Finite Element Method Method Research Articles

On Neumann ‐ Dirchlet coupling strategy of Finite Element and Boundary Element method in elastodynamics

AbstractThe Finite Element Method (FEM) and the Boundary Element Method (BEM) are the most used numerical tools for solid mechanics analysis. Each one of these methods has advantages and drawbacks in different cases. In order to take advantage of both methods, a nonoverlapping domain decomposition method FEM ‐ BEM in elastodynamics is presented. The domain is divided in two subdomains and each one of them is analyzed separately and only the interface information is exchanged. An iterative Neumann ‐ Dirchlet algorithm with relaxation is used, to get continuity and the equilibrium conditions at the interface. The FEM time integration is carried out using the Newmark's method and the BEM approach in time domain is based in the Convolution Quadrature Method developed by Lubich. Numerical examples are presented to show agreement with other available numerical results. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Approximate analytical models of temperature and thermal stresses for 2D axis-symmetry object with temperature-dependent properties

This paper presents the approximate analytical models of temperature and thermal stress in a two-dimensional axis-symmetry object. The models can be used to deal with some non-linear factors caused by temperature-dependent properties using multiple parameter perturbation method. Two cases have been used to test the models proposed in this paper. The first case study is the comparison of analysis of the rotor with our models and FEM (finite element method) and it is shown that our models have a satisfactory accuracy. The second case is the application of our models to sensitivity studies. The models proposed reduce computational time significantly compared with FEM method and hence can be used for online analyzing of thermal state of a two-dimensional axis-symmetry object and inverse heat conduction problems.

Deformation and failure mechanisms of single crystal superalloy under temperature gradient

The crystallographic constitutive model under temperature gradient is developed and introduced to study the deformation and failure mechanisms of single crystal superalloy. Tensile tests of thin-walled pipe specimen at different temperatures without cooled air flow were carried out. Based on the experimental results, the temperature dependence of constitutive model was studied and the basic parameters of constitutive model were obtained. To investigate the deformation and failure mechanisms, the thin-walled pipe specimen with cooled air flow under temperature gradient were tested. Considered the fluid–solid interface (FSI), a finite element method (FEM) was proposed to simulate the process of tension. In FEM, the activation rate of slip system was defined as the failure law of specimen under temperature gradient. The simulation result was in good agreement with the experiment result. Furthermore, the fracture surface of the specimen was observed by the scanning electron microscopy (SEM). The microstructure revealed that the slip deformation belonged to {1 1 1} crystalplane is a principal failure mechanism of single crystal superalloy under temperature gradient. The results of the SEM also implied that the proposed FEM method can be used to systemically study the deformation and failure behavior of single crystal superalloy cooled blade.

A robust weakly compressible SPH method and its comparison with an incompressible SPH

SUMMARYThis paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering‐induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods. Copyright © 2011 John Wiley & Sons, Ltd.

Numerical Simulation Using FE-SPH Method for Concrete Slabs Penetrated and Perforated by Steel Projectiles

The explicit dynamic code LS-DYNA3D is used to simulate limited-thickness concrete slabs penetrated and perforated by steel projectiles with velocities from 381 m/s to 1058 m/s. The concrete slab is modeled with Smooth Particle Hydrodynamics (SPH) elements near the trajectory while Finite Element Method (FEM) elements in the others of the target, which is called FE-SPH method. The elastic-plastic model and Johnson-Holmquist concrete model are used to describe the mechanical behaviors of the projectiles and target slabs, respectively. The residual velocities computed by both FEM and FE-SPH method agree well with those of experimental results. For brittle concrete, the penetration and perforation phenomenon modeled by FE-SPH are in closer agreement with the experimental results than those modeled by FEM. Simulation of penetration and perforation by FEM require artificial element erosion set, which would lead to distortion of modeled results.

Direct Measurement of Inter-Filament Resistance in Superconducting Multifilamentary NbTi and ${\rm Nb}_{3}{\rm Sn}$ Strands

A quantitative knowledge of inter-filament transverse resistance will allow us to describe current redistribution processes inside strands more accurately. This is particularly important for the analysis of the influence of strain and crack distribution patterns in Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn filaments on the shape of the voltage-current curves. Several indirect methods are commonly used to assess inter-filament resistance. Here we use a direct method to measure transverse inter-filament resistance and filament-to-matrix contact resistance. Two four-probe voltage-current methods are developed for measurements below 10 K at various background magnetic fields. In addition to FEM (Finite Element Method) simulation, also a new 3D strand model is developed to simulate the current- and voltage distributions. The experimental methods, first results as well as the simulations using the FEM method and new 3D strand model are described.

