Finite Element Method Results Research Articles

Finite‐element analysis combined with an ensemble Gaussian process regression to predict the damper eddy current losses in a large turbo‐generator

A method combining the finite-element method (FEM) numerical calculation with machine learning is developed and used to calculate the eddy current losses of the rotor damping slot wedge of generator with different structures and electromagnetic properties. FEM simulation data is used as the input, and the stacking method is used to build the ensemble Gaussian process regression model for eddy current loss prediction to predict and analyse the calculation results. The error is tiny. The FEM results are highly consistent with the prediction data. As demonstrated by comparison experiments, the prediction accuracy of the stacking Gaussian process regression (SGPR) model is greater than that of other models. Therefore, the SGPR model provides a new auxiliary design method for large generators that can help improve generator design efficiency.

Experimental Verification and Analytical Study of Influence of Rotor Eccentricity on Electromagnetic Characteristics of Permanent Magnet Machine

Rotor eccentricity occurs during manufacturing, causing the device to vibrate and make noise, thereby shortening its life. Its characteristics can be analyzed via the existing finite element method (FEM); however, analyzing characteristics according to design variables is time-consuming. Therefore, we implemented an analytical method that can rapidly identify the characteristics according to the design variables. We derived the magnetic flux density, the back-electromotive force, and the torque through the analytical method according to rotor eccentricity. The rotor eccentricity was considered to be based on the perturbation and the electromagnetic theories; accordingly, the governing equations and boundary conditions were derived. The analytical method was validated through FEM and experimental result.

Modelling of elastic modulus of CaZrO3-MgO composites using isotropic elastic and anisotropic models

Starting from synthetic raw materials (CaZrO3 and MgO), microstructural and mechanical properties were optimised in order to obtain dense multiphasic ceramic, then finite element method (FEM) of an equimolar (1:1) CaZrO3-MgO composite was performed in order to obtain the effective elastic modulus.Composite presents two main phases of orthorhombic CaZrO3 (81.5 wt.%) and cubic MgO (18.5 wt.%); For 1500 °C, relative density of 99.9%, characteristic strength of 168 MPa, hardness of 7.8 MPa and toughness of 2.5 MPa.m1/2 were obtained. FEM simulation was performed using two representative volume elements (RVE’s) with edge lengths of 14 μm (933 grains) and 17 μm (1670 grains), using isotropic elastic model, and anisotropic on specific set of crystallographic planes.The results of FEM using isotropic approach for the two RVE’s are perfectly aligned with the experimental (245 GPa), while the anisotropic model shows a difference of 6.5%.

Crashworthiness assessment of thin-walled double bottom tanker: Influences of seabed to structural damage and damage-energy formulae for grounding damage calculations

This work presents results of numerical analyses with focus on structural performance accounting for seabed topology, and investigation of energy formulae for application in calculation of grounding damage. Study in this work is divided into three stages, i.e. finite element method (FEM) verification using laboratory experiment, numerical calculation of ship grounding using FEM, and comparison of the FEM results with empirical formulae of damage-energy calculation. Fundamental formula of Minorsky is considered with other improvement expression, such as Woisin and Zhang. Investigation suggested that the recent-developed expression produces the closest estimation to the verified FEM results. On the other hand, fundamental formulae of Minorsky is the farthest compared to the FEM, which indicates constant value in the expression needs to be more specific as improved in the Woisin formula.

Comparison of A Multi-Stage Axial Flux Permanent Magnet Machine With Different Stator Core Materials

This paper proposes a multi-stage axial flux permanent magnet machine (MAFPMM) and the properties with different stator core materials are analyzed. The mentioned MAFPMM has three rotor-disks and two stator-disks. As a key part of the flux path, stator core of silicon steel sheet, soft magnetic composite (SMC) and amorphous magnetic metal (AMM) are studied by three dimensional (3-D) finite element method (FEM), respectively. The performances such as flux density distribution, no-load back-electromotive force (EMF), cogging torque, output torque, and core loss are analyzed. FEM results indicate that the three materials have almost equal influence on flux density distribution, no-load back-EMF, cogging torque, and output torque. But in terms of core loss, difference appears between silicon steel sheet, SMC and AMM. Considering the disadvantages in mechanical property of AMM and silicon steel sheet, a prototype is fabricated using SMC stator core. The FEM results are verified by the experimental results of the prototype.

