Finite Element Method Research Articles

Prediction of Forming Limit Diagram by Convolution Neural Networks and Crystal Plasticity Finite Element Method

This paper presents a novel deep learning (DL) approach to predict the forming limit diagrams (FLDs) of sheet metals, addressing the limitations of traditional experimental and numerical simulation methods. By utilizing orientation distribution function (ODF) data and crystal plasticity finite element (CPFE) results, an efficient DL prediction model was developed. First, numerous orientation datasets of the AA6061 alloy were generated and converted into ODFs to assess the impact of various texture components. Then, FLD data were computed using virtual forming tests via CPFE analysis and transformed into a format suitable for training the DL model. The model is based on the ResNet18 architecture and its hyperparameters were optimized using the Optuna framework. The model demonstrated rapid loss reduction, achieving an R<sup>2</sup> score of approximately 0.7 on the test dataset. However, a decline in prediction performance was observed, particularly when minor strain values were greater than zero. This suggests the need to incorporate additional input data such as the positional information of representative volume elements in future work. This study demonstrates that leveraging microstructural data for FLD prediction via DL can reduce time and costs compared to traditional methods, and it opens new possibilities for predicting material behavior under diverse conditions.

Temperature Field Analysis of Ancient City Wall: Measurement and Simulation

ABSTRACT An ancient city wall exposed to solar radiation often experiences a non-uniform temperature field, significantly influencing its structural responses and potentially posing safety hazards. This study combined a structural health monitoring (SHM) system with the finite element method (FEM) to investigate the temperature field of a city wall under solar radiation. A SHM system was used to monitor the crack width, strain, and temperature of the wall. The collected data revealed the relationship between the structural responses and the wall temperature. An FEM was developed considering solar radiation and convective heat transfer. A comparison of the simulated and monitored temperature data showed a strong consistency, validating the accuracy of the model in simulating the temperature field. Analysis of the simulated results indicates that the temperature distribution of the city wall is closely related to solar radiation. When the solar radiation was intense, the temperature of the masonry surface was higher than that of the interior. As solar radiation weakens, the interior temperature begins to exceed the surface temperature. Meanwhile, the temperature of the inner rammed earth remained relatively stable and was minimally affected by solar radiation.

Technical Advisory Group on the Structural Integrity review of the fatigue crack growth approach to transient cycles and other parameters used.

TAGSI is the UK Technical Advisory Group for the Structural Integrity of high-integrity components (HICs) and has a role in reviewing specific technical questions from its sponsors through peer review utilizing independent experts. EDF-Nuclear Services (NS) asked TAGSI to review some proposed optimizations for calculating fatigue crack growth (FCG) and to provide some further insight into the basis of certain relevant parameters. The areas covered were as follows: numerical approaches to FCG evaluation using elastic-plastic cracked-body finite-element (FE) methods; the function of R-ratio term f(R) in RSE-M for ΔKeff; and a new proposal for ordering and pairing transients aligned with plant operating conditions (POCs), referred to as the POC approach. This paper provides an overview of the review and associated discussions to address these questions. The main findings were as follows: TAGSI considers that the use of the ΔJ parameter for estimating FCG in the elastic-plastic regime is consistent with UK guidance, though some caveats and points for consideration were noted. Although the basis for the f(R) term in RSE-M is not well documented, some suggestions were made for how this may be better understood and developed. The POC method adopts a different approach to traditional methods for both the ordering and pairing of transients. TAGSI considers that the chronological POC approach (when including a modification, POC-mod, to combine start-up and shutdown transients) is an appropriate method for the ordering of transients for assessment. Some areas of non-conservatism were noted, to be assessed on a case-by-case basis.This article is part of the theme issue 'Future challenges for structural integrity of high-integrity components'.

