Finite Element Method Calculations Research Articles

Numerical modelling of mechanical degradation of canvas paintings under desiccation

Mechanical damage in oil paintings on canvas show up as cracks and loss of original paint. Several parameters can contribute to this type of degradation. These paintings have a complex layered structure, typically composed of minimum four or more hygroscopic materials, each of which has different (non-linear) material properties and geometrical complexities. The mechanical degradation of canvas paintings occurs because each of these materials have diverse responses under fluctuating environmental conditions, especially temperature and relative humidity (RH). By examining the geometrical complexities and the non-linear material properties, this paper presents an investigation of three degradation phenomena under desiccation: (1) bulging formation around the corners, (2) crack formation in glue and ground layers, and (3) plastic deformation in the ground and oil paint layers.This on-going investigation provides further insights into the global and local stress distribution in typically constructed oil canvas paintings. This includes finite element method (FEM) and extended-FEM (XFEM) computer models at various scales, under desiccation from the initial RH of 90%, and 50–10%. The models consist of four to five different materials, namely lead white oil paint, red iron oxide oil paint, rabbit skin glue, linen canvas, and a spruce stretcher. The models were constructed using several combinations of materials to conduct parametric studies on the effects of glue shrinkage in paintings due to desiccation, and changing the mechanical properties of the ground layers. The relevant geometrical and mechanical properties with respect to the stress relaxation conditions are discussed in detail.The simulation results of the full-scale models show that the shrinkage of glue lowers the level of induced tension stresses in the paint layers in the central area of the painting due to the inward bowing of the stretcher. The inward deformation of the stretcher can be 4.5 times as large in a painting with a glue layer as in one without. This indicates the difficulty in forming cracks near the center of paintings purely by desiccation; however, in close-up cross-section model, cracks of 20 μm in length could still be observed in the ground exposed to an extreme RH change of 90% to 10%.The analysis of cross-section models with the full geometrical complexity for the corners showed that multiple cracks are likely to form in ground and paint layers in the corners when desiccated by 40%; RH 50–10%. Furthermore, in extreme cases with stiffer ground/paint such as zinc white, cracks can form from smaller drop in RH; RH 50% to 35%. Such cracks are form in the ground layers, and therefore, are not initially visible as they are positioned below the uncracked paint layer. This result can be the possible explanation for cracks in the ground, which are initially invisible with the naked eye, but can be revealed with X-radiographs.The results support the hypothesis that fluctuations in relative humidity can cause hidden cracks in the lower layers, which can eventually propagate further into the upper-lying paint layers of paintings. The cracks typically form when the desiccation reaches a 40% drop, but in cases of brittle materials the drop causing cracks can be lower. The actual RH drop causing cracks depends on the specific material composition.

An Efficient Air-Gap Flux Density Analysis Method for the Design of Induction Machines

The magnetic field distribution in the air gap is of great importance in the design of rotary machines. In this article, an efficient analytical method is presented, which is capable of plotting the air-gap flux density waveform of induction machines (IMs) less time-consuming than the finite element method (FEM) does. The proposed method, based on the product of the current linkage waveform and the permeance waveform, utilizes the calculations of the steady-state equivalent circuit to ensure the accuracy and an equivalent air-gap reluctance model to take into account both the slot opening effect and the rotor movement. The method is tested on a general IM with different load cases and different design parameters, and the results are compared to the FEM calculations. It can be concluded that the proposed analytical method is an efficient option in the motor design to investigate the influence of the parameters on the flux density distribution.

Microstructure Evolution Mechanism of Ultra-Thin Dual Phase Magnesium-Lithium Alloy during Asymmetric Warm Rolling.

