Contribution to the Full 3D Finite Element Modelling of a Hybrid Stepping Motor with and without Current in the Coils

The paper presents our contribution to the full 3D finite element modelling of a hybrid stepping motor using COMSOL Multiphysics software. This type of four-phase motor has a permanent magnet interposed between the two identical and coaxial half stators. The calculation of the field with or without current in the windings (respectively with or without permanent magnet) is done using a mixed formulation with strong coupling. In addition, the local high saturation of the ferromagnetic material and the radial and axial components of the magnetic flux are taken into account. The results obtained make it possible to clearly observe, as a function of the intensity of the bus current or the remanent induction, the saturation zones, the lines, the orientations and the magnetic flux densities. 3D finite element modelling provide more accurate numerical data on the magnetic field through multiphysics analysis. This analysis considers the actual operating conditions and leads to the design of an optimized machine structure, with or without current in the windings and/or permanent magnet.

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

Propagations of Rayleigh and Love waves in ZnO films/glass substrates analyzed by three-dimensional finite element method

Propagation characteristics of surface acoustic waves（SAWs） in ZnO films/glass substrates are theoretically investigated by the three-dimensional（3D） finite element method. At first, for（11ˉ20） ZnO films/glass substrates, the simulation results confirm that the Rayleigh waves along the [0001] direction and Love waves along the [1ˉ100] direction are successfully excited in the multilayered structures. Next, the crystal orientations of the ZnO films are rotated, and the influences of ZnO films with different crystal orientations on SAW characterizations, including the phase velocity, electromechanical coupling coefficient, and temperature coefficient of frequency, are investigated. The results show that at appropriate h/λ, Rayleigh wave has a maximum k^2 of 2.4% in（90°, 56.5°, 0°） ZnO film/glass substrate structure; Love wave has a maximum k^2 of 3.81% in（56°, 90°, 0°） ZnO film/glass substrate structure. Meantime, for Rayleigh wave and Love wave devices, zero temperature coefficient of frequency（TCF） can be achieved at appropriate ratio of film thickness to SAW wavelength. These results show that SAW devices with higher k^2 or lower TCF can be fabricated by flexibly selecting the crystal orientations of ZnO films on glass substrates.

STUDY ON THREE-DIMENSIONAL FINITE BODIES CONTAINING CRACKS USING THE FINITE ELEMENT METHOD OF LINES

The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.

3D numerical simulation in acoustic-elastic coupled media with staggered-grid finite-difference method

Acoustic-elastic coupled media is often encountered in most marine explorations, and accurate simulation of acoustic-elastic coupled media is of great significance. At present, the study of acoustic-elastic coupled media still assumes that the solid of the acoustic-elastic coupled media is isotropic, but this assumption is not in accordance with the actual situation. In this paper, we derive the solid media of acoustic-elastic coupled media from isotropic media to anisotropic media, and propose an acoustic-elastic coupled medium based ontransverse isotropic media with vertical symmetric axes(VTI) to improve the accuracy of forward modeling. Based on the relationship between the Thomsen parameter and the coefficient matrix of the anisotropic elastic wave equation, we transform the Thomson parameter into a velocity model with anisotropic properties. We use a staggered grid finite difference method to simulate the propagation of a wavefield in a three-dimensional acoustic-elastic coupled media. We obtain the snapshots of the wave field when the solid of the acoustic-elastic coupled media is an isotropic medium and a VTI media. When the solid of the acoustic-elastic coupled media is considered VTI media, we can observe the qP wave and qS wave that cannot be observed in the isotropic medium from the wave field snapshot. We can also find that the seismic records obtained by the method we use are more realistic. The algorithm proposed in this paper is of great significance for high-precision ocean numerical simulation.

3-D Finite-Element Numerical Simulation of Centrifugal Induction Electrosalg Casting Solidification Process

A 3-D finite-element numerical simulation model of temperature field for CIESC casting solidification process was developed with the aid of ANSYS software and a series of corresponding experiments were made. The results showed that the good agreement was obtained between the numerical simulation and the experiments. Based on the numerical simulation results, the characteristics of temperature distribution in the castings during CIESC solidification process were analyzed and summarized. According to the G/R-1/2 method and numerical simulation results, there is no any shrinkage defect in the CIESC casting and structure or casting is fine and compact.

