Finite Element Method Results Research Articles

Prediction of structural deformation of a deck plate using a GAN-based deep learning method

During the manufacturing process, vessels typically undergo structural deformation during the erection stage because of the heavy loads they are subjected to. In this study, the out-of-plane mechanical deformation of a deck plate in an erection stage was predicted using a deep learning model. As model inputs, the initial deformation of the deck plate after assembly, the dimensional information of all the reinforcing structures installed on the deck plate, and the normal reaction force acting along the boundary in the erection stage were used, and the artificial intelligence model was trained to create an image of deformed shape of the deck plate from the inputs in a supervised manner. Three different types of commercial vessels were used in the training, and the training data were supplied from a nonlinear buckling finite element method (FEM) simulation. The adopted deep learning model was a convolutional neural network-based generative adversarial network, which was designed to translate the input images to the deformation predictive image. The deep learning model successfully predicted the 3-D deck distortion, and the accuracy reached 99.7794% (R-Squared) with respect to the FEM results. The prediction time was within a few seconds.

Phase-field simulation of microstructure evolution during friction stir welding of 304 stainless steel

Dynamic recrystallization (DRX) is the most significant metallurgical phenomenon during friction stir welding (FSW) and friction stir processing (FSP). In order to simulate the microstructure evolution during FSW, the phase-field method was applied. For this purpose, the growth and shrinkage of a nucleus in the matrix of a grain using the DRX mechanism models was simulated using the phase-field method. In order to have suitable parameters for microstructure modeling, the finite element method (FEM) was used for numerical simulation of the FSW process, including thermal, computational fluid dynamics (CFD) and mechanical simulations. The phase-field simulation of DRX microstructure evolution was performed based on the FEM results. The simulation results were validated by being compared to the experimental findings reported by other researches. It was found that the rotating speed plays a significant role in the formation of the final microstructure in the process. Grain size distribution is nearly interdependent of the nucleation rate, growth and therefore, recrystallized fraction areas. Grain boundary fraction was also predicted by post-processing of the simulation results. It was also found that the rotating speed affecting the nucleation and growth rate significantly affected the grain boundary fraction in FSW process.

Analytical method for the mechanical response of buried pipeline under the action of strike-slip faulting

Buried pipelines are commonly damaged when laid across strike-slip faults, always leading to some level of destruction with fault movement. The moment of the neutral axis of a pipe section was obtained by integration, and the equations for the bending moment and the bending strain on a pipeline’s section were presented here, based on a trilinear stress–strain model. The calculation method for the lateral soil pressure and pipeline’s bending strain near the fault-crossing point was improved. Lateral soil pressure was regarded as being related to lateral pipeline movement and, for accurate calculation, this part of the pipeline was divided into finite element segments. An iterative process for solving for pipe bending strain was derived, and the algorithm and program for calculating bending strain and the potential damage position of the pipeline’s sections was compiled based on Matlab software. Compared with finite element method (FEM) results and the current standard method, in the situation of a pipeline being in tension under the action of a strike-slip fault (intersection angle < 90°), the result of the proposed method is in good agreement with FEM results. This shows that the proposed analytical method possessed a good reference value for the strain response analysis of tensile steel pipelines under strike-slip faulting.

Finite Element Method Parameter Estimation of Atomic Sensor Based on Thermal Network Method

The heat distribution is one of the key factors which affects the performance of the atomic sensor. Analysis of component temperature is indispensable when determining the need for heat preservation or cooling. Finite element method (FEM) is a commonly thermal analysis method that is widely used in many fields and finite element analysis software is also an essential tool in various thermal analysis cases. Both need accurate parameters to solve the thermal problems. However, some parameters are difficult to be measured in the atomic sensor. To obtain more accurate parameters, a heat transfer model based on the thermal network method is available for parameter estimation that only needs simple conditions to solve problems, which can be measured by experiment. Based on the classical heat transfer theory and thermal network method, the heat transfer model is developed to analyze the heat distribution in the atomic sensor and achieve the parameter estimation of FEM. The model accuracy has been validated by the finite element analysis software and experimental results. The contour maps of the temperature are obtained by finite element analysis software. It is shown that the maximum error of parameter estimation is within 7.8% and the optimal results can achieve 2.1%. The heat transfer model based on the thermal network method can obtain the parameters that can't be measured by experiment under limited boundary conditions, effectively achieve parameter estimation, and make the simulation results closer to the experiment. With the parameters from heat transfer model, the results of FEM become more accurate.