Wave propagation in laminated structure through wave finite element method

Wave propagation in laminated structure through wave finite element method

The Systematic Design of Voice Coil Motor Structures for Rapid Zoom Optical Lens

In order to solve the zoom delay issue for high-magnification zoom optical systems, a voice coil motor (VCM) is used to achieve rapid zooming. In this paper, the structural design of VCMs is systematically analyzed through magnetic field numerical computations. Firstly, finite element method (FEM) is used to analyze magnetic field of single magnets, and simulations correspond to experimental results. Both FEM and equivalent magnetic charge (EMC) results confirm that increasing magnet thickness while reducing its lateral dimensions will contribute to magnetic enhancement. Furthermore, the influence of structural parameters VCM is analyzed, validating the yoke’s critical role in suppressing edge effects and optimizing magnetic circuit efficiency, and optimal yoke thickness and magnet width range are determined. Moreover, a simple EMC calculation method is proposed for rapid and accurate determination of the magnetic field distribution in the VCM air gap. Optimal structural parameters of VCM are determined for a 40× rapid zoom lens with cost and space limitations. Driving force Fdrive = 5.58 N is about 5 times the demand force Fd = 1.06 N, and the prototype fabrication of the rapid zoom lens is successfully accomplished. Moving group reaches 35.4 mm destination within 0.18 s, and photographs confirm that the rapid zoom system achieves 100-ms-level short/long-focus transition. Rapid zoom lens shows great potential in applications including security surveillance, industrial visual inspection, and intelligent logistics management.

Natural Frequency Analysis of a Stepped Drill String in Vertical Oil Wells Subjected to Coupled Axial–Torsional–Lateral Vibrations

Drilling oil and gas wells is a complex process that requires a combination of several parameters to dig into the ground. Inappropriate drilling parameter settings and reaction forces can lead to unwanted vibrations, which can negatively impact the drill string and cause damage to drill bits. To reduce unwanted oscillations, drilling vibration modeling is the first approach used to determine the behavior of the drill string under various conditions. Natural frequencies, one of the modal characteristics of a vibrating drill string, can be estimated by analytical or numerical models. However, as the field conditions become more complicated, analytical models become increasingly difficult to use, and alternative approaches must be adopted. The main objective of this paper is to investigate the natural frequencies of drill strings with real geometry under coupled vibration modes using both analytical and finite element methods. This study bridges the literature gap in modeling stepped drill string geometries, which are usually represented as uniform beams. This paper used analytical and finite element models to determine the drill string’s lateral, axial, and torsional natural frequencies under varying lengths of drill pipes and drill collars. To assess the reliability of finite element models under complex geometry, the drill string was approximated as a stepped beam rather than a uniform beam. Then, a comparison was made with analytical models. The results showed that the length of drill pipes has a pronounced effect on the natural frequencies of the overall drill string for the three vibrational modes, while drill collar length only has a notable impact on the torsional mode. These findings contribute to drilling systems’ reliability and efficiency in the oil and gas energy sector.

Stability Analyses of Rock Slopes and Improvement Solutions: A Case of Muğla Bakıcak, Turkey

This study evaluates the overall stability of the rock slopes in Muğla Bakıcak and discusses how these slopes can be made safer with specific measures. In this context, the stability of the rock slopes in Muğla Bakıcak was investigated using various analysis methods. In the study, the different processes affecting the instability of rock slopes and the effect of these processes on rock mass strength were examined in detail. In particular, the effect of discontinuity characteristics on rock slope stability is discussed in detail in the study. The rock material constituting the rock slopes, engineering properties of the rock mass, discontinuity properties, and orientations were determined in the analyses. The stability of rock slopes was investigated by limit equilibrium analysis, finite element method, and kinematic analysis. As a result of kinematic analysis, it was determined that planar, wedge, and overturning-type instabilities are possible. To mitigate the identified failure risks, stabilization solutions including rock bolts, steel mesh, and shotcrete were recommended.

In Silico Modeling of Safe Force Limits for Trismus Therapy Following Jaw Reconstruction.

