3D Finite Element Method Research Articles

Analysis of Behavior of Soil Cement Column Wall Associated with Base Improvement by Cross Wall with 3D Finite Element Method

Analysis of Behavior of Soil Cement Column Wall Associated with Base Improvement by Cross Wall with 3D Finite Element Method

Identification of bored pile defects utilizing torsional low strain integrity test: Theoretical basis and numerical analysis

The torsional low strain integrity test (TLSIT), known for its advantages such as a smaller detection blind zone, improved identification of shallowly buried defects, stable phase velocity for signal interpretation, and better adaptability for existing pile testing. However, it lacks a comprehensive understanding of the authentic three-dimensional (3D) strain wave propagation mechanism, particularly wave reflection and transmission at defects. To address this gap, a novel 3D theoretical framework is introduced in this context to model the authentic 3D wave propagation during the TLSIT. The proposed approach is validated by comparing its results with those obtained from 3D finite element method (FEM) simulations and simplified 1D (one-dimensional) and 3D analytical solutions. Additionally, a parametric study is conducted to enhance insights into the formation mechanism of high-frequency interference observed during the TLSIT. Finally, a defect identification study is performed to provide guidance for interpreting the wave spectrum in terms of defect characteristics.

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.

Modelling the effective thermal conductivity and porosity of an open-cell material using an image-based technique coupled with machine learning

Effective thermal conductivity is considered one of the most important parameters in the characterization of insulating materials. The effective thermal conductivity of open-cell porous materials is influenced by both their microstructure and the types of solid and fluid phases present. Currently, many analytical models are available for predicting the final performance based on material porosity, as well as the thermal conductivity of the solid and fluid phases. However, these procedures have two main drawbacks: difficulty in selecting the correct prediction model and challenges in accurately determining porosity. Moreover, when attempting to measure effective thermal conductivity, strict procedural conditions and defined sample geometries are required, necessitating multiple samples due to variations in porosity from specimen to specimen. The procedure proposed here aims to address these challenges. Utilizing microtomography coupled with 3D virtualization and finite element method simulation, this procedure provides validated results which are then used as a dataset to train a machine-learning model capable of predicting thermal conductivity across a comprehensive range of porosities, solid thermal conductivities and fluid thermal conductivities. Comparative analysis has demonstrated that this procedure is significantly more accurate than conventional analytical models or measurement procedures and it has the potential to be applied to any material.

Tailoring Deformation Homogeneity of WE43 Alloy through Strain Rate Sensitivity and Back Pressure during Equal Channel Angular Pressing

AbstractEqual channel angular pressing (ECAP) of the magnesium alloys at room temperature owing to their limited workability is challenging. Successful ECAP processing of WE43 magnesium faces two main difficulties, heterogeneous distribution of the strain rate and also tensile strain accommodation on the top surface of the workpiece, leading to catastrophic segmentation of the alloy. In this paper, strain rate sensitivity (SRS) was studied to adopt a proper preprocessing of the material before ECAP processing. The SRS exponents, obtained from compression tests, revealed that solution treatment reduced the SRS of the alloy. To mitigate strain accommodation, an ECAP core-sheath configuration was used to induce back pressure for the sake of deformation homogeneity improvement. A combination of experimental processing and 3D finite element method simulations was applied to the solution-treated WE43 alloy with different core sizes and sheath materials. By finding the optimized core sizes and sheath materials with higher strengths, the differences in microhardness and equivalent plastic strain were reduced. Besides, the adequate magnitude of back pressure and the imposed fully compressive stress prevent fragmentation of the WE43 core during ECAP. After stepwise modifications, the plastic strain inhomogeneity index decreased from 1.340 to 0.671.