A Comparative Study on the Wind Deflection of Railway Overhead Contact Line Based on Empirical Formula and Finite Element Approach

The assessment of wind deflection of the railway overhead contact line (OCL) is of great importance to ensure the safe and reliable operation of the electrified railway. This paper performs a comparative study of the railway OCL wind deflection based on the traditional empirical formula and finite element method (FEM). Considering the geometrical nonlinearity, a nonlinear finite element approach is adopted to model the OCL. The crosswind load is applied to the OCL through an iterative procedure. The comparative study indicates that the maximum wind deflection estimated by the empirical formula is generally the same as the FEM result when the turbulence intensity is 10%. However, with more than 10% of the turbulence intensity, the empirical formula may give a risky result. Then, some coefficients are introduced to modify the empirical formula according to the FEM results. The numerical examples are presented with different OCL tension classes to verify the validation of the modified empirical formula.

Stress distribution on a soil tillage machine frame segment with a chisel shank simulated using discrete element and finite element methods and validate by experiment

Soil tillage machinery must be highly reliable during its operation. For a limited time following harvest, tillage machines must perform a significant amount of work, and any downtime has a significant negative impact on farm economics. For this reason, manufacturers of agricultural machinery aim to design machines that are both reliable and inexpensive. The development of technologies, especially electronics, has led to completely new possibilities for the design and optimisation of agricultural machinery. During work, a tillage machine may not only be loaded by its own weight, but also by the interaction of any tools interacting with the soil that transmit loads to itsframe. To analyse loads a numerical model of tillage machine was compiled. The stresses acting on the chisel shank during tillage were simulated using a numerical model. The frame of the agricultural machine was also simulated with particular emphasis on the locations where the stresses could be measured. Strain gauges were attached at the same locations in a real-life model, and predicted stress values verified experimentally. A discrete element method (DEM) model was used to create and optimise a comprehensive soil model, and its results were used in a finite element method (FEM) model for a transient analysis. The results from the experimental stress measurements and simulation data from the model showed good agreement. Therefore, the procedures of this study can therefore be used for the design and optimisation of tillage machinery. • Determination of stress on chisel shank and tillage machine frame. • Soil model penetration resistance was modelled using DEM. • Transient task analysis made by ANSYS using FEM. • Calibrated DEM and FEM results were validated by field tests.

R-Function and variation method for bending problem of clamped thin plate with complex shape

Solving ordinary thin plate bending problem in engineering, only a few analytical solutions with simple boundary shapes have been proposed. When using numerical methods (e.g. the variational method) to solve the problem, the trial functions can be found only it exhibits a simple boundary shape. The R-functions can be applied to solve the problem with complex boundary shapes. In the paper, the R-function theory is combined with the variational method to study the thin plate bending problem with the complex boundary shape. The paper employs the R-function theory to express the complex area as the implicit function, so it is easily to build the trial function of the complex shape thin plate, which satisfies with the complex boundary conditions. The variational principle and the R-function theory are introduced, and the variational equation of thin plate bending problem is derived. The feasibility and correctness of this method are verified by five numerical examples of rectangular, I-shaped, T-shaped, U-shaped, and L-shaped thin plates, and the results of this method are compared with that of other literatures and ANSYS finite element method (FEM). The results of the method show a good agreement with the calculation results of literatures and FEM.

Lamb wave inspection using piezoelectric diaphragms: An initial feasibility study

Lamb wave-based inspection has been extensively investigated and reported in the literature as a non-destructive technique in structural health monitoring and other applications. The generation and reception of Lamb waves are typically performed with piezoelectric ceramics operating as actuators and sensors, respectively. This article presents a study of the feasibility of piezoelectric diaphragms as an alternative transducer, allowing to expand the research as well as to accelerate the implementation of Lamb wave-based SHM systems with lower installation costs. Piezoelectric diaphragms are sound components widely used in everyday electronic devices and, in addition to the low cost, they have the advantage of being mass-produced by different manufacturers in standard sizes and are readily available. To assess the feasibility of these components, basic analysis by finite element method (FEM) and experimental tests were carried out on aluminum plates and the results obtained with the diaphragms were compared with those obtained using conventional piezoelectric ceramics. Structural damage was simulated by making cracks and drilling holes in the structure and an imaging algorithm together with damage index based on the wavelet transform was used to detect and locate damage. In addition, tests were carried out to evaluate and compare the reproducibility of the results and the effects of temperature variation on the two types of transducers. FEM and experimental results show that piezoelectric diaphragms are feasible for generating and receiving Lamb waves, as well as detecting structural damage. Therefore, these commercial sound components can also be alternative transducers for applications involving Lamb waves.