Magnesium–lithium alloy is the lightest metal alloy material so far, and the ultra-thin plate is also one of the main trends in the future development of Mg-Li alloy. In order to explore how to prepare LZ91 ultra-thin Mg-Li alloy, this topic adopts the combination of the finite element method (FEM) and visco-plastic self-consistent (VPSC) calculation, electron back-scattered diffraction (EBSD) and tensile experiment, and uses the asymmetric warm rolling process to realize the processing of ultra-thin LZ91 Mg-Li alloy plate with a thickness of 0.25 mm. The experimental results show that the maximum basal texture strengths of 1 mm initial plate and 0.25 mm ultra-thin rolled plate are 36.02 mud and 29.19 mud, respectively. The asymmetric warm rolling process not only reduces the basal texture strength but also significantly refines the grains. The tensile strength and yield strength of 0.25 mm ultra-thin rolled plate along the rolling direction reached 206.8 MPa and 138.4 MPa, respectively. This has a positive effect on the mechanical properties of subsequent materials. VPSC results show that the base slip is the main factor in Mg-Li alloy asymmetric warm rolling, and a large number of tensile twinning are initiated due to the coordinated deformation of the body-centered cubic (BCC) phase, which is beneficial to improve the plastic deformation capacity of Mg-Li alloy.

Recent advances and applications of surrogate models for finite element method computations: a review

Recent advances and applications of surrogate models for finite element method computations: a review

Magnetic Field Visualization Teaching Based on Fusion Method of Finite Element and Neural Network

We developed a visual teaching platform that can calculate the magnetic field of magnetic core inductance in real time. The platform adopts the combination of two theories of finite element calculation and neural network technology. It can enhance students’ understanding and application of the basic knowledge of electromagnetic fields. First, the finite element method was used to calculate the magnetic field of the magnetic core inductance, and the magnetic field data set under different input parameters was obtained. On this basis, the neural network method was used to learn the data set and train the corresponding model. Then the trained neural network model was used to calculate the magnetic core inductance magnetic field. After comparing with the finite element calculation results, we found that the calculation results of the neural network model combined with the finite element were in good agreement with the finite element calculation results. Compared with the finite element calculation method, the calculation speed of the magnetic field distribution calculated by the neural network was faster. Taking the calculation of the magnetic core inductance magnetic field as an example, the calculation time was shortened by about 170 times. Finally, we built a magnetic field visualization teaching platform based on MATLAB. The example magnetic field was quickly predicted by the neural network, saving computing time and effectively improving the teaching of electromagnetic field theory.

Numerical Computations of Entropy Generation and MHD Ferrofluid Filled in a Closed Wavy Configuration: Finite Element Based Study

In this article, the thermal flow effects of inclined magnetohydrodynamics ferrofluid filled in a wavy cavity are studied by adopting the finite element method (FEM). The non-dimensional governing equations and model for different parameters are evaluated. The system of non-linear algebraic equations is computed by adopting the Newton method. A space involving quadratic polynomials (ℙ2) has been selected to compute for the velocity profile, while the pressure and temperature profiles are approximated by linear (ℙ1) finite element space of functions. The discrete systems of non-linear algebraic equations are computed by utilizing the Newton method. The vertical walls are considered cold, whereas the bottom wavy surface is considered hot and the top wavy surface is insulated. The effect of the pertinent parameters, like Ra=105, volume fraction (0.00≤ϕ≤0.06), inclination angle (0∘≤γ≤90∘), and amplitude of the wavy surface (0.02≤AR≤0.08) is investigated. Computational results are addressed as streamlines out, isotherms, and proper graphs for substantial amounts of interest. Increasing Hartmann number (Ha) leads to an increase in Bejan number (Be), while opposite behavior can be observed in the case of viscous, magnetic, and thermal irreversibility, that is, curves are decreased by increasing Ha. Under the influence of an inclined magnetic field, the mathematical structuring of the problem is manifested by continuity, momentum, and energy equations. These equations are solved by using the finite element method computation. The graphs of velocity and isotherm are compared to the relevant parameters. To predict the flow characteristics at different locations, cross-sectional lines representing the velocity field in the horizontal and vertical directions are also drawn. Magnetization’s impact on flow control, heat transfer, and various irreversibilities are also discussed. The Nuavg progressively declined with the enhancement in the amplitude of the wavy surface AR.

