Static Finite Element Method Research Articles

Accurate Modeling and Control System Simulation of Bearingless Brushless DC Motor

Background: Precise modeling and control system design are the basis of highperformance control of dual-winding bearingless brushless DC motors (BL-BLDCM), and the existing research is relatively few. Objective: This paper takes 12-slot/tooth 4-pole BL-BLDCM as the research object, establishes a set of a detailed mathematical model, and designs the control system of BL-BLDCM. Methods: Firstly, the structure of BL-BLDCM and the radial suspension force generation principle were introduced. Secondly, a set of an accurate mathematical model of BL-BLDCM was established which was finally verified by static and dynamic finite element method (FEM), the motor body model and control system were built by Matlab/Simulink software, and the simulation analysis of control performance was completed. Results: The established mathematical model is correct. The BL-BLDCM can generate stable electromagnetic torque and radial magnetic suspension force, and the control system has strong ability of resisting load torque disturbance and radial force load disturbance. Conclusion: It has certain reference significance for the accurate modeling and control system design of later BL-BLDCM.

Development of Calculation Technique for FEM Thermal Simulation Using Virtual Fluid Elements

In recent years, CAE (Computer-aided engineering) using FEM (Finite element method) simulations were generally used in the design field. FEM simulations were classified as static implicit and explicit dynamics methods. Particularly FEM simulations using the static implicit method were very generally and usefully used in the industrial world. The static implicit method FEM consists of static, buckling, thermal, vibration analyses, and so on. This FEM thermal analysis can't calculate the phenomena of heat transfer and internal forced cooling in some enclosures of a machine tool. On the other hand, when the temperature distributions in a structure such as that are calculated, FVM fluid simulation was used for that. However, this simulation can't exactly calculate a complex structure in a machine tool, needs very long calculation times and the calculation accuracy is very poor. Therefore, in this research, the calculation technique regarding FEM thermal simulation using 4 virtual fluid elements was developed and evaluated for the phenomena of heat build-up and internal forced cooling in some enclosures of a machine tool. The algorithms and the calculation models regarding 4 virtual fluid elements were developed, then the proposed method was evaluated in the experiment. It is concluded from the results that; (1) the 4 virtual fluid elements were developed for FEM thermal simulation instead of FVM fluid simulation, (2) FEM thermal simulation with the developed 4 virtual fluid elements has high calculation accuracy and a short calculation time, (3) the proposed method was very effective in the design.

In-wheel, outer rotor, permanent magnet synchronous motor design with improved torque density for electric vehicle applications

In electric vehicle applications, the torque density of electric motor plays an important role in improving the performance of the vehicle. The main objective of this paper is to investigate a possible method for improving the torque density of a permanent magnet synchronous motor used in electric vehicles. At the same time, other machine specifications were taken into account and kept within the acceptable level. This was achieved by incorporating performance enhancement strategies such as investigating ofhigh-efficient winding topology for the motor’s stator to give the highest winding factor and optimizing the machine dimensions to achieve the best performance. MagNet 7.4.1 software package with static and transient finite element method solver was used for implementing the proposed design. The results showed a significant improvement in the torque density with keeping the overall machine performance.

Pore-scale modelling of elastic properties in hydrate-bearing sediments using 4-D synchrotron radiation imaging

Gas hydrate contains abundant methane gas, which is considered to be a promising energy resource to mitigate the influence of climate change in the future. Understanding the effect of fluids-solid-hydrate spatial distribution on elastic properties of hydrate-bearing sediments benefits the well-log interpretation. We constructed 4-D hydrate-bearing models covering a wide hydrate saturation range based on high-resolution digital images obtained by Synchrotron Radiation X-Rays Computed Tomography (SRXCT). We analysed the elastic moduli and elastic wave velocities of these models by the static Finite Element Method (FEM). The results demonstrated that the dominant hydrate morphology transits from pore-filling to load-bearing when hydrate saturation increases. At low hydrate saturations, the hydrate formed around some gas bubbles blocks local pore space. Therefore a great enhancement in compressional wave velocity was observed at low hydrate saturations. While the shear wave velocity was less affected due to the presence of thin water films. Based on the simulated results, an empirical model was developed to compute the compressional and shear wave velocities considering the free gas phase. The comparison with some experimental measurements validated the applicability of the model.

