Enhanced Field Reconstruction Method for the Efficient Analysis of Permanent Magnet Synchronous Machines

The handling and control of towed cable and body systems onboard surface ships and submarines presents a significant technical challenge to design engineers in the defense and ocean industries. The current approaches rely heavily on the empirical methods and the time-consuming and costly prototype testing. Computer simulation provides a cost effective way to reduce the high risks associated with the towed cable/body system. However, the current dynamic analysis of towed cables is mostly done by the finite difference (FD) method in stead of the finite element (FE) method that is widely used in almost all engineering fields. This paper presents an alternative FE method to simulate the dynamics of towed cable and body system, in which the large rigid body motion is coupled with small elastic deformation. The newly derived FE method is formulated in terms of element nodal positions, which is different from the existing FE methods that use displacements. The alternative FE method solves for the cable position directly in order to eliminate accumulated numerical errors arising from existing FE methods that solve for displacements first in order to obtain the cable position over very long period of time. The alternative FE formulation is implemented and applied to real applications to demonstrate its robustness by comparing simulation results with the experimental and sea trial data.

This study proposes a new configuration for line start permanent magnet (PM) motors with low consumption of PM material, providing improved performance. The configuration is developed by analysing PM flux density distribution in the machine airgap and focusing on the d ‐axis armature reaction flux path and also different magnetisation types in the PM poles. It features double flux barriers for each rotor pole to facilitate near sinusoidal flux density distribution. Main characteristics of a motor with the proposed configuration are analysed by finite element method (FEM) and compared with the characteristics of a motor with the conventional configuration. Finally, the motor is built and tested. The FEM and experimental results verify the advantages of the proposed configuration. The results show that the required PM material reduces by one‐third, while desirable performance is provided. The machine is capable of working with delta connection causing negligible circulating current and low torque ripples.

This paper presents a surface contact static stress of a spur gear system combined with dynamic characteristic using transient Finite Element Method (FEM). Traditionally, the static stress analysis is done separately with dynamic properties due to limitation of complex equation and avoiding of error occurred. However, in this paper, static stress information is combined with the dynamic mechanism due to the time consuming during the design and analysis stage. A transient FEM analysis is carried out to formulate and solve large systems of algebraic equations in order to obtain a relationship between the contact parameter and the kinematics function. The methodology of the research is started with static stress analysis on tooth surface contact of a pair of the spur gear. Finite element modeling is run by choosing a certain static condition. The loading conditions are applied suitable with the gear mechanism. Degree of freedom controlled is based on the transmission system. The process is repeated until diagnosing work is satisfied. The result of the surface contact stress is visualized at each condition. Modeling of spur gear system is continued by combining stress analysis with dynamic characteristic via transient finite element method. Analysis of gear mechanism is obtained by investigate the stress distribution on real time application. Time range is set at the beginning of the analysis. Duration of the analysis is depended on a time frame chosen. By the transient FEM analysis, the stress occur at each step of the work cycle is performed. Results of the kinematics functions are derived and qualitative kinematics variations due to contact changes in time-step domain is identified. The simulation results from static and transient FEM are compared due to the validating procedure. The finite element results are in good agreement compared with the theory calculation.

Real-world groundwater modeling deals with heterogeneous and anisotropic aquifer systems. Numerical models, particularly the finite difference and finite element methods, are extensively used for modeling such a complex aquifer system. The finite difference method is an age-old straightforward approach, whereas the finite element method is more idealistic, relatively new, and has emerged as a popular approach. The unique advantages with the finite element method are (i) an irregular-shaped domain can be discretized into elements with a matching boundary, (ii) a node can be connected with the neighboring nodes in any direction. Thus, the finite element analysis allows water/solute to flow more freely toward the surrounding nodes along nodal links. On the other hand, the mathematical formulation of the finite element technique follows a set of rules step by step. Conventionally, this idealistic approach uses shape functions and integration techniques to develop element matrices, which, in turn, are assembled to form the global matrix. This conventional global matrix was found to be inconsistent with the basic partial differential equation representing the mass balance in a nodal domain as a control volume. As a result, the matrix solution, particularly for nonlinear problems (e.g., vadose zone flow, density dependent flow, and so forth) becomes unstable and computationally burdensome. To overcome the limitations of the conventional finite element method for real-world groundwater modeling, a new approach, called the direct-formulation finite element (DFFE) method, has been developed. In this approach, a two-dimensional model domain is discretized into triangular elements. Element matrices are formed directly based on flow principles and material properties of elements without using shape functions and integration process. The DFFE method is robust. The global matrix is consistent, and the solution is stable and efficient. The results obtained from this approach were found in a good agreement with that obtained from analytical and other widely used models.