Estimation of zero sequence impedance in power transformers using 2D and 3D FEM

This paper describes calculation of zero sequence impedance in three phase, three leg core type power transformers using 2D and 3D finite element method (FEM) calculation on example of 100 MVA power transformer. Paper also describes how winding connection and arrangement affects the size and calculation of zero sequence impedance.

Modelling of the sheet forming while 3-roller bending process

3-roller bending process was investigated using physical modelling and computer simulation. Main technological parameters influence on the formation of tube billet diameter are present; these main technological parameters are upper roller displacement and distance between axes of bearing rollers. Complete factorial experiment was conducted using bending machine, radius of the produced tube billet was set as response function. Conditions for conducting the complete factorial experiment using bending machine and techniques of tube billet radius estimation by graphical-analytical method are presented. At that least square method and SolidWorks software were applied. Regression equations for calculating tube billet diameter conditionally upper roller displacement and distance between axes of bearing rollers were obtained. Influence of these two factors on tube billet radius formation was demonstrated. Finite element method (FEM) computer simulation of the forming process was done with respect to parameters corresponding to parameters of physical modelling experiment using bending machine. FEM computer simulation was done using QForm software. QForm simulation was realized for elastic-plastic bending in terms of two-dimensional deformation. Point tracking was applied to calculate coordinates of the points of the formed sheet and bending parameters. It allowed estimation of the neutral line location in the formed sheet when bending stage was finished. Presented results of computer simulation are figures with trajectories of the tracked points; figures illustrating changing of distance between tracked points; graph of accumulated strain changing through sheet’s thickness. New criterion for neutral line (neutral surface) was proposed for sheet bending process. Results of the research can be effective when exploring Heausler AG bending equipment.

Enhancing nonwoven fabric material sound absorption using embedded labyrinthine rigid structures

Nonwoven materials are fibrous porous materials that are widely used as acoustic absorbers. Although they exhibit satisfactory performances, their applications are still constrained by the thickness requirement of a quarter of the sound wavelength for realizing efficient absorption. In this research, a labyrinthine rigid structure is introduced and embedded into nonwoven fabrics to slow the wave speed; therefore, sound absorption enhancement is present at a lower frequency. For a fixed thickness, such an enhancement can enable conventional absorbers to be subwavelength absorbers, which is useful for addressing the quarter-wavelength constraint. In the current study, the characteristics of the system are evaluated using a theoretical model that is developed based on effective medium theory (EMT). Finite element method (FEM) calculations are also performed to verify the results of the EMT approach. An anisotropic porous material is employed in the calculations rather than an isotropic material since the nonwoven material is laid down in layers. The results show that a labyrinthine rigid structure embedded into a nonwoven material can help lower the sound speed to improve the absorption performance of the nonwoven fabric at lower frequencies. The absorption enhancement produced by the system can be almost double that of the porous material at the same frequency. Moreover, the overall characteristics of the resulting absorber are dictated by embedded structure geometrical properties for the same porous material properties. For this, varying the labyrinthine shape and orientation can be beneficial.

Tape-Like Vibrational Energy Harvesters Using Flexible Fluorinated Polyethylene Propylene (FEP) Piezoelectret as Transduction Material

Energy harvesting is a promising strategy utilizing renewable energy to power low-power-consumption electronics, such as wireless sensor network (WSN) nodes and wearable electronics. In this article, a tape-like vibrational energy harvester, using flexible fluorinated polyethylene propylene (FEP) piezoelectret films as transduction material, is reported. Due to a specific air-filled parallel tunnel structure, the FEP piezoelectret films in this study exhibit both significant longitudinal and transverse piezoelectric effects and could be made into tape-like flexible transduction devices. The results show that the experimental data are consistent with the theoretical prediction and the finite-element method (FEM) calculation. For a device with an effective area of 18 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times25$ </tex-math></inline-formula> mm and a seismic mass of 0.195 g on one edge, the output power at a resonant frequency of 16 Hz amounts to 3.1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{W}$ </tex-math></inline-formula> for an acceleration of 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${g}$ </tex-math></inline-formula> . Owing to the tape-like and flexible transduction elements, the power generated by the device can be enhanced readily by either enlarging area of the transduction elements or multiplying a few transduction elements in series or parallel to meet the power requirement of electronic devices, which makes the practical application flexible.