Experimental and finite element simulation of natural rubber foams using real 3D structures

Natural rubber (NR) foams were prepared via a one-step foaming process, the effect of density and morphology on micro-level and macro-level mechanical properties was studied. In particular, experimental data were used to validate different numerical models based on actual three-dimensional (3D) foam structures built using a combination of 2D scanning electron microscopy (SEM) images. Then the uniaxial compression behavior was simulated at two levels (micro-scale and macro-scale) with finite element methods (FEM). The FEM results were finally compared with experimental data and different hyper-elastic models. SEM images showed that increasing the relative foam density from 0.3 to 0.5 led to a 55% decrease in cell size and a 1000% increase in cell number. The real 3D structures showed that foams with higher density have a more homogenous structure with lower structural defects or cell connections. The results also revealed that FEM at the macroscopic level is in good agreement with experimental results, especially for high density foams. On the other hand, FEM at the microscopic level showed that the maximum stress concentration and related micro-strain substantially decreased with increasing foam density.

Study on reducing the risk of stress corrosion cracking of austenitic stainless steel hydraulically expanded joints

Stress corrosion cracking (SCC) is one of the main failure modes of tube-to-tubesheet expanded joints in tubular heat exchangers, and the residual tensile stress is an important factor in the development of these cracks. Many tubular heat exchangers in nuclear-power stations are made of 304L stainless steel, and SCC often occurs in the tube-to-tubesheet expanded joints during service. However, few studies on the failure analysis of these expanded joints of 304L stainless steel have been reported. In this paper, the residual stresses in the hydraulically expanded joints of a high-pressure heater used in one nuclear-power station were evaluated by the finite element method (FEM) to reveal the cause of crack formation. Meanwhile, the effects of the expansion pressure and yield strength on the residual stress of 304L tubes in the expanded joint were studied by the FEM and SCC tests. The FEM results showed that the residual stress of the tube in the expanded zone decreased with the increase in the expansion pressure. But the maximum residual stress, which was located at the transition zone between the expanded and unexpanded zone of the joint, was not affected by the expansion pressure. The yield strength of the tube had a significant influence on the residual stress in the hydraulically expanded joint. Reducing the yield strength of the tube could reduce the maximum residual tensile stress to reduce the risk of SCC. The FEM results were in good agreement with the SCC test results, which were performed following the Design and Construction Rules for Mechanical Components of PWR Nuclear Islands (RCC-M). This study provides a basis for the manufacturing process of austenitic stainless-steel tube-to-tubesheet hydraulically expanded joints.

Material Analysis of Steel Fibre Reinforced High-Strength Concrete in Terms of Flexural Behaviour. Experimental and Numerical Investigation.

The paper presents the results of tests for flexural tensile strength (fct,fl) and fracture energy (Gf) in a three-point bending test of prismatic beams with notches, which were made of steel fibre reinforced high-strength concrete (SFRHSC). The registration of the conventional force–displacement (F–δ) relationship and unconventional force-crack tip opening displacement (CTOD) relationship was made. On the basis of the obtained test results, estimations of parameters fct,fl and Gf in the function of fibre reinforcement ratio were carried out. The obtained results were applied to building and validating a numerical model with the use of the finite element method (FEM). A non-linear concrete damaged plasticity model CDP was used for the description of the concrete. The obtained FEM results were compared with the experimental ones that were based on the assumed criteria. The usefulness of the flexural tensile strength and fracture energy parameters for defining the linear form of weakening of the SFRHSC material under tension, was confirmed. Own equations for estimating the flexural tensile strength and fracture energy of SFRHSC, as well as for approximating deflections (δ) of SFRHSC beams as the function of crack tip opening displacement (CTOD) instead of crack mouth opening displacement (CMOD), were proposed.

Analysis of Winding MMF and Loss for Axial Flux PMSM With FSCW Layout and YASA Topology

This article takes 12-slot/10-pole axial flux permanent magnet (PM) synchronous machine (AFPMSM) with fractional-slot concentrated windings and yokeless and armature (YASA) topology as the research object. Winding magnetomotive force (MMF) of three-phase double-layer layout is analyzed by three kinds of methods, which are star diagram method, winding function method, and holographic spectrum method. The analysis results of finite-element method (FEM) show that the three methods are effective and consistent in analyzing winding MMF. Comparative analysis of iron loss density and B–H magnetizing curves of four typical iron materials are studied. B–H hysteresis loops of silicon steel sheet and soft magnetic composite are measured by magnetizing and measuring equipment to validate iron core per unit mass. The three-dimensional FEM is used for analyzing eddy-current loss in PMs considering radial segmentation. Finally, an AFPMSM prototype is manufactured adopting YASA topology and segmented PM. Load experiments show that solid–liquid coupling computational fluid dynamics model can precisely predict temperature distribution of AFPMSM. Improved cooling jacket is beneficial to afford large current load.

