Optimal Element Size Research Articles

Overload capacity of a Wolfrom type planetary system

Purpose – The purpose of this paper is to introduce an alternative approach to the FE modelling and simulation of complex gear trains, such as the Wolfrom planetary system, in order to study their overload capacity. This is a challenging task because of the following: first, multiple contacts occur between complex geometric parts. Second, the model has to be solved for many instances in order to determine the relative position of the planetary system members at which the maximum bending stress and surface pressure occur. Third, the maximum allowable overloading torque has to be determined iteratively. Design/methodology/approach – A Wolfrom planetary system with transmission ratio 19.2 is modelled and simulated using the finite element method. The optimum element size is selected by modelling and solving key areas of the system. Then, a complete model is built using balanced element length at the flanks and roots, with respect to low solution time and result accuracy. A single loading torque is applied at the input shaft and the load distribution results from the solution when equilibrium is achieved. The input torque is increased until the maximum allowable stress or pressure is reached. Findings – Combining the load distribution derived from a mixed density mesh with Hertzian pressure calculations, improves the accuracy of the results and decreases the total evaluation time of overload conditions. Furthermore, meshing disturbances due to the elastic deformation of the matting tooth pairs can be identified. It is shown that in the Wolfrom reducer analysed, the limiting mode of failure is the tooth breakage, which occurs when the input torque is increased by a factor of 3.8. Research limitations/implications – The balanced element length meshing requires individually meshed key areas and additional workflow steps. In this way, the complexity is increased but the solution time minimised. Automation tools can improve the simulation process. Originality/value – The balanced element length model and the result evaluation provides an improved approach of the overload capacity estimation where analytical methodologies cannot be applied.

Unified finite element methodology for gradient elasticity

In this paper a unified finite element methodology based on gradient-elasticity is proposed for both two- and three-dimensional problems, along with some considerations about the best integration rules to be used and a comprehensive convergence study. From the convergence study it has emerged that for both two and three-dimensional problems, the implemented elements show a convergence rate virtually equal to the corresponding theoretical values. Recommendations on optimal element size are also provided. Furthermore, the ability of the proposed methodology to remove singularities in statics has been demonstrated through a couple of examples, in both two and three dimensions.

Analysis of vertebral bone strength, fracture pattern, and fracture location: a validation study using a computed tomography-based nonlinear finite element analysis.

Finite element analysis (FEA) is an advanced computer technique of structural stress analysis developed in engineering mechanics. Because the compressive behavior of vertebral bone shows nonlinear behavior, a nonlinear FEA should be utilized to analyze the clinical vertebral fracture. In this article, a computed tomography-based nonlinear FEA (CT/FEA) to analyze the vertebral bone strength, fracture pattern, and fracture location is introduced. The accuracy of the CT/FEA was validated by performing experimental mechanical testing with human cadaveric specimens. Vertebral bone strength and the minimum principal strain at the vertebral surface were accurately analyzed using the CT/FEA. The experimental fracture pattern and fracture location were also accurately simulated. Optimization of the element size was performed by assessing the accuracy of the CT/FEA, and the optimum element size was assumed to be 2 mm. It is expected that the CT/FEA will be valuable in analyzing vertebral fracture risk and assessing therapeutic effects on osteoporosis.

Mesh Sensitivity Study of Soil Barrier Subjected to Blast Loading: Numerical Methods Using AUTODYN 3D

The accuracy of numerical result depends on many factors, among which is the selection of appropriate element size. An optimum mesh size is capable in reducing the percentage error and computational time consumption. In this study, a numerical tool i.e AUTODYN 3D is used to determine the optimum element size for the soil barrier subjected to air blast load. The pressure results on barrier surface obtained through one third scale are able to produce results that are in good agreement with published experimental test data as compared to full scale simulation. In this study, the selection of mesh size 20 mm x 20 mm x 20 mm found considerably as the best element size for the case study of a rectangular soil barrier subjected to air blast load by using AUTODYN 3D software.

