Finite Element Method In Order Research Articles

Polycrystalline models of anisotropic sintered magnets: Influence of grain alignment on mechanical properties and residual stresses

Models of polycrystalline microstructures, representative for sintered permanent magnets with various grain size distributions and alignment degrees, were generated by the Voronoï tessellation technique. The polycrystalline models were meshed and then a stress/strain analysis was performed with the Finite Element Method (FEM) in order to derive the relation between the homogenized properties (thermal expansion coefficient, elastic constants) and the degree of grain alignment. Residual stresses after sintering were also analyzed and a possible mechanism involved in the decrease in mechanical strength is discussed. It is argued that small sized and poorly aligned grains dispersed in the polycrystalline material are highly stressed after elaboration and could be responsible for the initiation of failure.

Numerical Methods for Solving Some Hydrodynamic Stability Problems

In this paper we solve the stability problem of the thermal convection in a thin fluid layer with free-free, slip-slip, and fixed-slip boundary conditions. We use different numerical methods to check their flexibility and accuracy where we use the following numerical methods: finite difference, High order finite difference, $$p$$ order finite element, Chebyshev collocation-1, Chebyshev collocation-2 and Chebyshev tau. Moreover, we solve the equations of Poiseuille flow in a Brinkman porous media with slip-slip boundary conditions using $$p$$ order finite element, Chebyshev collocation-1 and Chebyshev collocation-2 methods. The advantage and disadvantage of each method have been discussed. According to our result, we believe that the finite difference and finite element methods are very flexible methods and we can apply them to solve any problem easily. However, the accuracy of the the finite difference and finite element methods is less than the accuracy of the Chebyshev methods.

Numerical analysis with experimental data of the joint of fuselage with main landing gear and wing‐strut, of a two‐seat aircraft built with composites

An analysis of the strut‐to‐fuselage and main‐landing‐gear‐to‐fuselage joint is realized in order to evaluate the zones with a high probability of failure. The whole section is analyzed using the finite element method in order to estimate static resistance behavior, therefore it becomes necessary to create a numerical model of the section, to measure the mechanical properties of the C‐Ep composite material, and to calculate the loads applied onto the section. The section is digitized with photogrammetry. Mechanical characterization is achieved with instrumented standardized tensile tests. Results of the analysis show that the zones with higher probability of failure are found around the wing strut and the fuselage joint, with a safety factor higher than necessary even for the most critical condition, and lower in comparison with the average safety factor used on aircrafts built mostly with metals. POLYM. COMPOS., 36:1072–1083, 2015. © 2015 Society of Plastics Engineers

Higher Order NEM and FEM Accuracy Comparison

The natural-element method (NEM) has proved to be able to provide more accurate and computationally efficient solutions than the finite-element method (FEM) for first-order consistency approximations. However, higher order approximations in the NEM framework are not obtained straightforwardly. This paper addresses a method of constructing higher order approximations out of the standard first-order NEM shape functions. This process is achieved through the de Boor algorithm. Accuracy of the scheme is compared with FEM. Results show that in second-order approximations context the NEM is still able to provide better accuracies for a given number of degrees of freedom.

Assessment of Knee Cartilage Stress Distribution and Deformation Using Motion Capture System and Wearable Sensors for Force Ratio Detection.

Knowledge about the knee cartilage deformation ratio as well as the knee cartilage stress distribution is of particular importance in clinical studies due to the fact that these represent some of the basic indicators of cartilage state and that they also provide information about joint cartilage wear so medical doctors can predict when it is necessary to perform surgery on a patient. In this research, we apply various kinds of sensors such as a system of infrared cameras and reflective markers, three-axis accelerometer, and force plate. The fluorescent marker and accelerometers are placed on the patient's hip, knee, and ankle, respectively. During a normal walk we are recording the space position of markers, acceleration, and ground reaction force by force plate. Measured data are included in the biomechanical model of the knee joint. Geometry for this model is defined from CT images. This model includes the impact of ground reaction forces, contact force between femur and tibia, patient body weight, ligaments, and muscle forces. The boundary conditions are created for the finite element method in order to noninvasively determine the cartilage stress distribution.

Geometrically Exact Theory of Contact Interactions—Applications with Various Methods FEM and FCM

Geometrically exact theory of contact interactions is aiming on the development of the unified geometrical formulation of computational contact algorithms for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, curve-to-surface, point-to-surface, curve-to-curve, point-to-curve, point-to-point. The construction of the corresponding computational contact algorithms is considered in accordance with the geometry of contacting bodies in covariant and closed forms. These forms can be easily discretized within various methods such as the finite element method (FEM), the finite discrete method (FDM) independently of the order of approximation and, therefore, the result is straightforwardly applied within any further method: high order finite element methods, iso-geometric finite element methods etc. As particular new development it is shown also the possibility to easy combine with the Finite Cell Method.