Restricted mouth opening (trismus) is a common complication following segmental mandibulectomy and autologous bone reconstruction. However, the biomechanical limits of reconstructed mandibles, particularly in cases without bone union, remain poorly understood. Restorabite is a novel jaw-stretching device designed to increase the safety of trismus therapy by controlling the applied force. This study estimates the patient-specific loading limits in compromised mandibular reconstruction using finite element analysis to guide safe trismus therapy. Based on patient imaging, the finite element method was used to model stress distributions in the bone, titanium plate, and screws of a reconstructed mandible lacking bone union. Various scenarios were simulated to determine safe loading parameters, which considered factors such as friction coefficients between bone segments, native bone, and the reconstructed plate, as well as force application sites, and concentrated versus distributed loading. Low friction coefficients significantly increased stress on the reconstruction plate. To simulate the worst-case scenario, a coefficient of 0.3 was applied in the subsequent simulations. Stress levels varied by loading sites, with concentrated loading on the posterior segment of grafted bone yielding the lowest stress. In contrast, distributed loading over the 4 cm region on the anterior segments of graft bone led to increased plate stress. This study highlights the importance of tailored approaches in trismus therapy to minimize osteolysis and plate failure in mandibular reconstruction providing valuable insights for future clinical practices and device development. The study found that concentrated loading on biomechanically favorable regions proved safer compared to distributed loading, as it occurs with traditional jaw-stretching devices.

Fast 3-D forward modelling of gravity field vector and its gradient tensor using FFT-based spectral method

Abstract In gravity anomalies forward modeling, traditional numerical approaches necessitate solving a complex linear system characterized by sparse equations through matrix inversion. Meanwhile, the calculated three-component gravity field and five-component gravity gradient, utilizing finite-difference or finite-element methods, may experience accuracy loss due to inherent numerical differentials in the gravitational potential. To overcome this issue, we present a fast Fourier transform (FFT)-based spectral approach for solving the 3-D gravitational potential Poisson equation associated with homogeneous Dirichlet boundary conditions. Initially, by applying the FFT technique along the x-, y-, and z-axes for the 3-D Poisson equation, the corresponding partial differential equations in spatial domain are converted to algebraic equations in the wavenumber domain, allowing us to easily obtain the 3-D wavenumber-domain gravitational potential. Furthermore, the precise computation of the three-component gravity field responses and the five-component gravity gradient responses in the spatial domain, leveraging the differential attributes of the Fourier transform for spatial derivatives, which significantly enhances the model's accuracy. Despite requiring an additional inverse FFT during the reduction of the research problem's dimensionality, the proposed method can avoid the challenges associated with large-scale matrix inversion. Finally, to validate the computational accuracy and performance of the proposed algorithm, we utilize two density models and a real-world terrain model. Additionally, in comparison to the hybrid wavenumber domain finite-element method in terms of computational efficiency, the FFT-based spectral method not only maintains high accuracy, but also reduces computational time, clearly demonstrating its superiority over conventional numerical methods.

Assessment of the mechanical properties and aging resistance of floating body for offshore floating photovoltaic platform

Abstract The development of offshore photovoltaic (PV) platforms is essential for addressing the challenge of land resources scarcity associated with traditional PV installations. Floating offshore PV platforms, specifically, exhibit significant promise for solar energy utilization. This study utilizes linear potential flow theory and a multi-field coupling finite element method to investigate the performance of an offshore PV experimental application platform developed by CHN Energy Investment Group (CHN Energy), located in Yancheng, Jiangsu Province. The hydrodynamic response, deformation, and stress characteristics of the floats are analyzed under extreme load conditions corresponding to 50-year return period sea conditions in the target region. Additionally, by considering the ultraviolet accelerated aging performance of the float materials, the study assesses the service life expectancy of the floats. The findings provide a robust foundation for the future large-scale implementation of this technology in engineering projects.