Design of an on-chip germanium cavity for room-temperature infrared lasing

Germanium (Ge) is one of the most promising material platforms to enable the realization of monolithically integrated laser on silicon because it is a group-IV material with a pseudo-direct-band structure that can be converted into direct-bandgap either through the application of tensile strain or via the tin (Sn) incorporation in Ge. The bandgap modification enhances the light emission efficiency of Ge, where lasing can also be observed if a suitable cavity preserving the strain can be realized. In fact, several different research groups have reported lasing from strained Ge and GeSn optical cavities, however they all report lasing at low temperatures and room-temperature lasing, which is the ultimate goal required for a fully integrated laser, has not been demonstrated yet. In this work, we design an on-chip germanium cavity that has all the ingredients combined to make the room-temperature lasing possible. The design includes a 4.6% uniaxially tensile strained Ge gain medium embedded in a Fabry-Perot like cavity composed of two distributed Bragg reflectors. 3-dimensional (3D) Finite Element Method (FEM) based strain simulations together with a proposed fabrication methodology provides a guideline for the realization of the structure. Furthermore, 3D Finite Difference Time Domain (FDTD) simulations demonstrate that the designed structure is suitable for the room-temperature lasing in a wavelength range of 2410–2570 nm. 3D FEM-based heat transfer simulations performed for the designed cavity verifies the eligibility of the room-temperature operation paving the way for a possible demonstration of on-chip laser that could take part in the fully integrated infrared systems for a variety of applications including biological and chemical sensing, as well as security such as alarm systems and free-space optical communications.

3D Shape Reconstruction of Ge Nanowires during Vapor-Liquid-Solid Growth under Modulating Electric Field.

Bottom-up growth offers precise control over the structure and geometry of semiconductor nanowires (NWs), enabling a wide range of possible shapes and seamless heterostructures for applications in nanophotonics and electronics. The most common vapor-liquid-solid (VLS) growth method features a complex interaction between the liquid metal catalyst droplet and the anisotropic structure of the crystalline NW, and the growth is mainly orchestrated by the triple-phase line (TPL). Despite the intrinsic mismatch between the droplet and the NW symmetries, its discussion has been largely avoided because of its complexity, which has led to the situation when multiple observed phenomena such as NW axial asymmetry or the oscillating truncation at the TPL still lack detailed explanation. The introduction of an electric field control of the droplet has opened even more questions, which cannot be answered without properly addressing three-dimensional (3D) structure and morphology of the NW and the droplet. This work describes the details of electric-field-controlled VLS growth of germanium (Ge) NWs using environmental transmission electron microscopy (ETEM). We perform TEM tomography of the droplet-NW system during an unperturbed growth, then track its evolution while modulating the bias potential. Using 3D finite element method (FEM) modeling and crystallographic considerations, we provide a detailed and consistent mechanism for VLS growth, which naturally explains the observed asymmetries and features of a growing NW based on its crystal structure. Our findings provide a solid framework for the fabrication of complex 3D semiconductor nanostructures with ultimate control over their morphology.

Development of a flexible arrayed eddy current sensor with three-phase excitation for inspection of rail rolling contact fatigue cracks

A Flexible Arrayed Eddy Current (FAEC) sensor can inspect a large area in a single probe pass, which is beneficial for customizing the profile of the inspected part. This paper presents the development of a flexible arrayed eddy current sensor with three-phase excitation for inspection of Rolling Contact Fatigue (RCF) cracks in rail. The excitation coils are driven by three-phase currents that are 120° apart in phase. The induced eddy current in the conductive rail sample shifts electrically along the phase variation direction of the excitation currents. The sensor measures a small background signal to determine if there is no defect in the rail sample. Therefore, the sensor has a high relative sensitivity to defects. We study the operating principle of the sensor using a 3D finite element method (FEM) model. The numerical results demonstrate the sensor's viability for fast inspection and characterization to detect RCF defects in conductive rail steel samples.

Experimental and Theoretical Analysis of Rayleigh and Leaky-Sezawa Waves Propagating in ZnO/Fused Silica Substrates.

Piezoelectric c-axis oriented zinc oxide (ZnO) thin films, from 1.8 up to 6.6 µm thick, have been grown by the radio frequency magnetron sputtering technique onto fused silica substrates. A delay line consisting of two interdigital transducers (IDTs) with wavelength λ = 80 µm was photolithographically implemented onto the surface of the ZnO layers. Due to the IDTs' split-finger configuration and metallization ratio (0.5), the propagation of the fundamental, third, and ninth harmonic Rayleigh waves is excited; also, three leaky surface acoustic waves (SAWs) were detected travelling at a velocity close to that of the longitudinal bulk wave in SiO2. The acoustic waves' propagation in ZnO/fused silica was simulated by using the 2D finite-element method (FEM) technique to identify the nature of the experimentally detected waves. It turned out that, in addition to the fundamental and harmonic Rayleigh waves, high-frequency leaky surface waves are also excited by the harmonic wavelengths; such modes are identified as Sezawa waves under the cut-off, hereafter named leaky Sezawa (LS). The velocities of all the modes was found to be in good agreement with the theoretically calculated values. The existence of a low-loss region in the attenuation vs. layer thickness curve for the Sezawa wave below the cut-off was theoretically predicted and experimentally assessed.