Comparison of different higher order finite element schemes for the simulation of Lamb waves

Structural Health Monitoring (SHM) applications call for both efficient and powerful numerical tools to predict the behavior of ultrasonic guided waves. When considering waves in thin-walled structures, so called Lamb waves, conventional linear or quadratic pure displacement finite elements soon reach their limits. The spatial as well as temporal discretisation, required to obtain good quality results has to be very fine. This results in enormous computational costs (computational time and memory storage requirements) when ultrasonic wave propagation problems are solved in the time domain. To resolve this issue several higher order finite element methods with polynomial degrees p>2 are proposed. The objective of the current article is to develop such higher order schemes and to verify their capabilities with respect to accuracy and numerical performance. To the best of the authors’ knowledge such comparison has not been reported in literature, yet. Specifically, spectral elements based on Lagarange polynomials (SEM), p-elements using the normalized integrals of the Legendre polynomials (p-FEM) and isogeometric elements utilizing non-uniform rational B-splines (NURBS, N-FEM) are discussed in this paper. By solving a two-dimensional benchmark problem, their advantages and drawbacks with respect to Lamb wave propagation are highlighted. The results of the convergence studies are then used to derive guidelines for estimating the optimal element size for a given finite element type and polynomial degree template. These findings serve the purpose to determine the optimal mesh configuration a priori and thus, save a considerable amount of computational effort. The proposed guideline is then tested on a three-dimensional structure with a conical hole showing an excellent agreement with the predicted behaviour.

Adaptive nodeless variable finite elements with flux-based formulation for thermal–structural analysis

A nodeless variable element method with the flux-based formulation is developed to analyze two-dimensional thermal–structural problems. The nodeless variable formulation provides accurate temperature distributions to yield more accurate thermal stress solutions. The flux-based formulation is used to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element meshes that can adapt and move along with the transient solution behavior. A version of a nearly optimal element size determination is proposed to provide high convergence rate of the predicted solutions. The combined procedure is evaluated by solving several thermal, structural, and thermal stress problems.

In Vivo Assessment of Lumbar Vertebral Strength in Elderly Women Using Computed Tomography-Based Nonlinear Finite Element Model

In vivo study of a computed tomography (CT)-based nonlinear finite element model (FEM). To establish an FEM with the optimum element size to assess the vertebral strength by comparing analyzed data with those obtained from mechanical testing in vitro, and then to assess the second lumbar (L2) vertebral strength in vivo. FEM has been reported to predict vertebral strength in vitro, but has not been used clinically. Comparison among the 3 models with a different element size of 1 mm, 2 mm, and 3 mm was performed to determine which model achieved the most accurate prediction. Vertebral strength was assessed in 78 elderly Japanese women using an FEM with the optimum element size. The optimum element size was 2 mm. The L2 vertebral strength obtained with the FEM was 2154 +/- 685 N, and the model could detect preexisting vertebral fracture better than measurement of bone mineral density. The FEM could assess vertebral strength in vivo.

A study of flow-through phenomenon in the press forging of magnesium-alloy sheets

Abstract The finite element analysis and experimental approach were employed to examine the flow-through phenomenon occurred in the press forging of AZ31 magnesium-alloy sheets. The material properties tests suggest that the press forging of AZ31 sheets is required to be performed at temperatures higher than 300 °C. An optimum element size was determined first to simulate the appearance of flow-through and the finite element analysis reveals that the formation of flow-through is mainly due to the insufficient material in the neighborhood of the embossment. The finite element simulation results also indicate that the sheet thickness and the dimension of the embossment are the major factors affecting the occurrence of flow-through. Based on the sheet thickness and the embossment dimensions, the limiting curves for the occurrence of flow-through were established in the present study to predict if the flow-through would occur. These curves provide an important guideline for the press forging design.

