Finite Element Method Research Articles

Stabilized equal lower-order finite element methods for simulating Brinkman equations in porous media

This paper demonstrates the mixed formulation of the Brinkman problem using linear equal-order finite element methods in porous media modelling. We introduce Galerkin least-squares (GLS) and least-squares (LS) finite element methods to address the incompatibility of finite element spaces, treating velocity, pressure, and vorticity as independent variables. Theoretical analysis examines coercivity and continuity, providing error estimates. Demonstrating resilience in theoretical findings, these methods achieve optimal convergence rates in the L 2 norm by incorporating stabilization terms with low-order basis functions. Numerical experiments validate theoretical predictions, showing the effectiveness of the GLS method and addressing finite element space incompatibility. Additionally, the GLS method exhibits promising capabilities in handling the Brinkman equation at low permeability compared to the LS method. The study reveals an increase in the average pressure difference in the Brinkman problem compared to the Stokes equations as the inlet velocity rises, providing insights into the behaviour of Brinkman equations.

Design and Failure Analysis of Piston Using Ansys

A piston is a component of reciprocating engines. The purpose of piston is to transfer force from expanding gas in the cylinder to the crankshaft via a piston rod and a connecting rod. It is one of the most complex components of an automobile. In This project we are describes the Thermal analysis by using finite element method (FEM). The specifications used for designing the piston belong to four stroke single cylinder engine of piston. Modeling of piston is done using SOLID EDGE v20. static structural, Thermal and fatigue analysis is performed by using ANSYS WORKBENCH 2022 R1. The parameters used for the simulation are operating gas pressure, material properties of piston. The results predict the maximum stress and strain on pistons using FEA. The best material is selected based on static structural, thermal and fatigue analysis. The analysis results are used to optimize piston geometry of best two Materials

A comprehensive review on crack detection schemes and modelling techniques in high-speed rotor systems

ABSTRACT The combination of a rotor and bearings plays a pivotal role in various industrial applications, including gas turbines, compressors, turbochargers, aircraft engines, and wind generators. Ensuring the structural integrity of the rotor-bearing assembly during static and dynamic conditions is most important, as any failure could lead to unpredictable losses. Due to their continuous operation, high-speed rotors are more susceptible to faults such as misalignment, bow, eccentricity, and cracks. Among these faults, cracks are the most predominant fault that affects the system’s reliability. Despite significant advancements in rotor dynamics, cracks still threaten the integrity and performance of the rotor-bearing assembly. This review paper aims to thoroughly review the challenges and issues associated with crack formation in high-speed rotor systems. Various crack detection methods are also explored using vibration signals obtained from the rotor-bearing unit and their associated processing techniques. This study also gives an extensive overview of different crack modelling and analysis techniques. Furthermore, a novel rotor-bearing model is modelled using the finite element method, and the numerical results obtained from this model are validated with the existing literature model. This review paper will serve as a valuable resource for researchers that offers insights into the latest advancements and emphasises the importance of crack detection for ensuring the reliability of high-speed rotor systems.

Numerical Analysis for a Non-isothermal Incompressible Navier–Stokes–Allen–Cahn System

In this paper we develop the numerical analysis for a non-isothermal diffuse-interface model, in dimension N=2,3,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=2, 3,$$\\end{document} that describes the movement of a mixture of two incompressible viscous fluids. This model consists of modified Navier–Stokes equations coupled with a phase-field equation given by a convective Allen–Cahn equation, and energy transport equation for the temperature; which admits a dissipative energy inequality. We propose an energy stable numerical scheme based on the Finite Element Method, and we analyze optimal weak and strong error estimates, as well as convergence towards regular solutions. In order to construct the numerical scheme, we introduce two extra variables (given by the gradient of the temperature and the variation of the energy with respect to the phase-field function) which allows us to control the strong regularity required by the model, which is one of the main difficulties appearing from the numerical point of view. Having the equivalent model, we consider a fully discrete Finite Element approximation which is well-posed, energy stable and satisfies a set of uniform estimates which allow to analyze the convergence of the scheme. Finally, we present some numerical simulations to validate numerically our theoretical results.