Experimental and Numerical Investigation of an Innovative Method for Strengthening Cold-Formed Steel Profiles in Bending throughout Finite Element Modeling and Application of Neural Network Based on Feature Selection Method

This study evaluates an innovative reinforcement method for cold-formed steel (CFS) upright sections through finite element assessment as well as prediction of the normalized ultimate load and deflection of the profiles by artificial intelligence (AI) and machine learning (ML) techniques. Following the previous experimental studies, several CFS upright profiles with different lengths, thicknesses and reinforcement spacings are modeled and analyzed under flexural loading. The finite element method (FEM) is employed to evaluate the proposed reinforcement method in different upright sections and to provide a valid database for the analytical study. To detect the most influential factor on flexural strength, the “feature selection” method is performed on the FEM results. Then, by using the feature selection method, a hybrid neural network (a combination of multi-layer perceptron algorithm and particle swarm optimization method) is developed for the prediction of normalized ultimate load. The correlation coefficient (R), root mean square error (RMSE), Nash–Sutcliffe efficiency (NSE), mean absolute error (MAE) and Wilmot’s index of agreement (WI) are used as the measure of precision. The results show that the geometrical parameters have almost the same contribution in the flexural capacity and deflection of the specimens. According to the performance evaluation indexes, the best model is detected and optimized by tuning other algorithm parameters. The results indicate that the hybrid neural network can successfully predict the normalized ultimate load and deflection.

Investigation of porous cells interface on elastic property of orthopedic implants: Numerical and experimental studies

Application of porous cells in orthopedic implants makes it possible to better approximation of elastic property of human bones. Although the mechanical and biological properties of orthopedic porous implants are studied in many researches, the interaction between different porous unit cells from geometrical compatibility and also, considering manufacturing conditions for the ultimate goal of bone ingrowth is not thoroughly investigated. In this study, a kelvin cell is designed with 530 to 810 μm pore sizes, which is the appropriate range for bone ingrowth. Due to anatomical position of implants in the human body and the limited range of the elastic modulus of kelvin cell with different geometrical parameters, this unit cell is combined with other cells to extend the range of its elastic modulus. After selecting the appropriate combination of cells to achieve desired properties, they are fabricated with Stainless Steel 316 L using radially gradient porosity in the range of 64% to 80%, and then finite element method (FEM) is performed to evaluate the elastic modulus, stress distribution, and strain energy of the proposed structures. Gradient and uniform structures are fabricated using selective laser melting (SLM) to validate FEM results. The simulation and experimental results are close to each other with an average error of about 4.5%. The elastic modulus derived from FEM for the designed gradient structures are in the range of 7.48 to 10.49 GPa, which can be modified, and present mechanical properties close to trabecular or compact bone based on the position and conditions of the bone defect.

Long-Term Numerical Analysis of Subsurface Delamination Detection in Concrete Slabs via Infrared Thermography

One of the concerns about the use of passive Infrared Thermography (IRT) for structural health monitoring (SHM) is the determination of a favorable period to conduct the inspections. This paper investigates the use of numerical simulations to find appropriate periods for IRT-based detection of subsurface damages in concrete bridge slabs under passive heating along a 1 year of time span. A model was built using the Finite Element Method (FEM) and calibrated using the results of a set of thermographic field inspections on a concrete slab sample. The results showed that the numerical simulation properly reproduced the experimental thermographic measurements of the concrete structure under passive heating, allowing the analysis to be extended for a longer testing period. The long-term FEM results demonstrated that the months of spring and summer are the most suitable for passive IRT inspections in this study, with around 17% more detections compared to the autumn and winter periods in Brazil. By enhancing the possibility of using FEM beyond the design stage, we demonstrate that this computation tool can provide support to long-term SHM.