How High a Degree is High Enough for High Order Finite Elements?

Abstract High order finite element methods can solve partial differential equations more efficiently than low order methods. But how large of a polynomial degree is beneficial? This paper addresses that question through a case study of three problems representing problems with smooth solutions, problems with steep gradients, and problems with singularities. It also contrasts h - adaptive, p -adaptive, and hp -adaptive refinement. The results indicate that for low accuracy requirements, like 1% relative error, h -adaptive refinement with relatively low order elements is sufficient, and for high accuracy requirements, p -adaptive refinement is best for smooth problems and hp -adaptive refinement with elements up to about 10th degree is best for other problems.

Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number

A preasymptotic error analysis of the finite element method (FEM) and some continuous interior penalty finite element method (CIP-FEM) for the Helmholtz equation in two and three dimensions is proposed. $H^1$- and $L^2$-error estimates with explicit dependence on the wave number $k$ are derived. In particular, it is shown that if $k^{2p+1}h^{2p}$ is sufficiently small, then the pollution errors of both methods in $H^1$-norm are bounded by $O(k^{2p+1}h^{2p})$, which coincides with the phase error of the FEM obtained by existent dispersion analyses on Cartesian grids, where $h$ is the mesh size, and $p$ is the order of the approximation space and is fixed. The CIP-FEM extends the classical one by adding more penalty terms on jumps of higher (up to $p$th order) normal derivatives in order to reduce efficiently the pollution errors of higher order methods. Numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the CIP-FEM in reducing the pollution effect.

A higher order FEM for time-domain hydroelastic analysis of large floating bodies in an inhomogeneous shallow water environment

The study of wave action on large, elastic floating bodies has received considerable attention, finding applications in both geophysics and marine engineering problems. In this context, a higher order finite-element method (FEM) for the numerical simulation of the transient response of thin, floating bodies in shallow water wave conditions is presented. The hydroelastic initial-boundary value problem, in an inhomogeneous environment, characterized by bathymetry and plate thickness variation, is analysed for two configurations: (i) a freely floating strip modelling an ice floe or a very large floating structure and (ii) a semi-fixed floating beam representing an ice shelf or shore fast ice, both under long-wave forcing. The variational formulation of these problems is derived, along with the energy conservation principle and the weak solution stability estimates. A special higher order FEM is developed and applied to the calculation of the numerical solution. Results are presented and compared against established methodologies, thus validating the present method and illustrating its numerical efficiency. Furthermore, theoretical results concerning the energy conservation principle are verified, providing a valuable insight into the physical phenomenon investigated.

강성계수의 전달을 이용한 횡방향 하중을 받는 축대칭 원판의 정적해석

Abstract: A circular plate is one of the important structures in many industrial fields. In static analysis of a circular plate, we may obtain an exact solution by analytical method, but it is limited to a simple circular plate. Thus, many researchers and designers have used numerical methods such as the finite element method. The authors of this paper developed the finite element-transfer stiffness coefficient method (FE-TSCM) for static and dynamic analyses of various structures. FE-TSCM is the combination of the modeling technique of the finite element method (FEM) and the transfer technique of the transfer stiffness coefficient method (TSCM). FE-TSCM has the advantages of both FEM and FE-TSCM. In this paper, the authors formulate the computational algorithm for the static analysis of axisymmetric circular plates under lateral loading using FE-TSCM. The computational results for three computational models obtained by FE-TSCM are compared with those obtained by FEM in order to confirm the accuracy of FE-TSCM.

해상풍력발전기 기초구조물의 강성이 모노파일 두부의 부재력 및 변위에 미치는 영향

Recently, the research on renewable energy against depletion of fossil fuel have been actively carried out in the world. Especially, offshore wind turbines are very economical and innovative technology. However, offshore wind turbines experience large base moments due to the wind and wave loading, so the monopile with large diameter needs to be applied. For the economical design of the large diameter pile, it is important to consider the flexibility of the foundation to estimate the maximum moment accurately, based on studies conducted so far. In this paper, the foundation was modeled using the finite element method in order to better describe the large diameter effect of a monopile and the results were compared with those of p-y method. For the examples studied in this paper, the change in maximum moment was insignificant, but the maximum tilt angle from the finite element method was over 14% larger than that of p-y method. Therefore, the finite element approach is recommended to model the flexibility effect of the pile when large tilt angles may cause serviceability issues.