Modeling and finite element analysis of transduction process of electromagnetic acoustic transducers for nonferromagnetic metal material testing

Facing the problems lack of considering the non-uniform distribution of the static bias magnetic field and computing the particle displacements in the simulation model of electromagnetic acoustic transducer (EMAT), a multi-field coupled model was established and the finite element method (FEM) was presented to calculate the entire transduction process. The multi-field coupled model included the static magnetic field, pulsed eddy current field and mechanical field. The FEM equations of the three fields were derived by Garlerkin FEM method. Thus, the entire transduction process of the EMAT was calculated through sequentially coupling the three fields. The transduction process of a Lamb wave EMAT was calculated according to the present model and method. The results show that, by the present method, it is valid to calculate the particle displacement under the given excitation signal and non-uniformly distributed static magnetic field. Calculation error will be brought about if the non-uniform distribution of the static bias magnetic field is neglected.

대형 풍력 발전용 필라멘트 와인딩 복합재 타워의 고유 진동수 해석에 관한 연구

The purpose of this study was to investigate the natural frequency of filament-wound composite towers for large scale wind-turbines using the finite element method (FEM). To define the material properties, we used both the effective property method and the stacking properties method. The effective properties method assumes that a composite consists of one ply. The stacking properties method assumes that a composite consists of several stacked plies. First, a modal analysis of the tower, filament-wound with angles of , was carried out using the two methods for composite material properties, the stacking method and effective method. Then, an FE analysis was performed for composite towers using filament winding angles of , , and . The FE analysis results using the stacking properties of the composite were in good agreement with the results from the effective properties method. The difference between the FEM and material properties methods was approximately 0~0.6%

Studying the Rock Seepage Parameters Identification Method Based on Finite Element Method and Difference Evolution Arithmetic

The seepage of rock and soil is a common problem in geotechnical engineering, because of the uncertainty property of rock and soil, how to ascertain the seepage parameter of rock and soil becomes a problem to solve. Aiming to the problem, after introducing the theory of seepage parameter identification, the paper combines unstable seepage finite element method (FEM) and difference evolution (DE) arithmetic, constructs intelligent identification FEM method of seepage parameter, and develops the procedure. The hydraulic head distribution of seepage field can be calculated accurately by FEM and the optimal solution can be obtained by DE, the seepage FEM being embedded in DE, overcoming the local optimization problems of conventional methods and improving the precision of identification. A tam sample is calculated by the method, it states that the convergence speed is quick and result is satisfied. It is a powerful method for seepage parameter identification.

Minimum drag shape of a semi-ellipsoid exposed to shear flow and its possible relation to the shape of endothelial cell

A semi-ellipsoid attached on a wall is considered as a model problem for the study of blood flow effect on the shape of an endothelial cell. Under the condition that the volume is fixed and one axis of the semi-ellipsoid is aligned to the flow direction, the shape for the minimum drag under the applied shear flow is determined. Both the analytical and numerical approaches are adopted for computation of the minimum drag shape. Since analytical solution is not available for the original model problem, analytical solution to a closely related problem is used to compute the approximate value of the drag force. Adopted is the classical result on the motion of an ellipsoidal particle in a viscous fluid [Jeffery, Proc. Roy. Soc. A (1922)]. To corroborate the analytically obtained results, the model problem has also been studied numerically by using the finite element method (FEM). The minimum drag shape predicted analytically by using Jeffery’s solution is ( a, b, c) = (1.71, 0.67, 0.88), where a is the dimensionless semi-axis in the flow direction, b the height, and c the half width of the semi-ellipsoid. The numerical approach predicts the minimal drag shape as ( a, b, c) = (1.96,0.64,0.80). This result obtained by the FEM method shows good agreement with the result obtained by the boundary integral method [Hazel and Pedley, Biophys. J. (2000)].

Finite element analysis of elastic property of concrete composites with ITZ

For better estimation of elastic property of concrete composites, the effect of Interfacial Transition Zone (ITZ) has been found to be significant. Numerical concrete composites models have been introduced using Finite Element Method (FEM), where ITZ is modeled as a thin shell surrounding aggregate. Therefore, difficulties arise from the mesh generation. In this study, a numerical concrete composites model in 3D based on FEM and random unit cell method is proposed to calculate elastic modulus of concrete composites with ITZ. The validity of the model has been verified by comparing the calculated elastic modulus with those obtained from other analytical and numerical models.