A Novel Method for Establishing an Efficiency Map of IPMSMs for EV Propulsion Based on the Finite-Element Method and a Neural Network

In this paper, we introduce a novel method for establishing an efficiency map of interior permanent-magnet synchronous motors that are used for electric vehicle propulsion, by employing the finite-element method (FEM) and a neural network (NN) to reduce the analysis time. The electro-magnetic analysis of motors using the FEM, particularly iron loss analysis, is significantly time-consuming owing to the nonlinearity and the post-processing. Moreover, to obtain an efficiency map, a data map of the d-q flux linkages based on the d-q currents should be established. At this stage, we compute the flux densities in all the elements, and they are learned by the NN to obtain a function of the d-q currents. Subsequently, the iron losses at all operating points are calculated using the learned data via the harmonic loss method. The results of the proposed method indicate that the time required to obtain the efficiency map is reduced; furthermore, the results are validated via a comparison with the FEM results.

A modified Sneddon model for the contact between conical indenters and spherical samples

Indentation techniques have proven to be effective to characterize the mechanical properties of materials. For the elastic deformation, the commonly used models are Hertz model and Sneddon model. However, neither of them works for indenting the spherical samples using the pyramid or conical indenter. Therefore, one modified Sneddon model has been developed to determine the Young’s modulus of spherical samples from indentation results. In this study, the effects of sample diameter and indenter angles on indentation tests were investigated by finite element method (FEM). The empirical correction parameters in the new mathematical model were introduced based on dimensional analysis and determined by the numerical fitting to FEM results. Experimental tests with different conical indenters have demonstrated that the new model is capable to reliably determine the Young’s modulus of the spherical samples. The new model can fill the gap of the contact mechanics and enrich the experimental solid mechanics for the interpretation of indentation results.Graphic abstract

Theoretical and experimental Raman study for mechanical stress in die-attach process

We measured the stress in a Si chip mounted on a Cu plate using Raman spectroscopy and compared the results with those calculated by using the finite element method (FEM). The difference in the stress observed at the vicinity of the chip edge was approximately 30 MPa, and the simulated value was smaller than that observed using Raman spectroscopy. We found that the difference occurred owing to the absence of the “filet” structure generated from the epoxy adhesive, and we subsequently modified the simulation model. The modified FEM results were in good agreement with the measured results. These results indicated that the “filet” structure, which was not the main structure of die-bonding, played an important role in residual stress formation. Feedback using Raman measurements is crucial, and we evaluated the stress in electronic devices with high accuracy by combining FEM with Raman microprobe measurements. In cross-sectional measurements, we observed discrepancy between the results, and the difference in the vertical stress was found to be dependent on excitation laser wavelength. Except for the discrepancy near the backside, the Raman results were in good agreement with the FEM results. This indicated that Raman spectroscopy can evaluate the stress components in the Si cross-section, and full three-dimensional stress in the packaging devices can be determined by combining FEM with cross-sectional Raman measurements, even if the internal stress is relaxed via cutting.

Investigation on the Acoustic Performance of Multiple Helmholtz Resonator Configurations

Helmholtz resonator is considered and widely accepted as a basic acoustic model in engineering applications and research. In this paper, the normal incidence sound absorption characteristics of series and parallel configurations of Helmholtz resonators is studied analytically, numerically and experimentally. The proposed analytical model for series configuration of HRs comprises of Johnson–Champoux–Allard model and transfer matrix method while parallel configuration of HRs is described using parallel transfer matrix method. The results from proposed analytical models fit well with the finite element method (FEM) results obtained from COMSOL multiphysics. Incorporation of parallel configuration and proper tuning of geometric parameters helps to overcome the trade-off between broad band sound absorption and minimum space utilization. Also, the experimental observations of one of the parallel configuration substantiates the FEM results. Moreover, the FEM models are more accountable for the variation in neck position and also provide better visualization of acoustic absorption with frequency.

The Influence of the Physical-Mechanical Parameters of Rock on the Extent of the Initial Failure Zone under the Action of an Undercut Anchor.

This paper presents the results of a numerical FEM (Finite Element Method) simulation of the formation of a rock failure zone in its initial stage of development. The influence of rock parameters, such as the Young’s modulus, Poisson’s ratio and friction factor of the rock in the contact zone with the working surface of the undercut anchor head, were taken into account. The obtained results of FEM simulations were compared with the results of field tests conducted in Polish mining plants extracting rock raw materials.