Contact-Stress-Based Stress Recovery Methods for Discontinuous Deformation Analysis

Discontinuous deformation analysis (DDA) has been widely applied for the simulation of block systems that have many discontinuous surfaces. The penalty method is utilized to ensure that there are no penetrations between blocks. A linear polynomial function for displacement leads to a constant stress for a block, which cannot precisely describe the stress field within the block. Therefore, a high-order polynomial displacement function and a fine mesh are always used to improve the precision of the stress field. However, these means are not practical for simulating block systems that have many contacts. In this paper, the contact-stress-based stress recovery methods are proposed for DDA. High-precision solutions for the contact stresses on the boundaries of the blocks are utilized. The first-order Gaussian point of a block is the block’s centroid, where the constant stress obtained via DDA is of higher precision. The high-precision solutions for the stresses are utilized in the least squares method to recover a single block’s inner stress field. The proposed methods enhance the resolution of the stress field inside a single block without increasing the computational effort in the main iterative process for displacement in DDA. Numerical examples are simulated using both the finite element method (FEM) with a fine mesh and the proposed DDA program. The recovered DDA results can accurately describe the distribution of the stresses in a single block and, in some areas, have the same precision as the FEM results. Moreover, the precision of the proposed methods improves as the gradient of the contact stress on the boundary decreases.

A novel 3D re-entrant unit cell structure with negative Poisson’s ratio and tunable stiffness

:In this paper, a novel three-dimensional (3D) unit cell structure with butterfly-like perforations was designed, and negative Poisson’s ratio and tunable stiffness were achieved in such a geometry. The Poisson’s ratio and strain-stress relationship of structures with different geometric parameters were determined using the finite element method (FEM). Samples with identical geometric variables to those of finite element models were fabricated via 3D printing technique, and their Poisson’s ratios and stress–strain relationships were experimentally determined and compared with the FEM results. Results showed that the proposed 3D cellular structures exhibit negative Poisson’s ratios, and a minimal value of −0.7091 could be reached. The stress–strain curve of each structure exhibited three distinct stages (elastic response, rib buckling and self-contact), with different elastic moduli being observed at each stage, and demonstrated a tunable range of the compressive stiffness ratio between stages varying from 0.1866 to 1.4006(tunable stiffness), as determined by FEM analysis. Good agreement was found between the experimental results and FEM predictions. The design concept can be implemented and optimized for specific applications via geometric parameters manipulation.

Experimental and Numerical Study on Methods of Testing Withdrawal Resistance of Mortise-and-Tenon Joint for Wood Products

Withdrawal resistance of the mortise-and-tenon (M&T) joint is an important indicator to evaluate the strength of the M&T joint. Generally, the T-shaped specimen is usually used to measure withdrawal resistance using tensile methods, but there has not been testing standard until now. In this study, the methods of measuring withdrawal resistance of the M&T joint were investigated systematically. A new method used to determine the withdrawal resistance of M&T joint was proposed to be named as the compressive method. In addition, withdrawal resistances of M&T joint determined using tensile and compressive methods were compared based on experiments and the finite element method (FEM). The experimental results showed that the effects of the testing method and glue on withdrawal resistance of M&T joint were statistically significant, specifically, the withdrawal resistance measured using tensile method was higher than the one determined by the compressive method. Meanwhile, the results of FEM also confirmed the experimental results in a visible way. The results of FEM indicated that the withdrawal resistance of the M&T joint was influenced by tenon member length; specifically, the withdrawal resistance of the M&T determined by tensile method increased with the increasing of tenon member length. In summary, the results of the study make sense in the measurement of withdrawal resistance of the M&T joint in practice, and in f theory, the study will contribute to instructing the design of furniture structures.