Influence of foundation stiffness on deformation of layered building structures

Widespread introduction into the industry of layered structures, in particular three-layer plates, shells and is impossible without effective methods of their strength and reliability. High strength and rigidity at relatively low weight damping and thermal insulation properties of these structures have led to their use in modern construction and mechanical engineering. Three-layer plates and shells, as a rule, are a combination of materials heterogeneous in their physical and mechanical properties. The calculation of such structures is a very complex task, the solution of which should be based on mathematical models with a high degree of reliability and reflect the real mechanical properties. During operation, three-layer structures are under the influence of significant static loads. Therefore, the development of effective and cost-effective methods for solving the problems of statics of three-layer systems is an urgent problem. In transport construction, the calculation scheme in the form of a plate on an elastic basis is used to calculate pavement, slabs. The paper considers the bending of a three-layer plate with a rigid filler, which is on an elastic basis. Hypotheses of a broken line are accepted for the description of kinematics of deformation. The contour of the plate has a rigid diaphragm, which prevents the relative displacement of the layers. Analytical and numerical calculations of the three-layer finite element method were performed. As a result of the calculation, the dependences of the deflection on the stiffness coefficient of the base were determined. Recommendations on the choice of stiffness factor are given. Taking into account the stiffness of the elastic base leads to a significant clarification of the stress state that occurs in the three-layer plate under external force. The influence of the stiffness of the base on the deflection of the structure is analyzed, it gives the opportunity to determine the optimal parameters of this mechanical system, and give the necessary recommendations for its use.

Dynamics study based on domain wall reorientation and translation in tetragonal ferroelectric/ferroelastic polycrystals

Domain dynamics have been investigated for lead zirconate titanate, using a finite element method (FEM) approach. Both reorientation and translation motions of 90° domain walls (DWs) were considered, following our previous work on observations of DW motion by scanning electron microscopy and X-ray diffraction. For incorporating the DW motion in the FEM, we introduced a dynamic model describing the motion, subjected to threshold energies for reorientation and a potential energy for translation. Volume fractions of different-angle domains vary as the DW moves, comparing these energies with applied external field strength. The description by the threshold energy carries irreversible poling and hysteresis phenomena. Single domain parameters and threshold/potential energies were extracted by fitting FEM calculations to experimental D–E hysteresis and S–E butterfly curves. This approach enabled us, for the first time, to extract the intrinsic and dynamic information of the DW motions, and the reproduction of full hysteresis and butterfly curves.

ELEMENT UP TO STRUCTURE MODELING WALL SHEET PILE WITH STEEL STRUTTING REINFORCEMENT IN FOUNDATION EXCUREMENT

&lt;p&gt;Evaluation modelling of the OT-22 steel sheet pile wall with type H-350 steel strutting reinforcement in the excavation for the foundation structure with a depth of 7.50 meters was carried out to get the value of the safety factor and wall stability. The evaluation stages include subgrade investigation using the SPT method, data collection of profile steel properties used, interpretation of soil data, staged-construction modeling using the Finite Element Method (FEM) computer application, and analysis of modeling results. From the research that has been done, the value of maximum bending moment (M&lt;sub&gt;max&lt;/sub&gt;) is 223.8 kNm/m', the magnitude of the axial force that occurs in the strut members is 22.51 kN, 121.91 kN, and 66.10 kN respectively. The value of maximum lateral displacement (U&lt;sub&gt;x&lt;/sub&gt;) is 62.4 mm. From these results, it can be concluded that the lateral displacement (U&lt;sub&gt;x&lt;/sub&gt;) that occurs is much larger than allowable displacement (U&lt;sub&gt;all&lt;/sub&gt;) 39 mm. Thus, it is necessary to modify the existing sheet pile wall system, such as to change the dimensions of the steel sheet pile, changing the dimensions of the steel strutting, or changing the distance of the steel strutting.&lt;/p&gt;