The parameter optimization and mechanical property of the honeycomb structure for Ti2AlNb based alloy

In this paper, the parameter optimization and the mechanical property of the honeycomb structure fabricated by superplastic forming/diffusion bonding (SPF/DB) process for Ti 2 AlNb based alloy were investigated. The uni-axial tensile test was carried out at different temperatures and strain rates. The results showed that the maximum elongation was 236 % at 970℃/0.0003s −1 and the strain rate sensitivity coefficient was 0.3. The mechanical model of the face sheet and core sheet forming was established and the forming process of the structure was analyzed by the finite element method(FEM). The FEM results showed that the grooves on the surface of the honeycomb structure gradually faded and disappeared with the width of the bonding joints increasing. And the honeycomb structure with the bonding width of 10mm was flexible and successfully fabricated. Finally, the thickness distribution of the structure was measured and it was consistent with the FEM results. The obvious microstructure evolution resulted in the reduction of tensile property. The compressive property of this structure in experiment and in FEM was investigated. The compressive strength of experimental test was 7.7MPa and that of the FEM was 6.6MPa, respectively.

Non-Linear Steady State Heat Conduction using Element-Free Galerkin Method

This study aims to interpret the non-linear steady-state heat conduction for temperature-dependent thermal conductivity ($k$ ($T$)) using Element-Free Galerkin (EFG) method. In this present study, a one-dimensional heat conduction problem with uniform heat generation was explicated. Moving Least Squares (MLS) approximants were applied to estimate the unknown function of temperature $T$ ($x$) with $T^h$ ($x$) using linear basis and weight functions. The variational method has been used to develop discrete equations. Essential boundary conditions are enforced by using the Penalty method. The results have been obtained for the one-dimensional model using essential MATLAB codes. The results obtained by the EFG method are compared with the analytical and finite-element method results. The results are also studied by increasing the number of nodes to study the convergence which indicated that EFG has good convergence behavior. The results have also been obtained for different values of the scaling parameter ($α_s$) and any values of αs between 1.8 and 2.0 were found suitable for providing better results in the EFG method.

Modal properties diagnostics of the high-pressure fuel injection pipes in off-road diesel engine

Injection systems of modern commercial vehicle power units are still a frequent topic for development engineers in terms of durability and reliability. Therefore, the content of this study is just an investigation of the dynamic behaviour of high-pressure injection pipes of a four-cylinder combustion engine. The modal properties of the injection tubes are evaluated by experimental modal analysis (EMA). Another phase of the measurements is the sensing and analysing of the acceleration on each injection pipe during the engine speed ramp in the entire range of the speed spectrum. There was investigated the modal behaviour of the structure to the operational character of the excitation. The work includes a numerical model established by finite element method (FEM), where the boundary conditions correspond to the real installation of injection pipes from the measurement. The modal properties of injection pipes were primarily investigated through the numerical approach, several variants of pipe attachments were considered in simulations. Comparing the FEM results of different pipe attachments, the suitability of the clamp position with respect to the specific installation in the power unit from the measurement is discussed. From the evaluated results, it is possible to assume the dynamic behaviour of the high-pressure injection pipe in the power unit. Based on the performed analyses, the critical mode shapes of the injection pipes are described considering the engine operating condition. When the engine speed frequency and some pipe eigen frequency interfere together, it is undesirable state. In many cases, this leads to a crack initiation and subsequent damage of the injection pipes during the cyclic load. The presented results and conclusions in this study should improve the overall knowledge on high-pressure fuel pipes in terms of modal properties and its vibration behaviour during operating condition.

Inf-sup stability of the trace $\mathbf {P}_2$–$P_1$ Taylor–Hood elements for surface PDEs

The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surface. A trace FEM based on standard Taylor-Hood (continuous P2-P1) bulk elements is proposed. A so-called volume normal derivative stabilization, known from the literature on trace FEM, is an essential ingredient of this method. The key result proved in the paper is an inf-sup stability of the trace P2-P1 finite element pair, with the stability constant uniformly bounded with respect to the discretization parameter and the position of the surface in the bulk mesh. Optimal order convergence of a consistent variant of the finite element method follows from this new stability result and interpolation properties of the trace FEM. Properties of the method are illustrated with numerical examples.