Finite element predictions of effective multifunctional properties of interpenetrating phase composites with novel triply periodic solid shell architectured reinforcements

In this paper, new interpenetrating phase composites (IPCs) based on the mathematically-known triply periodic minimal surfaces (TPMS) are proposed. In these IPCs, different TPMS architectures are used as reinforcing solid shells to increase the effective multifunctional properties of IPCs. Several three-dimensional representative volume elements (RVEs) are generated and studied using the finite element method in order to predict the effective properties for various TPMS-based IPC architectures. The calculated properties are compared with some analytical bounds and conventional composites. The proposed IPCs have superiority against the conventional composites, and they possess effective properties close to the upper Hashin-Shtrikman bounds. Limited experimental validation of the computational prediction of effective conductivity is presented where the TPMS is made of conductive carbon nanostructured-based polymer composite.

Optimization method for the determination of material parameters in damaged composite structures

An optimization method to identify the material parameters of composite structures using an inverse method is proposed. This methodology compares experimental results with their numerical reproduction using the finite element method in order to obtain an estimation of the error between the results. This error estimation is then used by an evolutionary optimizer to determine, in an iterative process, the value of the material parameters which result in the best numerical fit. The novelty of the method is in the coupling between the simple genetic algorithm and the mixing theory used to numerically reproduce the composite behavior. The methodology proposed has been validated through a simple example which illustrates the exploitability of the method in relation to the modeling of damaged composite structures.

Schrödinger eigenbasis on a class of superconducting surfaces: Ansatz, analysis, FEM approximations and computations

In this work we focus on the efficient representation and computation of the eigenvalues and eigenfunctions of the surface Schrödinger operator (i∇+A0)2 that governs a class of nonlinear Ginzburg–Landau (GL) superconductivity models on rotationally symmetric Riemannian 2-manifolds S. We identify and analyze a complete orthonormal system in L2(S;C) of eigenmodes having a variable-separated form. For the unknown functions in this ansatz, our analysis facilitates the identification of approximate spectral problems whose eigenvalues lie arbitrarily near corresponding eigenvalues of the Schrödinger operator. We then develop and implement an arbitrary order finite element method for the efficient numerical approximation of the eigenvalue problem. We also demonstrate our analysis, algorithm and its convergence rate using parallel computations performed on a variety of choices of smooth and non-smooth surfaces S.

Simulation study of magnetorheological testing cell design by incorporating all basic operating modes

Magnetorheological (MR) fluid is one of the field-responsive fluids that is of interest to many researchers due to its high yield stress value, which depends on the magnetic field strength. Similar to electrorheological (ER) fluid, the combination of working modes is one of the techniques to increase the performance of the fluids with limited focus on MR fluids. In this paper, a novel MR testing cell incorporated with valve, shear and squeeze operational modes is designed and constructed in order to investigate the behaviour of MR fluid in combined mode. The magnetic field distribution in the design concept was analyzed using finite element method in order to verify the effective areas of each mode have the acceptable range of flux density. The annular gap of valve and shear were fixed at 1 mm, while the squeeze gap between the parallel circular surfaces was varied up to 20 mm. Three different coil configurations, which were made up from 23 SWG copper wires were set up in the MR cell. The simulation results indicated that the magnetic field distributed in the squeeze gap was the highest among the other gaps with all coils were subjected to a constant applied current of 1 A. Moreover, the magnetic flux densities in all gaps were in a good range of magnitude based on the simulations that validated the proposed design concept. Hence, the 3D model of the MR testing cell was designed using Solidworks for manufacturing processes.

Mechanism of hydrogen embrittlement cracking produced by residual stress from indentation impression

Abstract This study investigated the mechanism of hydrogen embrittlement (HE) cracking, produced by residual stress that develops around an indentation impression crater. A spherical indenter was used to indent a high strength steel, forming locally compressive plastic deformation (i.e., an impression crater). Subsequently, hydrogen was charged into the specimen with the impression. It is found that HE cracking occurs around the impression, and propagates radially. The radial crack morphology was changed by varying the applied indentation force and time of hydrogen charging. In fact, two types of cracks were observed, short cracks (less than 50 μm in length) and long ones. The impression due to a small indentation force produced only short cracks, while a large force yielded both short and long cracks. In order to clarify the mechanism of crack morphology formation, the finite element method (FEM) was used to compute the residual stress field surrounding the impression. It was found that circumferential stress with a tensile component was developed around the impression, leading to initiation and propagation of HE cracks. For the smaller indentation force, the potential area for crack initiation is at the rim of the impression (on the material surface). However, a larger force induced crack initiation additionally beneath the surface leading to longer crack formation. Crack propagation was simulated using a cohesive zone model (CZM) in FEM in order to elucidate the crack morphology showing both short and long cracks. Multiple crack propagation was simulated using two CZM elements in order to investigate the interaction between two cracks. It was found that the crack length becomes shorter when the distance between the two cracks is closer (the crack angle is small). This is due to the fact that the stress as the driving force decreases owing to neighboring crack generation. On the contrary, when the distance between the two cracks is large (the cracks are away from each other), the lengths of the two cracks are identical, since there is no interaction between them. This study also investigated the relationship between crack growth resistance (i.e., threshold stress intensity factor, Kth) and simulated crack length. From the length of the long crack, the HE crack growth resistance, Kth, can be estimated. It was found to be strongly dependent on hydrogen content, while there is little influence of the indentation force. This study thus established the computational framework for the prediction of HE damage (crack morphology) surrounding the indentation impression for various applied indentation forces and hydrogen content. The findings will be useful for predicting HE cracking from an indentation impression crater, when the crater formed, for instance, due to shot peening or foreign object contact, is exposed to a hydrogen environment.