Ancient restorations: computer-based structural approach for the identification and reinterpretation of the Medracen’s constructive sequence

This paper addresses the importance of a structural approach for identifying and interpreting building chronology, as well as for the establishment of historical stratigraphy. Through structural analyses, carried out on the oldest extant royal mausoleum in North Africa, the Medracen (4th-3rd century BC), located in eastern Algeria, it has been possible to identify building sequences and structural characteristics; a reinterpretation of its constructive sequence within a specific historical context was also suggested. A static linear Finite Element Method (FEM) analysis was performed on a simplified 3D model conceived with solid elements to assess the structural behaviour of the structure under the effect of its self-weight and to identify, consequently, its construction sequence. The equilibrium approach was effective in identifying the structure’s geometry. Results show that Medracen’s ancient restoration was a strengthening intervention strategy and had a symbolic aim related to the function of the funerary building. Restoration works, consisting of repairing specific parts of the building and adding an external cladding, as a whole architectural entity, contributed to reducing the effect of tensile stress, therefore, stabilizing the inner core. Besides, this same action was a means for the Numidian elite to transform an ancient monumental burial (sepulchrum) into a monument (monumentum) with cultural significance likely to convey socio-political messages relating to power and sovereignty. Therefore, we can speak of an “evolutionary restoration” that reflects the ambitions of the Numidian elite to become part of the Mediterranean orbit.

A method to directly estimate the dynamic failure peak ground acceleration of a single-layer reticulated dome

The present paper gives a method to directly estimate the dynamic failure peak ground acceleration of single-layer reticulated domes according to the Chinese earthquake response spectrum. A method given by the Japanese code for seismic design of buildings is presented first, which can be used to estimate the dynamic failure peak ground acceleration of a single-layer dome. However, the existing method cannot be used to calculate the dynamic failure load for a structure in China because of the different codes and methods used for the seismic design of single-layer reticulated domes. Meanwhile, the existing method needs to repeat the finite element method (FEM) elasto-plastic static analysis and FEM nonlinear time–history response analysis to calculate the FEM plasticity adjustment factor and the dynamic ductility index of different domes. Secondly, on this basis, 28 Kiewitt-8 (K8) single-layer reticulated domes with different key structural design parameters are designed using the relevant Chinese specifications, they will be used for the parameter revision of the peak ground acceleration and the dome’s design spectral acceleration, the fitting of the formula to calculate the FEM plasticity adjustment factor, and the statistical analysis of the dynamic ductility index respectively. Thirdly, the peak ground acceleration and the dome’s design spectral acceleration in the existing method are revised according to the Chinese code for the seismic design of buildings. Fourthly, the FEM elasto-plastic static analysis is carried out to get a fitting formula to directly calculate the FEM plasticity adjustment factor with the static safety factor K of the dome. The calculation results of this formula are smaller than that of FEM analysis, which can ensure the safety of the dome. Fifthly, the failure criteria with clear physical meaning are selected from the existing dynamic failure criteria to predict the dynamic failure load of the domes. Then, a FEM nonlinear time–history response analysis is carried out using the FE package ANSYS for the 28 typical domes subjected to 30 different ground motions, and the dynamic failure loads are calculated by the selected failure criteria. It is found that the dynamic failure loads correspond to two different failure modes, one is the local failure caused by the sudden increase of the displacement of the dome’s local node, the other is the global failure caused by the sudden increase of the overall energy of the single-layer reticulated dome. After this, the lower bound failure accelerations with a certain guaranteed rate of those dynamic failure loads are determined using a lognormal distribution. The dynamic ductility index is then revised by the lower bound failure accelerations and the statistical analysis of the dynamic ductility index of the 28 typical domes is conducted to get a lower bound value for it. Finally, a method directly estimating the dynamic failure load of a dome is constructed and verified. The research will provide a new method under a certain degree of reliability to directly estimate the dynamic failure loads of single-layer reticulated shells in the earthquake area of China and contribute to the structural design with more overall confidence.

Rational Choice of Reinforcement of Reinforced Concrete Frame Corners Subjected to Opening Bending Moment

This paper discusses a choice of the most rational reinforcement details for frame corners subjected to opening bending moment. Frame corners formed from elements of both the same and different cross section heights are considered. The case of corners formed of elements of different cross section is not considered in Eurocode 2 and is very rarely described in handbooks. Several reinforcement details with both the same and different cross section heights are presented. The authors introduce a new reinforcement detail for the different cross section heights. The considered details are comprised of the primary reinforcement in the form of straight bars and loops and the additional reinforcement in the form of diagonal bars or stirrups or a combination of both diagonal stirrups and bars. Two methods of static analysis, strut-and-tie method (S&T) and finite element method (FEM), are used in the research. FEM calculations are performed with Abaqus software using the Concrete Damaged Plasticity model (CDP) for concrete and the classical metal plasticity model for reinforcing steel. The crucial CDP parameters, relaxation time and dilatation angle, were calibrated in numerical tests in Abaqus. The analysis of results from the S&T and FE methods allowed for the determination of the most rational reinforcement details.