Local and global response of sandwich beams made of GFRP facings and PET foam core in three point bending test

In the paper behaviour of laminated sandwich beams (FRP face sheet – PET foam core – FRP face sheet) subjected to three point bending is studied. The paper aim is to find practical descriptions enabling effective and accurate estimation of the elastic response, damage and failure of the beams, basing on experiments and static calculations. Therefore a number of tests are described, that were done on laminated coupons and foam specimens in order to choose appropriate material models and find their constants. Experimental results of three-point bending tests of sandwich beams with three types of PET cores are analysed to evaluate the chosen material laws. The beam responses are predicted in numerical static simulations. The equations of problem are solved by means of finite element method (FEM). In the end the experimental and FEM results are compared. They are similar in terms of both their quantity and quality.

Deep neural network-based cost function for metal cutting data assimilation

Metal cutting is a complex process in machining that is typically not easily modeled via the finite element method (FEM) due to insufficient models or uncertain conditions. To improve FEM analysis of such a complex process, it is desirable to estimate the model parameters and uncertain conditions based on measurements of actual machining processes, which could be realized by data assimilation. However, the application of data assimilation to complex processes such as metal cutting is not straightforward because a comparison of the actual process and the corresponding FEM images is not trivial. To overcome this issue, we consider an extension of the cost function based on the object detection and classification capabilities of deep learning by evaluating the similarity between the FEM results and the images acquired during the actual machining process. The overall procedure is demonstrated by investigating a cutting chip in a turning process, whose shape depends on the workpiece material, cutting conditions, and the cutting tool. We first trained a deep neural network using chip images acquired from a turning experiment. This resulted in 85.5% detection and classification accuracy for testing data obtained from the same experiment. The trained network is then used to detect the images generated based on FEM. It was confirmed that the confidence score calculated using the trained deep neural network can be used to quantify the difference of the cutting chip shape generated by FEM. This preliminary study revealed that a realistic cutting chip shape can be generated by estimating the work-hardening exponent and the static friction coefficient in FEM based on images obtained during the turning process. This confirms that a deep learning-based cost function can be used to achieve image-based data assimilation.

Theoretical and numerical studies on the fracture properties of pre-cracked single-layer graphene

Based on the theories of solid state physics and quantum fracture mechanics, a theoretical model is proposed to investigate the fracture properties of pre-cracked single-layer graphene, and the analytical expressions of failure strength and fracture toughness of pre-cracked graphene are derived. Simultaneously, the failure strength of pre-cracked graphene is calculated by finite element method (FEM) based on molecular structure mechanics. The results of FEM are in good agreement with the theoretical counterparts. Via the theoretical analyses and numerical calculations, the effects of crack length, crack tip radius and domain size of graphene on the failure strength and fracture toughness of pre-cracked graphene are systematically studied. It is found that the failure strength of pre-cracked graphene gradually decreases with increasing crack length and domain size of graphene. However, as the crack tip radius increases, the failure strength gradually increases. In addition, it is also found that the crack length and domain size of graphene have little impact on the fracture toughness of graphene. The fracture toughness is significantly affected by crack tip radius.

Effects of the Size, the Number, and the Spatial Arrangement of Reactive Patches on a Sphere on Diffusion-limited Reaction Kinetics: A Comprehensive Study.

We investigate how the size, the number, and the spatial arrangement of identical nonoverlapping reactive patches on a sphere influence the overall reaction kinetics of bimolecular diffusion-limited (or diffusion-controlled) reactions that occur between the patches and the reactants diffusing around the sphere. First, in the arrangement of two patches, it is known that the overall rate constant increases as the two patches become more separated from each other but decreases when they become closer to each other. In this work, we further study the dependence of the patch arrangement on the kinetics with three and four patches using the finite element method (FEM). In addition to the patch arrangement, the kinetics is also dependent on the number and size of the patches. Therefore, we study such dependences by calculating the overall rate constants using the FEM for various cases, especially for large-sized patches, and this study is complementary to the kinetic studies that were performed by Brownian dynamics (BD) simulation methods for small-sized patches. The numerical FEM and BD simulation results are compared with the results from various kinetic theories to evaluate the accuracies of the theories. Remarkably, this comparison indicates that our theory, which was recently developed based on the curvature-dependent kinetic theory, shows good agreement with the FEM and BD numerical results. From this validation, we use our theory to further study the variation of the overall rate constant when the patches are arbitrarily arranged on a sphere. Our theory also confirms that to maximize the overall rate constant, we need to break large-sized patches into smaller-sized patches and arrange them to be maximally separated to reduce their competition.