New Fully Mixed Finite Element Methods for the Coupled Convective Brinkman-Forchheimer and Nonlinear Transport Equations

New Fully Mixed Finite Element Methods for the Coupled Convective Brinkman-Forchheimer and Nonlinear Transport Equations

A Multi-Scale Approach for Finite Element Method Structural Analysis of Injection-Molded Parts of Short Fiber-Reinforced Polymer Composite Materials

Short fiber-reinforced polymer composites are extensively used in automotive structural components, such as engine mounts and motor mount brackets, due to their favorable strength-to-weight ratio. For motor mount brackets, accurate structural analysis requires consideration of fiber orientation, as it significantly affects the mechanical behavior of the composite. This study aims to investigate the influence of fiber orientation heterogeneity on the mechanical properties of short fiber-reinforced polymer composites formed by injection molding. The spatial variation of the fiber orientation tensor, which evolves from the gate to the flow end during molding, presents challenges in experimental characterization. To address this, microscale analysis was conducted using injection-molded tensile specimens, followed by mesoscale modeling through representative volume elements (RVEs). Homogenization techniques were applied to predict effective mechanical properties, which were subsequently used to evaluate the performance of actual components at the macroscale. The findings demonstrate the importance of multi-scale modeling in capturing the anisotropic behavior of fiber-reinforced composites and provide a framework for more reliable structural analysis in automotive applications.

Acoustic black hole ultrasonic radiator for high-efficiency radiation.

Acoustic black hole ultrasonic radiator for high-efficiency radiation.

Optimising dental restorative composites: Numerical and statistical analysis of polymerization shrinkage and elastic modulus effects.

Light-cured resin-based dental restorative composites face challenges from polymerization shrinkage, which induces stress, potentially leading to microleakage, debonding, and recurrent caries. The elastic modulus (E) of these composites also influences stress distribution, with high-stress concentrations potentially leading to fractures in restored teeth. While finite element analysis (FEA) has been used to understand stress distribution, there is a lack of comprehensive studies exploring the combined effects of volumetric polymerization shrinkage (PS%) and E on restored molars. No research has addressed the influence of these factors on stress intensity at crack tips during mastication after shrinkage. This study investigates how variations in E and PS% affect the stress distribution at the restoration-enamel junctions (REJ) and restoration under mastication stimuli and shrinkage. Additionally, the study examines the impact of E and PS% on the stress intensity factor at the crack tip of a restored molar tooth. A 3D model of an upper molar was created from scanned images, converted into a mesh using 10-node tetrahedral elements, and analysed with finite element methods. The values of E ranged from 5GPa to 25GPa, and PS% ranged from 1% to 5%. Results showed that maximum principal stress varied with different E and PS% values, with the lowest stress occurring at E=5GPa and PS%=1% and the highest at E=25GPa and PS%=5%. Changes in these parameters also affected the locations of peak principal stress. Additionally, stress intensity factors decreased with increasing E but rose with higher PS%. Changes in E and PS% influence where and how much the principal stresses occur at the REJ and during restoration in response to shrinkage and mastication stimuli. This highlights the crucial role of material properties in the performance and durability of restorations, providing evidence-based insights that could guide material selection for MOD-restored molar teeth, ultimately enhancing restoration longevity and clinical outcomes.

Development of a 2D equivalent model for predicting linear and nonlinear aeroelastic behavior of a cantilever NACA0012 wing

Structural weight reduction is one of the main strategies explored nowadays to reduce manufacturing costs, impacting environmental costs. However, this structural weight reduction is often related to a reduction of material and may affect the structural mechanics of the system. Elasticity problems such as flutter can appear in lightweight structures. Therefore, this work presents a refined two-dimensional (2D) equivalent model for predicting the linear and nonlinear aeroelastic response of a cantilever wing based on a NACA0012 airfoil. The study aims to overcome the limitations of traditional 2D approaches, such as representing the wing by a single airfoil section at 75% span, which often leads to significant inaccuracies in flutter analysis. A 3D aeroelastic simulation framework is developed using Finite Element Method (FEM) analysis and unsteady Reynolds-averaged Navier-Stokes (URANS) computations. Based on the FEM results, a 2D model is developed, accounting for flexural and torsional dynamics considering the first vibration modes. Special attention is given to the elastic axis location, whose variation is shown to significantly influence the aeroelastic response. The 2D model is then validated against 3D simulations through parametric studies across a range of torsional stiffness values, capturing both flutter onset and limit-cycle oscillations. Results show that the proposed 2D model, when properly calibrated, replicates key 3D behaviors with significant reductions in computational cost, making it a reliable and efficient tool for preliminary aeroelastic assessments.