Mechanical analysis of al/foam composite sandwich panels under elastic and elastoplastic states

This study performs mechanical analysis for Al/Foam composite sandwich panels under 3-point bending using numerically and experimentally. The flexural rigidity, elastic deflections, and normal, shear stresses are obtained by analytical calculations of the Timoshenko beam equation and compared finite element (FE) models for 3-point bending loading conditions. The FE models are constructed using 2D single-layer shell and 3D solid discrete-layer models. The validity of FE models at the analysis is evaluated for Al/PVC Foam sandwich composites for the elastic state. The experimental bending results of Al/XPS Foam sandwich composites are compared with numerical models at elastic and elastoplastic states. The elastic results indicate that the out-of-plane deflection results agree well across numerical and analytical models. Normal stresses at the core are higher in 3D discrete-layer solid models compared to laminated shell theory-based models for thick plates, due to the more accurate characteristics of the discrete-layer solid models. The Timoshenko beam theory-based analytical bending results show a good correlation with the results from laminated shell theory-based finite element method (FEM) analyses. Elastoplastic FEM analysis indicates that discrete-layer-based 3D solid FEM models effectively predict local effects dependent on indentation failure.

Modeling electrical impedance in brain tissue with diffusion tensor imaging for functional neurosurgery applications

Abstract Objective. Decades ago, neurosurgeons used electrical impedance measurements in the brain for coarse intraoperative tissue differentiation. Over time, these techniques were largely replaced by more refined imaging and electrophysiological localization. Today, advanced methods of diffusion tensor imaging (DTI) and finite element method (FEM) modeling may permit non-invasive, high-resolution intracerebral impedance prediction. However, expectations for tissue-impedance relationships and experimentally verified parameters for impedance modeling in human brains are lacking. This study seeks to address this need. Approach. We used FEM to simulate high-resolution single- and dual-electrode impedance measurements along linear electrode trajectories through (1) canonical gray and white matter tissue models, and (2) selected anatomic structures within whole-brain patient DTI-based models. We then compared intraoperative impedance measurements taken at known locations along deep brain stimulation (DBS) surgical trajectories with model predictions to evaluate model accuracy and refine model parameters. Main results. In DTI-FEM models, single- and dual-electrode configurations performed similarly. While only dual-electrode configurations were sensitive to white matter fiber orientation, other influences on impedance, such as white matter density, enabled single-electrode impedance measurements to display significant spatial variation even within purely white matter structures. We compared 308 intraoperative single-electrode impedance measurements in five DBS patients to DTI-FEM predictions at one-to-one corresponding locations. After calibration of model coefficients to these data, predicted impedances reliably estimated intraoperative measurements in all patients (R=0.784±0.116, n=5). Through this study, we derived an updated value for the slope coefficient of the DTI conductance model published by Tuch et al., k=0.0649 S·s/mm3 (original k=0.844), for use specifically in humans at physiological frequencies. Significance. This is the first study to compare impedance estimates from imaging-based models of human brain tissue to experimental measurements at the same locations in vivo. Accurate, non-invasive, imaging-based impedance prediction has numerous applications in functional neurosurgery, including tissue mapping, intraoperative electrode localization, and DBS.

Dislocation-based finite element method for homogenized limit domain characterization of structured metamaterials