Coupling of peridynamics with finite elements for brittle crack propagation problems

In this work, a new coupling model of finite element method (FEM) and ordinary state-based peridynamics (OSBPD) is proposed to accurately predict brittle fracture under quasi-static and dynamic loading. PD grids are directly coupled with FEM meshes without an overlapped zone. The transferred forces between PD grids and FEM meshes are reciprocal and balanced inherently, which avoids the complexity of the transitional zone-based coupling models and the non-equilibrium phenomenon of the structural force reported in the sharing nodes-based coupling model. More importantly, the proposed coupling model is free of significant influence of ghost forces and significant wave reflection at the coupling interface. Also, the surface effect of PD can be approximately removed. The accuracy of the proposed coupling model is verified through comparing with the FEM results and pure OSBPD results.

Effectiveness factors for a partially wetted catalyst based on the rivulet flow model

Partial wetting is a common phenomenon in a trickle bed reactor, which causes nonuniform mass transfer flux at the external surface of the catalyst. Previous work on effectiveness factor for a partially wetted catalyst are mainly based on the assumption that the spherical catalyst is wetted by a liquid film. In fact, it is only true when the liquid-solid contact angle is very small. In most situations, rivulet flow prevails. The purpose of the article is to calculate effectiveness factors for both gas-limited and liquid-limited reactions under the two wetting modes by using finite element method (FEM). The effects of wetting efficiency, Biot number, and Thiele modulus on effectiveness factors are investigated. On the basis of the FEM results, the intrinsic reason for the variation of effectiveness factors with respect to wetting efficiency is revealed, and good agreements are observed between this work and the conventional models.

Numerical Investigation on Plastic Hinge Length of Ultra-high Performance Concrete Column under Cyclic Load

ABSTRACT The unique features of ultra-high performance concrete (UHPC) in terms of damage tolerance, energy absorption, and deformability make this material suitable for applications in piers or columns of structures. However, few studies were available in literature regarding seismic test under cyclic load to investigate the plastic hinges of UHPC columns. As the cost of testing is relatively high, this study focuses on determining the plastic hinge lengths of UHPC columns under cyclic load based on numerical analysis. Analysis is conducted using finite element method (FEM) with the software OpenSees, and calibrated by test results. Parametric study is performed to investigate the effect of horizontal loading angle, axial force ratio, reinforcement diameter, yield strength of reinforcement, and length of the column on the plastic hinge length. The applicability of the empirical models of reinforced concrete (RC) columns for UHPC columns is discussed, and a multivariate regression expression for the equivalent plastic hinge length of a UHPC column is proposed. The results indicate that the length of the plastic zone decreases with the increase in axial load ratio, and monotonously increases with the increase in the length of the column. The trend of initial increase followed by a decrease in the length of plastic zone is observed with the increase in horizontal loading angle, reinforcement diameter, and yield strength of reinforcement. The empirical models are found to underestimate the plastic deformation of UHPC columns. The proposed expression for equivalent plastic hinge length has a reasonable agreement with FEM results.

Investigation of the time elapsed effect on residual stress measurement in a composite plate by DIC method

In composite plates, there are generally amounts of residual stresses that can have adverse effects in final parts. So, it is very important to know about the residual stress's type, location and amounts in composite plates. The measurement methods of the residual stress are commonly indirect and the displacement and strain is calculated at first. Two-dimensional digital image correlation (2D DIC) is a practical and effective tool for quantitative in-plane deformation measurement of a planar object surface and now widely accepted and commonly used in the field of experimental mechanics. In the hole drilling method, the residual stress is measured immediately just after drilling and the other researchers have paid less attention to the amount and pattern of changes in released stress around the hole after drilling at different times. It can be stated that the novelty of this research may identify the optimal measurement time after the drilling and the holes with different diameters is considered and the displacement and strain fields are measured at different times. So in this research, the residual stress measurement of a composite plate in the time elapsed is discussed. Also, the effects of hole's diameter and elapsed time after drilling in amount of released residual stresses are investigated by 2D DIC method. The point-wise local least-squares fitting technique (PLS) is used for strain estimation from displacement fields. The residual stress is calculated by the estimated strain, determination of calibration constants in orthotropic materials and considering the properties of composite plate that has already been calculated. The finite element method (FEM) is used for determination of calibration constants and the correction factor in FEM is obtained by comparing of the FEM and experimental tensile test results.