Study on Numerical Methods for Acoustic Radiation of Open Structure

For acoustic radiation of open thin-walled structure, it was difficult to analyze directly by analytical method. The problem could be solved by several numerical methods. This paper had studied the basic theory of the numerical methods as FEM (Finite Element Method), BEM (Boundary Element Method) and IFEM (Infinite Element Method), and the numerical methods to solve open structure radiation problem. Under the premise of structure-acoustic coupling, this paper analyzed the theory and flow of the methods on acoustic radiation of open structure, including IBEM (Indirect Boundary Element Method), DBEM (Direct Boundary Element Method) coupling method of interior field and exterior field, FEM and BEM coupling method, FEM and IFEM coupling method. This paper took the open structure as practical example, and applied the several methods to analyze it, and analyzed and compared the several results to get relevant conclusions.

Development of High-Order Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities

Structural analysis problems are traditionally solved using the Finite Element Method (FEM). However, when the structure of interest contains discontinuities such as cracks or re-entrant corners, a large number of elements are required to accurately reproduce the stress characteristics in the region of the discontinuities. As a result, the FEM method requires a large storage space and has a slow convergence speed. It has been shown that the Infinite Element Method (IEM) overcomes these limitations and provides a feasible means of solving various types of elasticity and singularity problems. Previous studies have generally focused on the use of IEM formulations based on low-order elements (2×2). By contrast, this study develops a high-order (3×3) IEM formulation. The solutions obtained using the proposed IEM method for various 2D elasto-static problems are compared with the results obtained using the traditional low-order IEM method and the analytical solutions presented in the literature. It is shown that the results obtained using the proposed method are more accurate than those obtained using the low-order IEM method and are in excellent agreement with the analytical solutions.

Three-Dimensional Numerical Modeling of the Transient Fluid-Structural Interaction Response of Tidal Turbines

The objective of this work is to develop and validate a coupled boundary element method-finite element method to simulate the transient fluid-structure interaction response of tidal turbines subject to spatially varying inflow. The focus is on tidal turbines, although the methodology is also applicable for the analysis and design of wind turbines. An overview of the formulation for both the fluid and solid domains, and the fluid-structure interaction algorithms, is presented. The model is validated by comparing the predicted thrust and power measurements, as well as cavitation patterns, with experimental measurements and observations for an 800 mm marine current turbine presented in the work of Bahaj et al. (2007, “Power and Thrust Measurements of Marine Current Turbines Under Various Hydrodynamic Flow Conditions in a Cavitation Tunnel and a Towing Tank,” Renewable Energy, 32, pp. 407–426). Additional numerical results are shown for the same turbine, but scaled up to 20 m in diameter, operating in a tidal boundary layer flow with a water depth of 30 m. The results show that transient cavitation will develop near the blade tip when the blades are near the free surface at highly-loaded off-design conditions, and the blades will undergo excessive deformation because of the high fluid loading and slender blade profile. The results also show that the natural frequencies of the blades are significantly reduced when operating in water, as compared with when operating in air, because of added-mass effects. In addition to demonstrating the need for proper consideration for fluid cavitation and structural response, current design challenges for both wind and tidal turbines are discussed.

Full-Wave Analysis of Monopulse Dielectric Lens Antennas at W-band

Lens antenna is a good substitute for the Cassegrain antenna at millimeter-wave frequencies, especially at W-band. On one hand, the antenna design, which is bulky and heavy at low frequencies, becomes compact and light-weighted at W-band. On the other hand, without the blockage caused by the sub-reflector and the feed horns which are unavoidable in a Cassegrain antenna, the lens antennas show better radiation characteristics. In this paper, several lens antennas fed by metal horns are analyzed using a full-wave method-finite element method based on the weak form of the Helmholtz equation (WF-FEM). Numerical results show that the lens antennas presented have low side lobe level (SLL), and good sum and difference performances.

Analysis and Comparison of a Permanent-Magnet DC Motor with a Field-Winding DC Motor

The influence of magnetic saturation on electromagnetic field distribution in both a permanent- magnet direct-current (PMDC) motor and a field-winding (wound-field) direct-current (FWDC) motor, with the same output mechanical power, has been studied. In this paper, an approximate analytical method and time-stepping Finite Element Method (FEM) are used for prediction of Back-EMF and electromagnetic torque. No-load and rotor-lucked conditions, according to experimental measurements, and the FEM and analytical method studies of the motors have been considered. A sensitivity analysis has also been successfully accomplished on the major design parameters that affect motor performance. At last, these two DC motors are compared, in spite of their differences, on the basis of measured output characteristics.