THE DYNAMIC FINITE ELEMENT MODEL OF NON-PNEUMATIC TIRE UNDER COMFORTABLE RIDING EVALUATION

The Non-Pneumatic Tire (NPT) has design potential to have desired mechanical characteristic upon usage requirements. The NPT also has no restriction on inflation pressure, maintenance, and less damage possibilities due to flat while driving. The optimum design of NPT to have required load carrying capacity and vertical stiffness can be easily achieved by mean of static Finite Element Method (FEM) with appropriated material models. However the models to predict dynamic response such as tire structure to road pavement interaction, shock absorption and ride comfort are still needed. This paper aims to develop FEM to study dynamic characteristics and evaluate the ride comfort property of the NPT. The FEM of NPT, which composed of Tread band and Spokes, was model using 3D hexagonal and 2D Quadrilateral elements respectively. The rebar elements and tying equation were used to model steel belt layers of the NPT. The visco-hyperelastic constitutive model was used to model the mechanical behavior which depends on time of the NPT’s components. The FEM of NPT was then assigned to traverse across cleats with different heights to study the effect of obstacle on tire-road interaction and dynamic response of NPT. The impact force history and deformation behavior of NPT at any given time was analyzed. The results were compared to discuss the validity of the model to capture important dynamic characteristic that considered useful in designing of NPT to have ride quality challenging the commonly used pneumatic tire.

Meso-scale tool breakage prediction based on finite element stress analysis for shoulder milling of hardened steel

In this article, finite element method (FEM) based tool stress analysis and breakage prediction are advanced for meso-scale shoulder milling of hardened stainless steel. Rather than using simplified line loads or uniformly distributed loads, the tool stress analyses are conducted with realistic chip load predicted by the previously developed 3D coupled Eulerian-Lagrangian (CEL) FEM model. A reliable distribution of contact forces obtained with a continuous tool-chip contact region is transferred to a static FEM model for tool stress analysis and breakage prediction at each angular location of an end mill. The simulation results are validated through dedicated cutting experiments with short cutting distances under various cutting conditions. The developed FEM models are found to be capable of making accurate predictions of tool breakage. Some key features of feed rate-related tool breakage are identified. It is found that the maximum tensile stress in the tool does not coincide with the maximum resultant cutting force in terms of cutter rotation. The tensile stress in the tool is not positively correlated with the resultant cutting force. In down milling, the maximum tensile stress is found to occur just after the tool starts to contact with the workpiece. It is also observed that the tensile stresses of the tool are much smaller in up milling configuration compared to down milling processes.

Static and Dynamic FEM Simulation of Packaging Tray Cup Pad for Korean Pears

Among the many packaging materials used in cushion packaging, there is a lack of optimum design for the tray cup pad used in fruit packaging for export and domestic distribution. It causes over-packaging due to excessive material input, and this could be solved by applying various parameters needed to optimize the design of the tray cup pad considering the packaging material and the quantity of fruits in the box. In the case of a tray cup for fruits, the economic efficiency of material and thickness should be considered. Therefore, it is possible to design a tray cup pad depending on the packaging material used by applying appropriate design parameters. The static and dynamic characteristics of the materials used for packaging of pears were analyzed by using the FEM (finite element Method) simulation technique to derive the optimal design parameters. And by applying the appropriate design parameters considering the quantity of fruit and distribution environment, it is possible to design an appropriate fruit tray cup pad. In this study, as a result of simulating the contact stresses between the fruit and the tray cup for the PP, PE, and PS materials used in the fruit tray cup, the material with the lowest contact stress was PP and the value was found to be 398 Pa. The contact displacement between fruit and tray cup using this material was about 0.0463 mm, which was the lowest value compared with other materials. Also the resonance frequency band of tray cup made of PP material was below 36.81 Hz, and the strain energy was below 12.20 J. The resonant frequency band of the pear is more than 80 Hz and it could be applied to all the tray cup materials as compared with the resonance band of 38.81 Hz or less which is the resonance band of all tray cup pads for packaging. Finally, PP is the most suitable material for the tray cup pad.