PurposeHeterogeneous and micro-structured materials have been the object of multiscale and homogenization techniques aimed at recognizing the elastic properties of the equivalent continuum. The proposed investigation deals with the mechanical characterization of the heterogeneous material structured metamaterials through analyzing the ultimate strength using the limit analysis of the Representative Volume Element (RVE). To get the desired material strength, a novel finite element formulation based on the derivation of self-equilibrated solutions through the finite elements devoted to calculating the lower bound theorem has been implemented together with the limit analysis in Melàn’s formulation.Design/methodology/approachThe finite element formulation is based on discrete mapping of Volterra dislocations in the structure using isoparametric representation. Using standard finite element techniques, the linear operator V, which relates the self-equilibrated internal solicitation to displacement-like nodal parameters, has been built through finite element discretization of displacement and strain.FindingsThe proposed work presented an elastic homogenization of the mechanical properties of an elementary cell with a geometry known in the literature, the isotropic truss. The matrix of elastic constants was calculated by subjecting the RVE to numerical load tests, simulated with a commercial FEM calculation code. This step showed the dependence of the isotropy properties, verified with Zener theory, on the density of the RVE. The isotropy condition of the material is only achieved for certain section ratios between body-centered cubic (BCC) and face-centered cubic (FCC), neglecting flexural effects at the nodes. The density that satisfies Zener’s conditions represents the isotropic geomatics of the isotropic truss.Originality/valueFor the isotropic case, the VFEM procedure was used to evaluate the isotropy of the limit domain and was compared with the Mises–Schleicher limit domain. The evaluation of residual ductility and dissipation energy allowed a measurement parameter for the limit anisotropy to be defined. The novelty of the proposal consisted in the formulation of both the linearized and the nonlinear limit locus of the material; hence, it furnished the starting point for further limit analysis of the structures whose elementary volume has been described through the proposed approach.

Modeling of 2D seismic wave propagation in heterogeneous porous media: a frequency-domain finite-element method formulated by variational principles

Summary We propose a frequency-domain finite-element (FDFE) method to model the 2D P-SV waves propagating in porous media. This specific finite element method (FEM) is based on the framework of variational principles, which differ from previously widely used FEMs that rely on the weak formulations of the governing equations. By applying the calculus of variations, we establish the equivalence between solving the stress-strain relations, equations of motion and boundary conditions that govern the propagation of P-SV waves, and determining the extremum or stationarity of a properly defined functional. The structured rectangular element is utilized to partition the entire computational region. We validate the FDFE method by conducting a comparison with an analytically-based method for models of a horizontal planar contact of two poroelastic half-spaces, and a poroelastic half-space with a free surface. The excellent agreements between the analytically-based solutions and the FDFE solutions indicate the effectiveness of the FDFE method in modeling the poroelastic waves. Modeling results manifest that both propagative and diffusive natures of the Biot slow P-wave can be effectively modeled. The proposed FDFE method simulates wave fields in the frequency domain, allowing for easily incorporation of frequency-dependent parameters and enabling parallel computational capabilities at each frequency point (sample). We further employ the developed FDFE method to model two simplified poroelastic reservoirs, one with gas-saturated sandstone and the other with oil-saturated sandstone. The results suggest that changing the fluid phase of the sandstone reservoir from gas to oil can substantially impact the recorded solid and relative fluid-solid displacements. The modeling suggests that the proposed FDFE algorithm is a useful tool for studying the propagation of poroelastic waves.

Study on visualization of impact damage characteristics of honey peaches based on finite element method.

The study of visualization of impact damage of fruit under different thicknesses of buffer materials can provide more efficient transportation and packaging solutions, and thus the economic losses caused by fruit damage can be reduced. Pearl cotton (EPE) is commonly used as a buffer material in the market, and the impact damage behavior of honey peaches under different thicknesses of EPE buffer material was studied by using the finite element method. Firstly, the damage area, maximum contact force and damage volume during the collision of honey peaches with EPE materials of different thicknesses (2, 4, and 6mm) were obtained by the single pendulum device, and then the Modulus of elasticity and Poisson's ratio of peach flesh were obtained by compression test. Finally, the finite element model of honey peach was built and the collision simulations were performed. The results of the study showed that the values of mechanical parameters of honey peach decreased with the increase of the thickness of the buffer material. When the collision angle was below 60°, the honey peaches were not damaged in the collision with the EPE material with a thickness of 4mm or more. By comparing the tested values with the simulated values, it was found that the errors of the damage area, damage volume and maximum contact force were less than 19.71%, 26.82%, and 25.88%, respectively. The study not only proves the possibility of the finite element method in the quantitative prediction of honey peaches damage but also provides rational support for the packaging design of honey peaches.