A Numerical Method to Enhance the Accuracy of Mass-Spring Systems for Modeling Soft Tissue Deformations

This technical note presents a numerical corrective technique that allows control of nonlinearity in a mass-spring system (MSS) independent of its spring constants or system topology. The governing equations of MSS in the form of ordinary differential equations or a regular function accompanied by any boundary or initial condition as known constraints, are employed to modify the results. A least-squares algorithm coupled with the finite difference method is used to discretize the basic residual function implemented in this corrective technique. This numerical solution is applicable to both static and dynamic MSS. This technique is easy to implement and has accuracy similar to that of the equivalent finite element method (FEM) solution to the same system whereas solutions are obtained in a fraction of the CPU time. The proposed technique can also be used to smooth solutions from other methods such as FEM or boundary element method (BEM).

Numerical analysis on water treeing deterioration of XLPE cable insulation using combination of FEM and Taguchi method

AbstractWater treeing is one of the main deterioration phenomena affecting the service lifetime of the underground crosslinked polyethylene (XLPE) power cables. Factors influencing the water tree growth can be classified in two major groups, namely, the external factors (operational factors) and the internal factors (material factors). The influences of the external factors on the number and the growth rates of water trees have fully understood through the long‐term research around the world for the past four decades. However, the effects of the internal factors have been not so much investigated as those of the external ones. Especially, it has been hardly discussed which among the probable internal factors is the most influential to the water treeing phenomena until now. In this paper, the authors have investigated the contributions of individual factors influential to the electric field distribution in the tip of the water tree initiated from the outer surface of XLPE cable insulation considering its thermal degradation, using both the finite element method (FEM) and Taguchi design of experiment methodology (Taguchi method). The numerical and water treeing experiments show that the dielectric properties of the water tree and the XLPE host material are more influential to the enhancement of the electric field intensity in the tree tip than its geometrical parameters, and that the permittivity distribution inside the tree is the most influential factor among all of the internal factors. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Force chains and resonant behavior in bending of a granular layer on an elastic support

In this paper we investigate the interaction between a granular layer and an elastic foundation using a coupled Discrete Element Method-Finite Element Method (DEM–FEM) computational model. We use this dynamics code to simulate quasi-static bending of the granular layer and we observe the changes taking place in the structure of the force chains for two cases: with and without rolling resistance. A reversal of the arches formed in the force chains leads to a bending resistance similar to that observed in dynamic experiments on resonant behavior under bending of a layer of sand in a container with an elastic bottom. The behavior of the force chains generated during bending may lead to enhanced mixing in vibrated granular media. In free vibration, the granular-layer/elastic-beam system behaves like a mass-loaded beam with no contribution to the stiffness from the granular layer, independent from the layer thickness and rolling resistance. This is observed to be due to the absence of the reversal of the force chain structures noticed in the quasi-static case when a push-up force bends the system upwards and the force chains rest against the middle of the beam and the side walls. Future studies are required for explaining the experimental observations related to the particle-size dependence of the bending stiffness in a granular layer as well as the resonant behavior of the system under forced bending vibrations.

Numerical modelling of electrostatic force microscopes considering charge and dielectric constant

PurposeThe purpose of this paper is to present a hybrid numerical simulation approach for the calculation of potential and electric field distribution considering charge and dielectric constant.Design/methodology/approachEach numerical method has its own advantages and disadvantages. The idea is to overcome the disadvantages of the corresponding numerical method by coupling with other numerical methods. An augmented finite element method (FEM), linear FEM and boundary element method are used with an efficient coupling.FindingsThe simulation model of microstructured devices is not so simple. During the simulation various types of problems will occur. It is found that by using several numerical methods these problems can be overcome and the calculation can be performed efficiently.Research limitations/implicationsThe present approach can be applied in 2D cases. But, in 3D cases the calculation of augmented FEM in a spherical coordinate becomes quite elaborate.Practical implicationsThe proposed hybrid numerical simulation approach can be applied for the simulation of the electrostatic force microscope (EFM) which is a very high‐resolution measuring tool in nanotechnology. This approach can be applied also to other micro‐electro‐mechanical systems.Originality/valueSince the scanning process of the EFM is dynamic, it requires the updating of the FEM mesh in each calculation time step. In the present paper, the mesh updating is achieved by an arbitrary Lagrangian‐Eulerian (ALE) method. The proposed numerical approach can be applied for the simulation of the EFM including this remeshing algorithm ALE.