Effective Medium Analysis of Stacked-Nanoparticles Array’s Optical Responses

Metallic nanoparticle-based material is currently implemented in many photonics-based applications such as biosensors, imaging, and color filter due to its remarkable properties called localized surface plasmon or LSP. Numerical methods are commonly used to calculate the optical responses arising from the nanostructure. However, a faster calculation can be provided by analytical methods. In this paper, we used an analytical calculation based on dipolar approximation and the transfer matrix method to calculate the optical responses of stacked-nanoparticles array on a dielectric substrate. Gold (Au) and silver (Ag) nanoparticles embedded inside a dielectric medium are considered. To validate the results, the analytical model was benchmarked to a finite element method (FEM) calculation. We found that the absolute difference of the absorbance peak of the analytical model to FEM calculation is less than 2 nm with the volume fraction of ~20% and it becomes better with a lower volume fraction. The field distribution analysis shows that lower volume fraction structures lead to weaker near-field coupling, therefore concluding that the analytical model is suitable only for sparse structure. Experimental data also can be replicated from the spectral profile showing opportunities to use the analytical model in the application design stage.

The discrepancy between the indentation curves obtained by the finite element method calculation with a Berkovich and a conical indenter

The discrepancy between the indentation curves obtained by the finite element method calculation with a Berkovich and a conical indenter

The study on the overloading effect on fatigue crack growth considering residual stress relaxation in Al 5456-H38

A numerical and experimental study was conducted on fatigue crack growth (FCG) of metallic components to investigate the effect of redistribution of mechanical residual stresses induced by overloading in notched specimens. The compact tension (CT) specimens of an aluminum alloy were used, and mechanical residual stresses were introduced in them by applying tensile overload (OL). Then, the specimens were subjected to fatigue loading. In the calculations of finite element method (FEM), the modified cyclic J-integral was used as the crack growth parameter. Good agreement was observed between the numerical and experimental results. The FEM results demonstrated a clear redistribution of residual stresses during FCG process. It was observed that after a few cycles, the residual stress field reached a lower magnitude value confining in a small zone around the around the crack tip. Furthermore, the effects of stress ratio, load amplitude, and OL ratio (OLR) on the redistribution of residual stresses are studied in this research. It was observed that the residual stresses are considerably released during the initial cycles of fatigue loading.

Regulating multiscale structures of nickel-iron-based electrocatalysts for efficient water oxidation

The oxygen evolution reaction (OER) has been widely studied as an efficient process in energy conversion, yet the majority of studies focus on the strategies to boost the intrinsic activity of the catalyst, rather than considering the enhancement of its mass transfer ability. Herein, we produce efficient NiFe-based OER electrocatalysts with rich oxygen vacancies and abundant transport channels by an argon plasma-engraving strategy. Compared with pristine NiFe, the obtained best NiFe-plasma catalyst yields a 12.5-fold increased current density (from 80 to ∼1,000 mA cm −2 ) at an overpotential of 300 mV, surpassing most OER catalysts in alkaline solution. Density functional theory calculations disclose that the introduction of oxygen vacancies improve the intrinsic activity and electronic conductivity, while finite element method calculations demonstrate that the construction of catalytic interface and the creation of nanoscale transport channels facilitates mass transfer. • Plasma simultaneously produces oxygen vacancies and slit pores on NiFe • FEM calculation illustrates that the slit pores can facilitate mass transport • The obtained NiFe-plasma catalyst yields a 12.5-fold increased current density Wang et al. prepare efficient NiFe-based OER electrocatalysts with abundant oxygen vacancies and transport channels by plasma engraving. Owing to the synergistic effect between high intrinsic catalytic activity and preferable mass transfer ability, the NiFe-P-200-15 exhibits a small overpotential of 302 mV to reach 1.0 A cm −2 in alkaline electrolyte.