Fracture prediction on patient-specific tibia model with Osteogenesis Imperfecta under various loading direction

This study aims to predict the fracture of bone with osteogenesis imperfecta (OI) by considering the homogenization properties of real patient. A Type-III of osteotomy in OI femur was used as bone specimen. Nine representative volume element (RVE) models were developed based on μCT-images of bone specimen. Homogenized properties particularly the Young’s moduli of the RVEs was obtained based on homogenization theory in Voxelcon software. The obtained homogenized properties were then assigned to the OI patient-specific model that was developed from CT-images of real patient. The fracture of OI bone was predicted based on linear static analysis and finite element method under loadings of activity daily living (ADL). The results found that the fracture might be happen to the patient under jumping load case, whereas the subject is expected to be safe under standing still and walking load case.

Theoretical and Finite Element Analysis of Static Friction Between Multi-Scale Rough Surfaces

The current work considers the multi-scale nature of roughness in a new model that predicts the static friction coefficient. This work is based upon a previous rough surface contact model, which used stacked elastic–plastic 3-D sinusoids to model the asperities at multiple scales of roughness. A deterministic model of a three-dimensional deformable rough surface pressed against a rigid flat surface is also carried out using the finite element method (FEM). The accuracy of the deterministic FEM model is also considered. At the beginning of contact, which is surface-point contact, the asperities or peaks are isolated, sharp, and the contact areas consist of an inadequate number of elements and sources of error. In this range of contact, the results are not presented as real or accurate. As the normal load increases, the number of the contact elements become larger, and thus, the results become more accurate. That is, the deterministic FEM results are most accurate at high loads. Spectral interpolation is used to smooth the geometry in between the original measured nodes. The effects of normal load and plasticity index on static friction are then analyzed. The results predicted by the theoretical model are also compared to other existing rough surface friction contact models and the FEM results. They are in a good qualitative agreement, especially for higher loads and higher plasticity indices. The FEM model also has significant error, but it is more accurate at higher loads where the proposed multi-scale static friction model and FEM model are in better agreement.

ABOUT METHODS OF SEISMIC ANALYSIS OF UNDERGROUND STRUCTURES

As is known, underground facilities are an integral part of the infrastructure of modern society. These objects have some specific characteristics such as complex construction, high cost, long life cycle, etc. Once it is destroyed, the direct and indirect losses are more seriousness than the general structure in the ground. Under-ground facilities built in areas subject to earthquake activity must withstand both seismic and static loading. Therefore, it is very important to carry on the seismic design of the underground structure in a safe and economi-cal way. The distinctive paper presents a summary of the current state of seismic analysis for underground struc-tures. Classification and brief overview of methods of seismic analysis of underground structures (force-based methods, displacement-based methods, numerical methods of seismic analysis of coupled system “soil – under-ground structure”) are presented, problems of soil-structure interaction are under consideration as well. So-called static finite element method with substructure technique for seismic analysis of underground structures is de-scribed.

About Contemporary Seismic Analysis of Underground Structures

This paper is devoted to actual problems of seismic analysis of underground structures. Brief classification and overview of corresponding methods of analysis (force-based methods, displacement-based methods, numerical methods of seismic analysis of coupled system “soil – underground structure” and approaches to problems of soil-structure interaction) is presented. Special static finite element method with substructure technique for seismic analysis of underground structures is described. Dynamic soil-structure interaction system can be decomposed into three sub-structures: structure, near-field and far-field soil. The first stage of static finite element method is solving the free field shear stress, acceleration, velocity and displacement, when the moment that the relative displacement of the soil that the underground structure located in reaches the maximum. The second stage is computing of internal forces and parameters of boundary conditions. The third stage is construction of the static finite element model and imposing the loads and constrains computed at the second stage and then making a static analysis.

EFESTS: Educational finite element software for truss structure – Part 3: Geometrically nonlinear static analysis

This article covers the modeling, formulation, solution, and software development of the geometrically nonlinear static finite element method of truss structure. Firstly, we summarize the total Lagrange bar elment formulation, which includes the tangent stiffness matrix and the internal force vector. Secondly, static class diagrams and dynamic sequence diagrams assist students in designing software architecture. Thirdly, the analytical example of the 2-bar truss structure and the numerical example of the 10-bar truss structure are presented to promote students’ understanding of geometrically nonlinear finite element theory and application. Finally, the developed software is free for educational research and can be downloaded from the website: http://mach.jlu.edu.cn/hb_images/xygk/xssz_sz_js.php?id=395 .

Design and validation of a large-format transition edge sensor array magnetic shielding system for space application.