Specifics of Experimental and Fem Approaches in Structural Integrity Assesment of Penstock Made of HSLA Steel

Taking into account the history of problems concerning high-strength low-alloyed (HSLA) steel used for manufacturing of penstocks (partly presented by authors in previous studies), this paper is oriented toward specifics on structural integrity assessment of construction in question. Experimental testing of parent material, i.e. HSLA steel, such as microstructure analysis, impact toughness testing and hardness measuring provide insight into characteristics of parent material properties. Considering geometry of penstock and specific requirements, finite element method (FEM), i.e. ABAQUS, was used to assess the structural integrity of penstock as a whole, specific the longitudinal welded joint under the different internal (working) pressure. It should be emphasized that a slight undermatching effect was investigated by FEM approach in this case. Focus is being put on plastic deformation investigation on aforementioned welded joint under maximum internal pressure of 120 bar.

A new design and analysis of low-profile soft rotary pneumatic actuator for enhanced rotation and torque

Soft actuators producing bending motions have gained significant attention for their advantages in mimicking the properties and movements of human muscles. However, the research on soft rotary actuators has yet to keep pace with other soft actuators. This paper makes two key contributions to the design and modeling of these actuators. First, we introduce a novel design for a soft rotary pneumatic actuator. This design outperforms existing cylindrical shaped soft actuators, especially in terms of torque. Second, we present an analytical model based on finite deformation. This model accurately describes the relationship between rotational movement and corresponding torque. The accuracy of this model is validated through Finite Element Method (FEM) simulations and corresponding tests. By providing a mechanically efficient design and a highly accurate analytical model, this work offers a comprehensive solution for the development of new soft pneumatic actuators.

A data‐assisted physics‐informed neural network (DA‐PINN) for fretting fatigue lifetime prediction

AbstractIn this study, we present for the first time the application of physics‐informed neural network (PINN) to fretting fatigue problems. Although PINN has recently been applied to pure fatigue lifetime prediction, it has not yet been explored in the case of fretting fatigue. We propose a data‐assisted PINN (DA‐PINN) for predicting fretting fatigue crack initiation lifetime. Unlike traditional PINN that solves partial differential equations for specific problems, DA‐PINN combines experimental or numerical data with physics equations as part of the loss function to enhance prediction accuracy. The DA‐PINN method, employed in this study, consists of two main steps. First, damage parameters are obtained from the finite element method by using critical plane method, which generates a data set used to train an artificial neural network (ANN) for predicting damage parameters in other cases. Second, the predicted damage parameters are combined with the experimental parameters to form the input data set for the DA‐PINN models, which predict fretting fatigue lifetime. The results demonstrate that DA‐PINN outperforms ANN in terms of prediction accuracy and eliminates the need for high computational costs once the damage parameter data set is constructed. Additionally, the choice of loss‐function methods in DA‐PINN models plays a crucial role in determining its performance.

Monolithic linear array fiber end cap for spectral beam combination

In this study, a fusion splicing system that facilitates the splicing of a monolithic linear array fiber end cap is constructed. The fusion splicing thermal field of the end cap irradiated by a CO2 laser is theoretically simulated using the finite element method. The experimental fusion splicing temperature agrees well with the simulation results. The splicing strength, misalignment, and high-power withstanding capacity of the fusion-spliced monolithic linear 3-fiber end cap are investigated. The use of the fabricated device in a dual-grating spectral beam combination (SBC) is also demonstrated with three-channel laser beams, achieving a combined beam with near-diffraction-limited beam quality M2=1.101. It shows that the development of the monolithic linear array fiber end cap is meaningful for achieving a compact high-brightness SBC system.

Galerkin Finite Element Methods Error Estimates Analysis for [1+2] Equations of Integro-Differential on Linear Triangular