Machine Learning to Predict Quasi TE₀₁₁ Mode Resonances in Double-Stacked Dielectric Cavities

We have applied machine learning in a neural network to calculate the quasi TE₀₁₁ mode of a cylindrical microwave cavity with two symmetrically stacked dielectric resonators (DRs) inside, with aspect ratios of the overall cavity being limited to the range of 0.25&#x2013;4. The neural network was trained with 99 970 samples and evaluated using 9564 samples from a holdout dataset. The samples were created using a supercomputer to solve random cavity configurations via finite-element method (FEM) programming. The trained neural network predicts the resonant frequency of the quasi TE₀₁₁ mode and expresses the mode in terms of expansion coefficients of empty cavity TE<inline-formula> <tex-math notation="LaTeX">$_{\mathrm {0\,np}}$ </tex-math></inline-formula> modes, from which plots of the electric and magnetic fields can be made. The predictions are extremely quick, taking &#x007E;0.05&#x2013;0.2 s running on a typical personal computer, and are very accurate when judged against the FEM results: the overall median error in the frequency neural network is 0.2&#x0025;, and the overall median error of the expansion coefficients neural network is 0.003&#x0025;. This should allow designers to much more rapidly determine optimal cavity and DR dimensions and other parameters in order to achieve the frequency and mode they desire, with a speedup of approximately <inline-formula> <tex-math notation="LaTeX">$10\,\,000\times $ </tex-math></inline-formula> compared with FEM calculations alone. A link to the Python implementation of our FEM code and our trained neural network code is provided.

ANALYSIS OF THE EFFECT OF PROJECTILE IMPACT ANGLE ON THE PUNCTURE OF A STEEL PLATE USING THE FINITE ELEMENT METHOD IN ABAQUS SOFTWARE

This paper deals with the punctureability of a steel plate by a projectile at different angles of attack. The effect of the projectile angle on the force required to penetrate a plate made of A36 steel is presented using Finite Element Method calculation software. Using Abaqus software, a dynamic model of a projectile striking a plate was modelled and the force required to penetrate a 5 mm thick steel plate was presented. The introduction gives an overview of the genesis of the topic and a brief historical background. The chapter on numerical analysis presents the numerical model used and how the simulation was modelled. In the conclusions, a summary of the results was formulated and conclusions were drawn regarding the observations and insights of the analysis. The force required to penetrate the plate was observed to increase with increasing projectile angle of attack and it was found that, as the angle of the plate increased, the force required to penetrate increased.

Research on the Bonding Performance of UHPC–NC Interfaces With Different Sizes of Grooves

The interfacial treatment between normal concrete (NC) and ultra-high–performance concrete (UHPC) is crucial to ensure bonding strength. Grooving is an effective method to treat the UHPC–NC interface, but the shear properties and failure modes at the composite interface remain under-investigated. This study focuses on the bonding performance of different groove designs (width, spacing, and angle) at the UHPC–NC interface, and push-off tests with 15 specimens were carried out to evaluate the strength and stiffness. Furthermore, a finite element model (FEM) and calculation methods were validated with the experimental study to reveal the bonding strength, and a parametric study on the groove depth was also carried out. The interface treated by grooves increases 3.32 and 2.48 times in strength and stiffness compared with specimens bonded by epoxy resin adhesive. The results also show that failing at the interface and NC matrix made up a majority of the failure modes. The shear strength of the UHPC–NC interface increased with the width and decreased with the space between the grooves. Grooves with 10 mm width, 100 mm space, 25 mm depth, and right angle were recommended. This paper will lay a foundation for the surface preparation of UHPC strengthening NC bridges.