Load sharing ability of the liner in type III composite pressure vessels under internal pressure

In this work, the load sharing ability of metallic liners in type III composite overwrapped pressure vessel was investigated by means of accurate numerical models based on finite element method in order to realistically represent the hybrid metal-composite structure. The varying thickness of the composite layers throughout the dome, as well as their angles, were accounted for in the model. The study focused on the influence of material properties and liner-to-composite thickness ratio on the stress and strain distribution between liner and composite at the cylindrical, dome, and polar boss regions. Two novel concepts for the evaluation of the structural response of a composite overwrapped pressure vessel were introduced, namely: (i) the liner stress and strain fractions, and (ii) the correlation with liner-to-composite thickness ratio. The results show complex overall behavior close to the onset of plasticity of the liner, which is critically investigated. A decrease in liner stress fraction was found for higher internal pressure loads since the stress field is increasingly dominated by the composite overwrap. Also, the von Mises equivalent stress along the longitudinal profile of the structure showed a peak at the dome of the liner, whereas for the composite, the peak was at the shoulder region. This was justified considering that, at low pressure, the liner operates elastically in compression-tension mode and the composite in tension-tension mode.

Finite Element Analysis to Improve the Accuracy of Parts Made by Stainless Steel 316L Material Using Selective Laser Melting Technology

One of the serious problems in the SLM process, using metallic powders is the thermal distortion of the model during forming. As a result of the locally concentrated energy input, the temperature gradient mechanism and the related processes lead to residual stresses and part deformations. Since the solidified part is cooled rapidly, the model tends to be deformed and cracked due to the thermal stresses. All these aspects were considered for a series of analyses that were made using the finite element method in order to determine the optimum process parameters (laser power, scanning speed, powder bed temperature) that are required in order to improve the accuracy of the metallic parts made by Stainless Steel 316L material using the Selective Laser Melting process.

Numerical analysis of hydrogen-assisted rolling-contact fatigue of wind turbine bearings

Offshore wind parks at locations further from the shore often involve serious difficulties, e.g. the maintenance. The bearings of offshore wind turbines are prone to suffer hydrogen-assisted rolling-contact fatigue (HA-RCF). Three important aspects linked with bearing failures are being extensively researched: (i) rolling contact fatigue (RCF), (ii) influence of carbide particles on fatigue life, and (iii) local microplastic strain accumulation via ratcheting. However, there is no reference related to bearing failure in harsh environment. This way, this paper helps to gain a better understanding of the influence of hydrogen on the service life of offshore wind turbine bearings through a numerical study. So, the widely used RCF ball-on-rod test was simulated by finite element method in order to obtain the stress-strain state inside the bearings during life in service and, from this, to elucidate the potential places where the hydrogen could be more harmful and, therefore, where the bearing material should be improved.

A replacement of chromate coating for adhesive bonding of stainless steel in a corrosive environment

For adhesive bonding of stainless steel to itself, a surface treatment involving chromates is used. However, chromates are environmentally unfriendly so a replacement is being sought. In this paper, an alternative to chromate was investigated. The standard test method, ASTM D 1002, was used to measure the failure load of adhesively bonded stainless steel samples. A general-purpose epoxy adhesive was used. To simulate marine exposure, adhesively bonded samples were placed in a 5% salt spray for extended periods of time, up to five weeks. Results indicated that the initial shear strength of adhesive joints prepared with a traditional chromate preparation was 25% greater than the new, alternative coating. However, more importantly, the rate of decrease in strength with salt spray exposure was greater for the chromate than for the alternative. After 21 days, both bonding surface treatments had the same strength. However, after this period of time, the alternative was stronger than the chromate treatment, indicating that the alternative was a more durable coating. An adhesive/adherent coated system was investigated using a finite element method in order to investigate the influence of adhesive thickness between the adhesive and the adherent, and the residual stress in the adhesive layer. Keywords: Adhesive, Alternative Coating, Crevice Corrosion, Potentio-Dynamic, Salt Spray.