A quadrilateral mesh generator for adaptive procedures in bulk forming processes

The simulation of real industry metal forming processes often requires the presence of adaptive procedures. With that purpose a quadrilateral mesh generator was developed. The algorithm is based on the simple fact that it is always possible to subdivide a region into quadrilaterals whenever the polygonal line that forms its boundary has an even number of sides and that, by joining two contiguous triangles, a quadrilateral may be formed. Rather than using an advancing front technique a cloud of nodal points is initially formed based on error estimators and criteria to define an optimal element size. With this procedure, using an adaptive process, the refinement is created where it will be needed.

Scaling issues in snow hydrology

The concept of scale can be used to quantify characteristic lengths of (a) a natural process (such as the correlation length of the spatial snow water equivalent (SWE) variability); (b) a measurement (such as the size of a snow density sample or the footprint of a satellite sensor), and (c) a model (such as the grid size of a distributed snow model). The different types of scales are denoted as process scale, measurement scale and model scale, respectively. Interpolations, extrapolations, aggregations, and disaggregations are viewed as a change in model scale and/or measurement scale. In a first step we examine, in a linear stochastic analysis, the effect of measurement scale and model scale on the data and the model predictions. It is shown that the ratio of the measurement scale and the process scale, and the ratio of the model scale and the process scale are the driving parameters for the scale effects. These scale effects generally cause biases in the variances and spatial correlation lengths of satellite images, field measurements, and simulation results of snow models. It is shown, by example, how these biases can be identified and corrected by regularization methods, At the core of these analyses is the variogram. For the case of snow cover patterns, it is shown that it may be difficult to infer the true snow cover variability from the variograms, particularly when they span many orders of magnitude. In a second step we examine distributed snow models which are a non-linear deterministic approach to changing the scale. Unlike in the linear case, in these models a change of scale may also bias the mean over a catchment of snow-related variables such as SWE There are a number of fundamental scaling issues with distributed models which include subgrid variability, the question of an optimum element size, and parameter identifiability. We give methods for estimating subgrid variability. We suggest that, in general, an optimum element size may not exist and that the model element scale may in practice be dictated by data availability and the required resolution of the predictions. The scale effects in distributed non-linear models can be related to the linear stochastic case which allows us to generalize the applicability of regularization methods. While most of the paper focuses on physical snow processes, similar conclusions apply and similar methods are applicable to chemical and biological processes.

Spin-Valve Heads for 20 Gbit/inch2 Recording

Spin-valve (SV) heads with antiferromagnetic control layers for 20 Gbit/inch2 recording were designed by solving the Landau-Lifshitz-Gilbert equation. The calculated SV-head model has a read track width of 500 nm and a detected minimum bit length of about 50 nm recorded on a medium whose thickness, tmag, is 14 nm, and the product of remanent flux density, Br, and thickness, tmag, is 50 Gµm. The head-to-medium spacing is 30 nm. When the sensing-current density is less than about 5.0×107A/cm2, the thickness of the pinning layer and the free layer is appropriate to be 2.0 nm and 3.0 nm, respectively. The resolution, Vhigh/Vlow, is about 0.67 when the optimum shield gap length, G, is 80 nm. The resolution depends on the sensing-current density, J, as well as the gap length G. We obtained a low-density output voltage of 700 µVp-p, which is practically applicable, by selecting the optimum element size.

Stress‐intensity factor computation in three dimensions with quarter‐point elements

AbstractA consistent method for computing stress‐intensity factors from three‐dimensional quarter‐point element nodal displacements is presented. The method is generalized to permit functional evaluation of stress‐intensity factors along the crack front. Embedded, surface, and corner crack problems are solved using the proposed technique. Results are compared to previous finite element and boundary element solutions. The comparison shows that use of the functional evaluation technique allows a dramatic decrease in problem size while still maintaining engineering accuracy. Next, a three‐dimensional stress‐intensity factor calibration of an unusual specimen configuration is presented. By taking advantage of the proposed technique, the calibration was performed with little difference in cost over the more usual two‐dimensional approach. Moreover, the three‐dimensional solution revealed intersting behaviour that would have been undetected by a two‐dimensional solution. Finally, the results of a study on optimum size of the quarter‐point element are presented. Surprisingly, Poisson ratio is shown to have marked effect on optimum element size.