Non-uniform critical current and stacking effect remedy for multi-filament REBCO tapes with potential defects

The high aspect ratio of REBCO tapes has a significant impact on several characteristics in high-temperature superconducting applications, such as critical current and AC loss. Narrow filamentary technology can effectively reduce the impact of magnetic field dependence and enhance the electromagnetic performance of REBCO tapes. However, the existing methods are constrained by the trade-off between the narrow degree of REBCO filaments and high current capacity. Meanwhile, when processing REBCO tapes for large-scale magnets, there is a great possibility that local defects are lurking. A striated narrow-stacked (NS) structure is proposed based on the existing narrowing methods to address these challenges. To verify the validity of this structure, it is imperative to explore the non-uniform critical current and stacking effect on performance for multi-filament REBCO tapes with potential defects. This article introduces a magnetic extended network (MEN) model to analyze the electrical characteristics of striated NS structures with different types of potential defects. Then, by coupling with a 3D finite element method electromagnetic module, the calculation results of the MEN model are visualized and used to analyze the electromagnetic characteristics including current sharing mechanism, magnetic field distribution, and critical current compensation due to stacking effect. It is found that stack structures successfully provide the performance remedy for multi-filament REBCO tapes with potential defects. This study aims to promote the narrowing improvement of REBCO tapes in high-field magnets and high-current applications.

Analytical model of an I-core coil inside a metal tube of finite length

An analytical solution is presented for the interaction of an I-core coil with a metal tube of finite length. Using the Truncated Region Eigenfunction Expansion (TREE) method, the impedance variation of the I-core coil is expressed in a closed form. Notably, the 1D finite element method (1D FEM) is adopted to calculate the complex eigenvalues and eigenfunctions of the steel tube, by which the overflow issue of complex eigenfunctions has been surmounted. And the 1D FEM also simplifies the calculation in the ferrite core region immensely. A performant algorithm is obtained due to the matrix formalization and the high speed of the sparse eigenvalue solver. The tubes made of aluminum alloy and stainless steel are investigated by the proposed method and tested in the experiment. The high reliability and efficiency of the proposed method are proved, and the results are also validated by the comparison with simulation and measurement data.

Analytical modelling of the linear transverse flux permanent magnet motor using magnetic equivalent circuit method

AbstractThe authors propose an analytical modelling approach for the linear transverse flux permanent magnet motor using the magnetic equivalent circuit method. The main focus of this study is to predict the phase flux‐linkage characteristic of the motor. Essential equations required for implementation of the model and how to solve it are described clearly so that someone can use it easily. A typical motor is selected to apply the proposed model and simulation results, including static characteristics of flux‐linkage and thrust, are presented. To validate the developed analytical model, the discussed motor is also analysed with 3D finite element method using MAXWELL software and the obtained simulation results are compared to each other.

RESEARCH ON APPLICATION OF FINITE ELEMENT METHOD TO ANALYZE LOAD TRANSFER EFFICIENCY ACCORDING TO DEFLECTION OF AIRPORT RIGID PAVEMENT

The load transfer between adjacent cement concrete slabs at expansion joint locations is affected by many different factors. The load-bearing capacity of the pavement will be limited and even lead to destruction if the load transmission ability of the dowel bars does not meet the requirements. Especially, for airports that have just been put into operation or have been in operation for a long time. In this article, the authors have researched and evaluated the effectiveness of load transfer according to deflection through the application of the 3D finite element method. The model utilizes material parameters and actual airport hard pavement structures and calculates for many types of aircraft commonly operating in Vietnam. Thereby calculating and evaluating the load transfer efficiency (LTE) according to deflection for each specific type of aircraft. The model also visually shows the deformation of the transmission dowel bars and concrete slabs at the expansion joint location. The authors tested the model's reliability through experiments conducted at Tan Son Nhat International Airport which is the largest-scale and oldest airport in Vietnam. The results of calculating LTE from the simulation and experimental models have a small error (3.39%) which shows that the model is highly reliable and can be used for similar research directions without being easily done through traditional methods.