Effect of heterogeneity on mechanical and micro-seismic behaviors of sandstone subjected to multi-level cyclic loading: A discrete element method investigation

In numerical simulation of the mechanical responses and acoustic emission(AE)characteristics of rocks under cyclic loading,the impacts of compositional heterogeneities of mineral grains have barely been considered.This will lead to a poor reproduction of rock’s behaviors in terms of stress-strain relationship and micro-seismic characteristics in numerical simulation.This work aims to analyze and reveal the impact of parameter heterogeneity on the rock’s fatigue and micro-seismic properties based on PFC3D.Two distribution patterns(uniform and Weibull distributions),are implemented to assign four critical parameters(i.e.tensile strength,cohesion,parallel bond stiffness and linear stiffness)for 32 sets of numerical schemes.The results show that the models with high heterogeneity of tensile strength and cohesion can better reproduce the stress-strain relationship as well as the patterns of cumulative AE counts and energy magnitude.The evolution of the proportion of three-level AE events in the laboratory test is consistent with the numerical results when the highly heterogeneous tensile strength and cohesion are distributed.The numerical results can provide practical guidance to the PFC-based modeling of rock heterogeneity when exposed to multi-level cyclic loading and AE monitoring.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone

The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system （LCS） is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching （FRAP） approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30-50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis （FEA） approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional （3D） linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform （FEBio） to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces （shear and drag forces） for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.

3D Finite Elements Technique for Collapse Causes of the Pylons in Egyptian Temples: A Study of the Great Pylon of Ramesseum Temple, Luxor, Egypt

This research presents damage causes of the pylons in the ancient Egyptian temples based on 3D finite elements analysis. The main purpose of the research determines the failure causes of the first pylon of the Ramessium temple, which is situated in Upper Egypt, at Luxor “Thebes” on the west bank of the Nile River. The first pylon of Ramessium temple subjected to seismic activity effects on long term, combined with several structural damage factors such as the defects resulting from the construction technique, where the builder used the poor quality of stones in foundations of the pylon, the building materials residue was used as filler for the core of the pylon walls, and it lacked vertical joints between the courses. In addition to it founded on alluvial soil that is vulnerable to contaminated water, it is still suffering damage factors and urban trespasses at the moment. All of the former factors helped the pylon to be affected by the earthquakes loads that occurred on it. The structural behavior of the pylon under self-weight and earthquakes loads were carried out by Numerical analysis to find out the loads and stresses which caused collapsing of the pylon. Results of the study indicated that the pylon subjected to a horizontal displacement due to old earthquakes force, led to collapse of the pylon. Finally, the study represents use of modern technique to study the structural behavior of the most important architectural units in ancient Egyptian temples to identify the causes of its collapse.

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.

Thre-dimensional topographic responses in MT using finite diference method

In this paper, the magnetotelluric response to 3-D earth topography was studied using the finite difference method for rectangular cells. Three numerical modeling calculations were carried out; the results indicate that the finite difference method is applicable to the magnetotelluric problem in estimating the 3-D topographic responses.

Numerical Study of the Biomechanical Behavior of a 3D Printed Polymer Esophageal Stent in the Esophagus by BP Neural Network Algorithm

Esophageal disease is a common disorder of the digestive system that can severely affect the quality of life andprognosis of patients. Esophageal stenting is an effective treatment that has been widely used in clinical practice.However, esophageal stents of different types and parameters have varying adaptability and effectiveness forpatients, and they need to be individually selected according to the patient’s specific situation. The purposeof this study was to provide a reference for clinical doctors to choose suitable esophageal stents. We used 3Dprinting technology to fabricate esophageal stents with different ratios of thermoplastic polyurethane (TPU)/(Poly-ε-caprolactone) PCL polymer, and established an artificial neural network model that could predict the radial forceof esophageal stents based on the content of TPU, PCL and print parameter. We selected three optimal ratios formechanical performance tests and evaluated the biomechanical effects of different ratios of stents on esophagealimplantation, swallowing, and stent migration processes through finite element numerical simulation and in vitrosimulation tests. The results showed that different ratios of polymer stents had different mechanical properties,affecting the effectiveness of stent expansion treatment and the possibility of postoperative complications of stentimplantation.

