potential distributions with upper and lower electrodes are obtained under different supported boundary conditions. The corresponding numerical results of electric potential are consistent with those obtained by the three-dimensional finite element method. Meanwhile, the theoretical results of electric potential are close to that of experiments. The influence of supported boundary conditions, piezoelectric effect, and plate thickness are analyzed. Numerical results show that the piezoelectric effect reduces the electric potential. The thickness of the pyroelectric plate enhances the electric potential but reduces the response speed of the detector. It is anticipated that the pyroelectric plate theory can provide a theoretical approach for the structural design of pyroelectric sensitive elements.

Case studies of the load-bearing performance of shield tunnel segment with misaligned defects

The segment misalignment is a common defect in the segment installation of a shield tunnel construction, due to the complexity and uncertainty of its construction conditions. This raises a concerning about the safety of the segment lining for the shield tunnel. In this paper, the integrated numerical models with surrounding rock, peastone grouting and segment lining were built using three-dimensional finite element method, by introducing two kinds of misaligned defects of segments. One was the misalignment that elongated the horizontal axis of the transversal ring section of segment lining, another was the misalignment between adjacent rings of segments. To eliminate the impact of boundary on numerical results, seven rings of segments are built for the three-dimensional finite element models, and the middle ring is dealt with for the results analysis under V-class surrounding rock, including the circumferential stress of outer and inner layers of the segment, the contact stress on joint surface between segments, and the stress of locating pins between adjacent rings. Results indicate that the two kinds of misaligned defects create pronounced impact on tensile stress of segment at the bottom and the crown segments, respectively, which produces a greater tensile stress to increase cracking risk even abrupt fracture of segment. However, the misaligned defects have a slight impact on the contact stress and the locating pins stress. Therefore, attention should be paid to the cracking of bottom or crown segments in the segment lining of shield tunnel.

Simulation study of a highly sensitive I-shaped Plasmonic nanosensor for sensing of biomolecules

This paper presents the design and simulation of an I-shaped metal insulator metal waveguide-based nanosensor for biosensing applications. The device’s sensing property is investigated using the three-dimensional finite element method. In the proposed design a I-shaped cavity is coupled to the main waveguide that serves as a resonator to generate the resonance peaks. The refractive index of the material to be sensed is filled inside the I-shaped cavity. This sensor operates in the near and mid-infrared wavelength ranges. The device can identify a variety of biomolecules, including cancer cells and bacterial samples. The simulation results reveal that device shows different resonance dips for different refractive indexes of cancer cells. The device can obtain sensitivity of 1550 nm RIU−1 and 1250 nm RIU−1 among refractive index of normal and cancerous cell for basal and hella cancer cells, respectively. Instead of all these biomolecules, the nanosensor shows different resonance dips in the transmittance spectrum for DNA, RNA, and ribonucleoprotein. Furthermore, the sensor has demonstrated potential applicability as an HB concentration detector and for sensing other blood components. Moreover, we improved the structure characteristics by varying the length and centre area of the cavity, demonstrating that modifying the device parameters can boost sensitivity. After making structural adjustments to the device, the maximum sensitivity of 3000 nm RIU−1 is achieved for some bacterial samples.

Nonlinear Analysis of Electric Potential in a Piezoelectric Thin Plate as Pressure Sensor

Piezoelectric materials are widely applied in electronic components due to their ability to couple electric and mechanical fields. For the piezoelectric thin plate as a pressure sensor, we extend the modified first-order piezoelectric plate theory to explore the nonlinear solution of electric potential and discuss the relevant regulation mechanisms. Based on the piezoelectric effect, the electric potential generated by deformation is not linear with thickness. A quadratic function of electric potential across thickness is introduced. However, the electric potential on upper and lower electrodes is an unknown constant, which can be determined by the nonlinear complementary equation based on the Gauss theorem. It is shown that the nonlinear results of electric potential are consistent with outcomes by the three-dimensional finite element method. Furthermore, relevant regulation mechanisms are discussed on electric potential, including supported conditions, plate thickness, and load area. In addition, the influence of load locations on the electric potential response is analyzed. It is expected that these findings will be instructive to the structural design of piezoelectric pressure sensors.