Multimaterial filtering applied to the topology optimization of a permanent magnet synchronous machine

PurposeThis study aims to propose a general methodology to handle multimaterial filtering for density-based topology optimization containing periodic or antiperiodic boundary conditions, which are expected to reduce the simulation time of electrical machines. The optimization of the material distribution in a permanent magnet synchronous machine rotor illustrates the relevance of this approach.Design/methodology/approachThe optimization algorithm relies on an augmented Lagrangian with a projected gradient descent. The 2D finite element method computes the physical and adjoint states to evaluate the objective function and its sensitivities. Concerning regularization, a mathematical development leads to a multimaterial convolution filtering methodology that is consistent with the boundary conditions and helps eliminate artifacts.FindingsThe method behaves as expected and shows the superiority of multimaterial topology optimization over bimaterial topology optimization for the chosen test case. Unlike the standard approach that uses a cropped convolution kernel, the proposed methodology does not artificially reflect the limits of the simulation domain in the optimized material distribution.Originality/valueAlthough filtering is a standard tool in topology optimization, no attention has previously been paid to the influence of periodic or antiperiodic boundary conditions when dealing with different natures of materials. The comparison between the bimaterial and multimaterial topology optimization of a permanent magnet machine rotor without symmetry constraints constitutes another originality of this work.

Robust Bayesian target vector optimization for multi-stage manufacturing processes

This research focuses on optimizing multi-stage manufacturing processes using Bayesian optimization (BO) with a robust Expected Improvement (EI) acquisition function. The aim is to optimize towards pre-selected target vectors, not to just minimize or maximize a function. To achieve this, we minimize the Euclidean distance between the actual and target output vectors, which requires transforming the Gaussian surrogate model posterior distribution into a non-central χ2(NCχ2) distribution. Furthermore, the distance measure additionally uses aleatoric uncertainty estimates of the actual output vectors to achieve robustness. We use a cascaded method that also considers the optimization results of intermediate stages, whereby optimization results are propagated from the last stage towards the first stage in each optimization iteration. By considering intermediate process outputs and aleatoric effects, our approach provides a robust optimization method for multi-stage manufacturing processes. To validate our method and to evaluate its properties, we use two artificial use cases. Moreover, we evaluate our approach in an industrial multi-stage forging process for the manufacturing of a nickel basis superalloy turbine disk, where involved stages are represented by corresponding 2D finite element method (FEM) DEFORM simulations. Evaluation suggests that our approach is superior in optimizing multi-stage manufacturing processes by considering all stage outcomes, robust distance measures, and the use of appropriate uncertainty distributions.

Modeling of contact resistivity and simplification of 3D homogenization strategy for the H formulation

The finite element method (FEM) provides a powerful support for the calculations of superconducting electromagnetic responses. It enables the analysis of large-scale high-temperature superconducting (HTS) systems by the popular H formulation. Nonetheless, modeling of contact resistivity in three-dimensional (3D) FEM is still a matter of interest. The difficulty stems from the large aspect ratio of the contact layer in numerical modeling. Nowadays, an available solution is to model the contact layer with zero thickness but requires the discontinuity conditions of the magnetic field. In this paper, the energy variational method is utilized to incorporate the contribution of contact resistivity into the H formulation. From the perspective of energy transfer, the contact resistivity is related to the energy dissipation of the radial current flowing through the contact interface. In terms of applications, this method can be employed to calculate the charging delay of no-insulation coils and the current sharing behaviors of CORC cables. One advantage of this model is that the magnetic field is continuous and hence can be easily implemented in FEM. Additionally, it requires fewer degrees of freedom and hence presents advantages in computational efficiency. Moreover, this method can be employed to simplify the 3D H homogeneous model for insulated coils. The above discussions demonstrate that the proposed model is a promising tool for the modeling of contact resistivity.

A physics knowledge-based neural network method for three-dimensional fracture mechanics of attachment lugs

The lug type joint serves as a critical connecting structure in aerospace vehicles, allowing for convenient assembly and disassembly, and transfer the load during service. However, cracks often initiate at the stress concentration location near the lugs hole, posing a significant threat to the safety of the aircraft structure. Therefore, evaluating the stress intensity factors for complex lug structures is of great significance. In this study, a physics knowledge-based neural network method of calculating the stress intensity factors of attachment lugs is proposed. Three types of cracked lug structures are analyzed: through-thickness crack in straight lug, quarter elliptical corner crack in straight lug and quarter elliptical corner crack in tapered lug. Various complex influencing factors in actual situations are also considered, such as the impact of the interference fit between the pin and the lug, as well as different loading directions and crack positions of tapered lugs. The stress intensity factor dataset generated by 3D finite element method, and then the neural network with its powerful learning ability and prior physical knowledge are used to achieve accurate fitting of the data. The results demonstrate that incorporating physical knowledge features significantly improves the model performance of the neural network. This method can be extended to analyze crack in structures with arbitrary geometry and complex loading conditions.