3D Finite Element Analysis of a Man Hip Joint Femur under Impact Loads

Objective: The biomechanical characters of the bone fracture of the man femoral hip joint under impact loads are explored. Methods:A biosystem model of the man femoral hip joint by using the GE (General Electric) lightspeed multi-lay spiral CT is conducted. A 3D finite element model is established by employing the finite element software ANSYS. The FE analysis mainly concentrates on the effects of the impact directions arising from intense movements and the parenchyma on the femoral hip joint on the stress distributions of the proximal femur. Results:The parenchyma on the hip joint has relatively large relaxation effect on the impact loads. Conclusion:Effects of the angle δ of the impact load to the anterior direction and the angle γ of the impact load to the femur shaft on the bone fracture are given;δ has larger effect on the stress and strain distributions than the angle γ, which mainly represents the fracture of the upper femur including the femoral neck fracture when the posterolateral femur is impacted, consistent with the clinical results.

Finite Element Simulation of the Polymeric Liquid Flow in Coat-hanger Die

A three - dimenslonal finite element model is developed to deal with the polymeric liquid flow in coat - hanger die. This model is used to predict the flow behavior of the 2％ CMC/watsr solution in the coat - hanger die with linearly taper manifolds and its validity is experimentally verified quantitatively and qualitatively by using Laser Doppler Velocimetry and Particle Image Velocimetry respectively.

Three-dimensional simulations of strong ground motion in the Shidian basin based upon the spectral-element method

The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical profiles within the basin are used to analyze the generation and propagation of surface waves and their relation to the basin structures in both the time and frequency domain.The amplification effects are analyzed by the distribution of peak ground velocity(PGV)and cumulative kinetic energy(Ek) in the basin.The results show that in the 3D basin,the excitation of the fundamental and higher surface wave modes are similar to that of the 2D model.Small bowls in the basin have great influence on the amplification and distribution of strong ground motion,due to their lateral resonances when the wavelengths of the lateral surface waves are comparable to the size of the bowls.Obvious basin edge effects can be seen at the basin edge closer to the source for constructive interference between direct body waves and the basin-induced surface waves.The Ek distribution maps show very large values in small bowls and some corners in the basin due to the interference of waves propagating in different directions.A high impedance contrast model can excite more surface wave modes,resulting in longer shaking durations as well as more complex seismograms and PGV and Ek distributions.

Three-Dimensional Boundary Element Method Applied to Nonlinear Wave Transformation

For higher accuracy in simulating the transformation of three dimensional waves, in consideration of the advantages of constant panels and linear elements, a combined boundary elements is applied in this research. The method can be used to remove the transverse vibration due to the accumulation of computational errors. A combined boundary condition of sponge layer and Sommerfeld radiation condition is used to remove the reflected waves from the computing domain. By following the water particle on the water surface, the third order Stokes wave transform is simulated by the numerical wave flume technique. The computed results are in good agreement with theoretical ones.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

Finite Element Simulation of Flexible Roll Forming with Supplemented Material Data and the Experimental Verification

Flexible roll forming is a promising manufacturing method for the production of variable cross section products. Considering the large plastic strain in this forming process which is much larger than that of uniform deformation phase of uniaxial tensile test, the widely adopted method of simulating the forming processes with non-supplemented material data from uniaxial tensile test will certainly lead to large error. To reduce this error, the material data is supplemented based on three constitutive models. Then a finite element model of a six passes flexible roll forming process is established based on the supplemented material data and the original material data from the uniaxial tensile test. The flexible roll forming experiment of a B pillar reinforcing plate is carried out to verify the proposed method. Final cross section shapes of the experimental and the simulated results are compared. It is shown that the simulation calculated with supplemented material data based on Swift model agrees well with the experimental results, while the simulation based on original material data could not predict the actual deformation accurately. The results indicate that this material supplement method is reliable and indispensible, and the simulation model can well reflect the real metal forming process. Detailed analysis of the distribution and history of plastic strain at different positions are performed. A new material data supplement method is proposed to tackle the problem which is ignored in other roll forming simulations, and thus the forming process simulation accuracy can be greatly improved.