The paper describes the development and the experimental validation of a cryogenic magnetic shielding system for transition edge sensor based space detector arrays. The system consists of an outer mu-metal shield and an inner superconducting niobium shield. First, a basic comparison is made between thin-walled mu-metal and superconducting shields, giving an off-axis expression for the field inside a cup-shaped superconductor as a function of the transverse external field. Starting from these preliminary analytical considerations, the design of an adequate and realistic shielding configuration for future space flight applications (either X-IFU [D. Barret et al., e-print arXiv:1308.6784 [astro-ph.IM] (2013)] or SAFARI [B. Jackson et al., IEEE Trans. Terahertz Sci. Technol. 2, 12 (2012)]) is described in more detail. The numerical design and verification tools (static and dynamic finite element method (FEM) models) are discussed together with their required input, i.e., the magnetic-field dependent permeability data. Next, the actual manufacturing of the shields is described, including a method to create a superconducting joint between the two superconducting shield elements that avoid flux penetration through the seam. The final part of the paper presents the experimental verification of the model predictions and the validation of the shield's performance. The shields were cooled through the superconducting transition temperature of niobium in zero applied magnetic field (<10 nT) or in a DC field with magnitude ∼100 μT, applied either along the system's symmetry axis or perpendicular to it. After cool-down, DC trapped flux profiles were measured along the shield axis with a flux-gate magnetometer and the attenuation of externally applied AC fields (100 μT, 0.1 Hz, both axial and transverse) was verified along this axis with superconducting quantum interference device magnetometers. The system's measured on-axis shielding factor is greater than 106, well exceeding the requirement of the envisaged missions. Following field-cooling in an axial field of 85 μT, the residual internal DC field normal to the detector plane is less than 1 μT. The trapped field patterns are compared to the predictions of the dynamic FEM model, which describes them well in the region where the internal field exceeds 6 μT.

A quasi-static FEM for estimating gear load capacity

Measurement of time-varying load capacity of gears is a vital process prior to manufacturing. There are two ways to evaluate the strength of gears, the analytical method proposed in AGMA and ISO standards and the finite element method (FEM). However, owing to the complex geometries and the use of empirical values, analytical model is not precise to perform the exact calculation. The current dynamic FEM and static FEM also have some disadvantages may cause the analysis of time-vary load capacity difficult. Therefore, the first aim of this study is to develop a new quasi-static FEM based on ANSYS Workbench to conduct the analysis of time-varying load capacity of gear system. The second aim is to compare results of the traditional method based on AGMA equations and quasi-static FEM. The effects of tip relief are also analysed using this new method.

Rotor Shape Investigation and Optimization of Double Stator Switched Reluctance Machine

This paper presents an optimal design for the rotor of a double stator switched reluctance machine. The effect of the rotor shape on the torque profile is analyzed first. Due to the nonlinearity of magnetic core and complex geometry, an iterative approach is developed to automatically shape the rotor geometry using static finite element method. The rotor of a 12/8/12 prototype is optimized. Simulation results validate the effectiveness of the optimal design.

Stress analysis of the tibial plateau according to the difference of blade path entry in opening wedge high tibial osteotomy

High tibial osteotomy (HTO) has been used to successfully treat patients with genu varus deformities that can improve mechanical function and condition in the knee joint. Clinical studies have reported that bow legs often occur with a concentrated load on the varus of the tibia. This study aimed to analyze and verify the clinical test data result by utilizing the three-dimensional (3D) static finite element method (FEM). The 3D model of lower extremities, which include the femur, tibia, meniscus, and knee articular cartilage, was created using the images from a computer tomography scan and magnetic resonance imaging. In this report, we compared changes in stress distribution and force reaction on the tibial plateau because of critical problems caused by unexpected changes in the tibial posterior-slope angle because of HTO. The results showed that the 5° wedge-angle virtual opening wedge HTO without and with the posterior-slope angle shows has a load concentration of approximately 60% and 45% in the medial region, respectively.

Comparisons of Linear and Nonlinear FEA of Adhesively Bonded Beams

The effect of boundary conditions on the stress distributions in single-lap adhesively bonded cantilevered beams has been investigated using the three-dimensional linear static and non-linear quasi-static finite element method. The displacement obtained from the linear static and the non-linear quasi-static analyses are compared under the same deformation scale factor for three typical boundary conditions. The analysis results indicate that there are significant differences between the linear static and non-linear quasi-static analyses only if there are significant bending effect on the bonded section. The bigger the bending effect on the bonded section, the bigger the difference between the linear static and non-linear quasi-static analyses.