Solving inverse problems in magnetic field leakage sensor array inspection of petroleum tank floor

The MFL method is a qualitative inspection tool and is a reliable, fast, and economical nondestructive testing method for tank floors. In this paper, before presenting the defect reconstruction procedure, we studied the effect of defect parameters on the magnetic field leakage measured by a single Hall sensor. As predicted, the study of each parameter has demonstrated that any variation in the geometrical parameters of the studied defect induce a significant influence on the MFL signal amplitude and distribution; for this reason, all the defect parameters must be determined precisely and prudently. After that, we have studied the performance of defect shape reconstruction from MFL array sensor imaging and depth estimation while using an iterative inversion method. Indeed, the first stage consists of determining the defect width and length from magnetic flux leakage mapping reconstructed from the recorded signals of the micro-integrated magnetic sensors. As a second step, after coupling Comsol and Matlab software, the defect depth is obtained by coupling the 3D finite elements method and a fast iterative algorithm recently developed. Consequently, the defect shape and size are obtained after a few iterations with a relative error of less than 2%; which makes this method very appropriate for real-time defect reconstruction and quantification. Furthermore, this method of defect reconstruction and seizing can be extended for irregular shape such as cracks and corrosion. In fact, this can be done while subdividing the affected area of non-constant depth into elementary zones of a constant depths. Then, while modifying the previous algorithm, we determine the corresponding depth of each zone.

Development of novel artificial intelligence functions based on 3D finite element method using February 6 Kahramanmaraş Seismic Records for earthquake effects prediction in various soils

The seismic events on February 6, 2023, in the province of Kahramanmaraş/Türkiye, caused severe damage and the collapse of numerous structures due to underlying soil issues. This catastrophe revealed the inevitable requirement to evaluate the effect of soil profile on structural safety. In the present study, novel artificial intelligence (AI) functions based on the three-dimensional finite element (3D FE) method considering various soil parameters were developed to predict the effects of earthquakes. A 3D FE model of the ten-story building with a known soil profile and structural elements was created in the first stage, accounting for the soil-pile-structure interaction. After model validation, numerous parametric time history earthquake analyses were performed using the February 6 Pazarcık/Kahramanmaraş (Mw = 7.7) earthquake records. Therefore, the effects of soil parameters on acceleration, settlement, and lateral deformations were investigated. An innovative coding infrastructure, leveraging the power of AI, was developed to generate optimal network solutions automatically for creating high-order regression prediction functions. The 3D FE data was integrated into the code, and subsequently, an artificial neural network was utilized to formulate a function that yielded statistically significant outcomes. The created function accurately predicted the accelerations, settlements, and deformations. A novel method for indicating the potential deformations and accelerations inflicted by earthquakes based on soil parameters was introduced. This methodology can serve as a practical guide for researchers and project implementers in the initial design phases.

An enhanced higher-order finite element formulation for wrinkling analysis of thick sandwich plates

Sandwich structures are susceptible to wrinkling when subject to in-plane compressive loads, which threatens structural safety. To accurately investigate the failure behavior, the following work is to be required. Firstly, the wrinkling behavior of sandwich plates is a typical three-dimensional (3D) issue. To consider a 3D effect, an enhanced higher-order finite element formulation including transverse normal strain has been proposed for the first time. Utilizing the proposed finite element formulation, a refined quadrilateral element model has been constructed. Secondly, the buckling and wrinkling behaviors of square sandwich plates have been investigated. The performance of the proposed model has been evaluated by comparing it with the quasi-3D solutions, the results obtained from the 3D finite element method (3D-FEM), and other models. The differences between the buckling and wrinkling failure behaviors have been carefully explained. Thirdly, the effects of boundary conditions on buckling and wrinkling deformation have been explored in detail. By utilizing the proposed model, the translation mechanism between the buckling and wrinkling deformations of sandwich plates under different boundary conditions has been revealed, which can help other investigators to well understand the buckling and wrinkling behaviors of sandwich plates. It can be shown that the wrinkling behaviors of thick sandwich plates occur earlier than the buckling behaviors when the thickness ratio of core to face panel is more than 35. Besides, it also can be shown that the buckling and wrinkling loads decrease gradually with the relaxation of the boundary restriction.