في هذا البحث تم حل المعادلة التكاملية التفاضلية المكافئة ذات الابعاد الثنائية باستخدام احدى الطرق العددية وهي طريقة العناصر المحدودة (جالركين) على العناصر المثلثة. تم اختيار هذه الطريقه للا ستفادة على نطاق واسع من العناصر المحدودة لأنها تحتوي على العديد من الخصائص العددية عالية الجودة. الفائدة الأساسية للعناصر المحدودة هي قدرتها على حل مجموعة واسعة من المشاكل في المجالات الحسابية المختلفة بأشكال مختلفة وخصوصا المعقده منها والتي لايمكن حلها بالطرق العددية الاخرى. نظرًا لتقديرات الخطأ شبه المنفصلة للمساحة الطبيعية ، تم استخدام مساحة عنصر الحدود الخطية متعددة الحدود المحددة في المثلثات لوصف المساحة وتم استخدام طريقة أويلر العكسية لوصف الوقت. يتم أيضًا اختيار القواعد التمييزية المستخدمة للتمييز بين مصطلح فولتيرا المتكامل لتكون متوافقة مع مخططات المرحلة الزمنية. بالإضافة إلى ذلك، تتم مقارنة الحلول العددية للمعادلة التكاملية التفاضلية ثنائية الأبعاد من النوع المكافئ مع الحلول الدقيقة، وأخيراً يتم عرض النتائج النهائية للحلول بيانياً باستخدام برنامج MATLAB. وتم أخذ تحليل خطأ جالركين للعنصر المحدود بعين الاعتبار عند استخدام شبكة من العناصر المثلثة على المعادلة التفاضلية في الفضاء ثنائي الأبعاد.

An IGBT coupling structure with a smart service life reliability predictor using active learning

Abstract An effective approach is proposed to evaluate the service life reliability of a multi-physics coupling structure of an insulated gate bipolar transistor (IGBT) module. The node-based smoothed finite element method with stabilization terms is firstly employed to construct an electrical-thermal-mechanical (ETM) coupling structure of the IGBT module, based on which the multi-physics responses can be accurately calculated to predict the service life of the IGBT module. By using the high-quality sample data obtained through the ETM coupling model, a Monte Carlo based active learning Kriging metamodel (AK-MCS) is developed to assess the service life reliability of the IGBT module, which can greatly reduce the computational cost needed by the surrogate model construction and reliability analysis. Numerical results show that the proposed ETM coupling structure can produce high-quality sample data of the IGBT dynamics and the AK-MCS machine learning technique can accurately estimate the service life reliability of the IGBT module.

An immersed multi-material arbitrary Lagrangian–Eulerian finite element method for fluid–structure-interaction problems

Fluid–structure-interaction (FSI) phenomena are widely concerned in engineering practice and challenge current numerical methods. In this article, the finite element method is strongly coupled with the multi-material arbitrary Lagrangian–Eulerian (MMALE) method to develop a monolithic FSI method named the immersed multi-material arbitrary Lagrangian–Eulerian finite element method (IALEFEM). By immersing the finite elements in the MMALE computational grid, the fluid–solid interface is directly tracked by the element boundary with accurate normal directions. The fluid–structure-interaction is implicitly implemented by assembling the nodal variables and updating the Lagrangian momentum equation on the MMALE grid. Combining the advantages of both MMALE and FEM with the immersed boundary method, the IALEFEM is effective for solving complicated FSI problems with multi-material fluid flow. A slip fluid–structure-interaction method is also proposed to enhance the computational accuracy in simulating FSI problems with significantly different velocity fields. The accuracy and effectiveness of the IALEFEM are verified and validated by several benchmark numerical examples including the shock-cylinder obstacle interaction, flexible panel deformation induced by shock wave, dam break problem with large structural deformation, water entry of a wedge, fragmentation of a cylinder shell induced by blast, response of elastic plate subjected to spherical near-field explosion and structural damage of open-frame building under blast loading.

Dual-channel photonic crystal fiber dual-parameter sensor exploiting surface plasmon resonance

A surface plasmon resonance (SPR) based sensor using a negative curvature circular side-polished photonic crystal fiber was proposed. The sensor’s sensitivity was analyzed using the finite element method. The impact of structural parameters was investigated. The sensor exhibits an average wavelength sensitivity (WS) of 7846 nm/RIU in the refractive index range of 1.370–1.396 and 2350 nm/RIU in the range of 1.330–1.370, with maximum WS of 46000 nm/RIU. For refractive index and magnetic field dual-parameter sensing, the simultaneously obtained magnetic field sensitivity is 0.84 nm/mT. The proposed SPR sensor demonstrates remarkable sensitivity, making it suitable for refractive index and magnetic field sensing applications.