The scientific basis of orthodontics is physics and Newtonian mechanics applied to the tooth-periodontal ligament-bone biologic system. The mechanical response of the periodontal ligament (PDL) to forces has a significant impact on bone remodelling and tooth movement. At the early stages, orthodontists mainly evaluated the PDL mechanical properties by in vitro experiments, which guided the use of forces in the orthodontic process. With the development of computers, finite element (FE) methods were increasingly used in the study of orthodontics. The phenomena and results of PDL mechanical tests are abstracted into constitutive equations. The identified constitutive equations are then implemented in finite element software. The finite element method could be used to simulate in vitro and in vivo experiments and predict the response of PDL under various complex working conditions. A visco-hyperelastic constitutive model is proposed and implemented in finite element technique based on prior static mechanical experiments of human PDL. Some complex experimental conditions are simulated to discuss the properties of the constitutive model.

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: (1) the boundary splitting and (2) the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.

Chapter 11 - Mixed finite element–computational fluid dynamics method for nonlinear fluid–solid interactions

It is common knowledge that conventional finite element method (FEM) has intrinsic limitations in analyzing large deformation problems like high-velocity impact, explosion, etc. because of mesh distortion and tangling; while these problems can be easily avoided by the meshfree method (MM), the latter involves greater computation time. Therefore, in this article, in order to simultaneously utilize the respective advantages of the two methods, a coupled simulation method between both FEM and MM was employed to analyze the high-velocity impact on ductile metal pipe with polymer coating. The impacted area with large deformation was discretized by SPH (smoothed particle hydrodynamics) particles, a classic meshfree model, and the remaining section was modeled by FEM meshes. By this method, the interfacial shear stresses between the coating and the substrate and the residual stresses beneath the contact points were studied, which would have referenced values in analyzing failure modes of components with similar composite structure. Then, the results were compared with sole FEM and MM too.

In many engineering problems, the meshfree methods (MMs) have been dynamically projected and increasingly advanced in order to overwhelm some hitches in the predictable numerical methods. Over the past three decades in many different application area, MMs have found their way ranging from solid mechanics analysis, fluid problems, vibration analysis, heat transfer and optimization to numerical solutions of all kinds of (partial) differential equations. As every technique has shortcomings, the meshfree method also has drawbacks like higher computational cost and imposition of boundary condition which can be overruled by coupling it with the finite element method (FEM). In the past two decades, coupled MMs and FEM have appeared into a new session of computational methods with significant achievement. In addition, a noteworthy amount of growth has been made in addressing the major deficiencies that were present in the conventional methods and MMs at the premature phases. The objective of the present work is to provide a comprehensive review of various coupling techniques used for interface elements of MMs and FEM and general discussion on shape function formulation of FE and element free Galerkin method (EFGM). Key contribution of coupling techniques for coupled EFGM and FEM to structure mechanics application as primary concern.

On the combination of finite element and splitting-up methods in the solution of parabolic equations

The interaction between off-road tires and granular terrain has a great influence on the tractive performance of off-road vehicles. However, the finite element method or the discrete element method cannot effectively study the interaction between off-road tires and granular terrain. The three-dimensional combined finite element and discrete element method is applied to handle this problem. In this study, a calibrated finite element method–discrete element method model is established, in which the finite element model of off-road tire is validated by stiffness tests, while the discrete element model of gravel particles is validated by triaxial compression tests. The calibrated finite element method–discrete element method model can describe the structural mechanics of the off-road tire and the macroscopic mechanical properties of the gravel road. Tractive performance simulations of the off-road tire on gravel road under different slip conditions are performed with the commercial software LS-DYNA. The simulation results are basically corresponded with the soil-bin test results in terms of granular terrain deformation and tractive performance parameters versus the slip rates. Finally, the effects of tread pattern, wheel load, and tire inflation pressure on tractive performance of off-road tire on granular terrain are investigated. It indicates that the calibrated finite element method–discrete element method can be an effective tool for studying the tire–granular terrain interaction and predicting the tractive performance of off-road tire on granular terrain.

Finite element and boundary element contact stress analysis with remeshing technique

In this master's thesis work, finite element method limitations are investigated in the dynamic analysis of reinforced panels. The panel was modelled using different meshes in order to show that, depending on the element length (or the number of degree of freedom) used in the model, the model does not properly stand for the real structure. In order to assess experimentally the model, an aluminum reinforced panel was built and, through experimental methods, a modal analysis was carried out. The finite element modelling limits were tested and compared to experimental results regarding mid-frequencies. A comparison between finite element and spectral element methods was carried out for computational cost reduction purposes. Due to uncertainties of some model input parameters, a statistical variation was performed using Monte Carlo and Surface Response methods. Results have shown that, at high frequencies the finite element method is not appropriete for dynamic analysis due to high computational costs in high frequency and it is highly sensitive to small variations of the input parameters.