Incipient plasticity of potassium-doped tungsten under nanoindentation: A comparison between experiments and defect dynamics simulations

Incipient plasticity of potassium-doped tungsten under nanoindentation: A comparison between experiments and defect dynamics simulations

Clay metaBrick-based motif to enhance thermal and acoustic insulationa).

Acoustic metamaterials have gained popularity as promising materials for enhancing noise reduction. Here, we explore the use of metamaterials, based on Helmholtz resonators (HRs), to enhance the performance of standard clay hollow brick. By incorporating HRs in the upper and lower hollows, we transform the standard brick into metaBrick, which is essentially designed based on metamaterial principles. We evaluate the acoustic and thermal performance of walls constructed with clay metaBricks, focusing on sound transmission loss and heat resistance. Both the finite element method and experimental analysis were employed to highlight the performance of metaBricks compared to standard clay bricks. Results show that metaBricks significantly enhance acoustic and thermal insulation, achieving an attenuation of 20 dB across a broad frequency range from 500 to 2500 Hz and an 8% increase in thermal resistance. However, compressive strength is reduced by 33%, though it remains above the standard requirements for building materials. These findings indicate that metaBrick is a promising building material, offering improved sound and thermal insulation.

Temperature fields calculation in heat exchangers using the finite element method

Temperature fields calculation in heat exchangers using the finite element method

Cut finite element methods

Cut finite element methods (CutFEM) extend the standard finite element method to unfitted meshes, enabling the accurate resolution of domain boundaries and interfaces without requiring the mesh to conform to them. This approach preserves the key properties and accuracy of the standard method while addressing challenges posed by complex geometries and moving interfaces.In recent years, CutFEM has gained significant attention for its ability to discretize partial differential equations in domains with intricate geometries. This paper provides a comprehensive review of the core concepts and key developments in CutFEM, beginning with its formulation for common model problems and the presentation of fundamental analytical results, including error estimates and condition number estimates for the resulting algebraic systems. Stabilization techniques for cut elements, which ensure numerical robustness, are also explored. Finally, extensions to methods involving Lagrange multipliers and applications to time-dependent problems are discussed.

Comprehensive Slope Stability Analysis: Floods and Rapid Drawdown Triggered Road Slope Instability (A Case Study)

The risks of erosion to road embankments due to increased river water volume, particularly during flood events, often disrupt economic activities such as food and clothing distribution between locations. Therefore, this research investigated the critical impact of rapid drawdown on slope stability for road infrastructure adjacent to the Laeya River in Southeast Sulawesi, Indonesia. To achieve this aim, a comprehensive two-stage method was adopted, and the first included hydrological analysis to simulate flood water levels and predict rapid drawdown scenarios. In the second stage, a detailed geotechnical analysis through finite element method (FEM) was used to assess the stability of the slopes. Consequently, the research findings showed essential safety factor (SF) values under various conditions. The initial SF for the existing condition was 1.20, but after implementing treatment measures, such as slope geometry modification and soil compaction, the value improved to 1.54. However, during flood water level conditions, SF decreased to 1.50 due to the submergence of the slope base. Observation showed that rapid drawdown conditions led to a critical reduction in SF to 1.22, signifying the need for further research on the implications of drawdown. This research provided valuable perceptions and engineering solutions for improving slope stability in river-adjacent road infrastructure.