Dissimilar joining of aluminum alloy and low-alloy carbon steel by resistance spot welding

In this work, the resistance spot welding (RSW) process was performed to join aluminum alloy and low-alloy carbon steel plates. The macro characteristics including nugget diameters and indentation rates, microstructure and tensile-shear strength of RSW joints were investigated. The results showed that the nugget of the RSW joints comprises a ‘bowl’ shape nugget on the aluminum side and an elliptical shape nugget on the steel side. Also, the intermetallic compound (IMC) layers containing Fe4Al13 and Fe2Al5 were formed around the aluminum/steel interface with the steel side having a tongue-shape and the aluminum side having a needle-shape. According to metallurgical evaluation and temperature distribution of RSW joints analyzed by the finite element method, the nugget on the aluminum side contained the dendritic grains and equiaxed dendritic grains. The nugget on the steel side consisted of a large amount of bainite and a small amount of coarse lath martensite. The nugget diameters and the indentations rates of RSW joints increased when increasing either welding current or welding time, and decreased when increasing the electrode pressure. The maximum values of nugget diameter and indentation rate of RSW joints were 9.076 mm and 4.144% when using the welding current of 16 kA, welding time of 450 ms and electrode force of 3 kN. In tensile-shear tests, the RSW joints showed a shear-off fracture mode. When increasing the welding current, welding time or electrode force, the tensile-shear strength of RSW joints increased first, and then reached a maximum, and finally decreased. The welding current of 16 kA, the welding time of 300 ms, and the electrode pressure of 3 kN were considered as the optimal welding parameters in the present study which resulted in the maximum tensile-shear strength of 2.24 kN. In addition, the IMC layers of the RSW joints exhibited a uniform and continuous appearance with a thickness of approximately 1.9 μm, and the IMC layer in the central area was thicker than that in the edge area.

Numerical Investigation of the Effects of Impactor Geometry on Impact Behavior of Sandwich Structures

The aim of this study is to examine the impact performance and damage behavior of sandwich composite structures with a core material of aluminum and a facesheet of glass fiber composites using the finite element method. In the study, the effects of impactor shape, impact velocity and number of core layers on peak force, absorbed energy efficiency, maximum displacement and damage deformation were examined. For low velocity impact simulation, progressive damage analysis was performed based on the Hashin damage criterion using the MAT 54 material model in the LS DYNA finite element program. While providing the connection between the core structure and its surfaces, a Cohesive Zone Model (CZM) based on the bilinear traction-separation law was created and examined. At the end of the study, it was determined that the shape of the impactor had a significant effect on impact resistance. Energy absorption efficiency may vary as impact energy changes. However, as the impact energy increases, the energy absorption efficiency increases. It was determined that the largest and dominant damage type for all three impactors was matrix damage.

Analysis of heat transfer modes in the cooling of blocks generating different heat quantities

Achieving improved cooling efficiency and control in electronic components with varying heat outputs can be realized through a thorough analysis of different heat transfer modes, focusing on their contributions and interactions within the system. The analysis is conducted within a cavity containing three circular blocks generating varying amounts of heat. The blocks are affixed to an insulated plate, dividing the cavity into two identical sections with different fluids and different cooling mechanisms. In the open portion of the divided cavity, block cooling is achieved through forced convection using a nanofluid, while the closed section dissipates heat through natural convection and surface radiation. The numerical solution of the governing equations is performed using Galerkin's Finite Element Method, with detailed examination of the cooling process considering various parameters, such as block displacement (1.5cm≤y1≤3.25cm) and dimensions (0.25cm≤R≤1.5cm), Reynolds number (10≤Re≤1000), nanoparticles nature and volumetric fraction(0 %–10 %), emissivity (0≤ε≤1), thermal heat ratio(0.125 to 8), and cavity inclination angle(0°–180°). The results show that the combination of natural convection and surface radiation can be highly effective, rivaling forced convection in cooling the blocks. The study shows that an increase in the Reynolds number results in a temperature reduction of up to 6 °C, while increasing the emissivity leads to a more significant drop of around 10 °C. Additionally, miniaturizing the blocks by reducing their radius by a factor of six causes the maximum temperature to rise by over 20 °C.