Element Mesh Size Research Articles

A Goal-Oriented High-Order Anisotropic Mesh Adaptation Using Discontinuous Galerkin Method for Linear Convection-Diffusion-Reaction Problems

We deal with the numerical solution of a linear convection-diffusion-reaction equation using the discontinuous Galerkin method of arbitrary polynomial approximation degree on anisotropic triangular grids. We derive a posteriori goal-oriented error estimates taking into account the anisotropy of mesh elements. The resulting error estimates are employed for the construction of an anisotropic mesh adaptation algorithm which locally optimizes the size and shape of mesh elements. The computational performance is demonstrated by several numerical experiments.

An Analytical Review of the Numerical Methods used for Finite Element Modeling of Traumatic Brain Injury.

Dozens of finite element models of the human brain have been developed for providing insight into the mechanical response of the brain during impact. Many models used in traumatic brain injury research are based on different computational techniques and approaches. In this study, a comprehensive review of the numerical methods implemented in 16 brain models was performed. Differences in element type, mesh size, element formulation, hourglass control, and solver were found. A parametric study using the SIMon FE brain model was performed to quantify the sensitivity of model outputs to differences in numerical implementation. Model outputs investigated in this study included nodal displacement (commonly used for validation) and maximum principal strain (commonly used for injury assessment), and these results were demonstrated using the loading characteristics of a reconstructed football concussion event. Order-of-magnitude differences in brain response were found when only changing the characteristics of the numerical method. Mesh type and mesh size had the largest effect on model response. These differences have important implications on the interpretation of results among different models simulating the same impacts, and of the results between model and in vitro experiments. Additionally, future studies need to better report the numerical methods used in the models.

On Evaluation and Comparison of Blast Loading Methods Used In Numerical Simulations

It is crucial to assess the dynamic behavior of structures exposed to blast loading in order to improve the integrity and survivability. Numerical simulations are widely used to predict the response of structures under blast loading. A commercial nonlinear finite element code, LS-DYNA provides three blast loading methods: Empirical blast modeling technique CONWEP, Arbitrary Lagrangian Eulerian technique (ALE), and hybrid CONWEP - ALE technique. In this study, an experimental testing of a flat plate subjected to blast loading is modeled using these three blast loading methods in LS-DYNA. Mesh resolution study of ALE formulation is conducted to determine the influence of element mesh size on predicting blast loading effects that is converted through fluid structure interaction algorithm from Eulerian to Lagrangian type of elements. It is drawn a comparison between peak pressures calculated in simulations and maximum dynamic deformation measured in the field test. Finally, the discussion and conclusion are provided.

Modelling of ground vibration from tunnels in a poroelastic half-space using a 2.5-D FE-BE formulation

This paper presents an improved two-and-a-half-dimensional (2.5-D) finite element-boundary element (FE-BE) model to predict train-induced vibrations from a tunnel with an arbitrarily shaped cross-section embedded in a poroelastic half-space. The proposed model considers both the saturated porous characteristic of the soil and the free surface effect. A 2.5-D BE model based on the Green’s function for a poroelastic half-space is developed to simulate the soil surrounding the tunnel. The discretization of the infinite ground surface is not required, which avoids spurious reflections induced by mesh truncations and significantly reduces the mesh size of boundary elements. The 2.5-D BE model for saturated soils and the 2.5-D FE model for tunnels are coupled via the boundary conditions on the soil–tunnel interface. The track components are coupled with the tunnel-soil model to more accurately predict vibrations induced by underground railways. After being verified via comparison with an existing model, the proposed model is used to assess train-induced vibrations from a quasi-rectangular tunnel in a poroelastic half-space. Analysis of vibrations induced by the single-line load and double-line load on rails is conducted, respectively. The results show that the insertion gain, which is greater than 30 dB, is highly dependent on the frequency and observation position. When the saturated soil is simplified as the equivalent single-phase elastic soil, the soil displacement tends to be overestimated while the soil stress is underestimated. A saturated soil model may more accurately describe train-induced vibrations from a tunnel in the water-rich region.

Analyzing the Effect of Voxel Mesh and Surface Mesh Application on Residual Stress by Simufact Additive Software

Supplementary tools are needed to perform the engineering process in additive manufacturing. Simufact Additive is a simulation tool of MSC Software that provides a solution for structural behavior during this process. Simufact Engineering and MSC Software have released a software solution to predict the most critical failure in metal AM (Additive Manufacturing) – part distortion. Analyzing provides a solution for industrial process engineers to shorten their process development time and produce high quality parts with this novel manufacturing methodology, reaching analyzing provides printing parts “right the first time”. Metal powder bed fusion manufacturing faces many challenges. The main issue is occurs distortions and high residual stresses. The aim of the study analysis of effects on voxel-based surface mesh applications on bracket part used in aviation. In this study, the voxel mesh element size increases, the amount of distortion calculated on the part decreases. Increasing the element size value will reduce the working time.

Strain-injection and crack-path field techniques for 3D crack-propagation modelling in quasi-brittle materials

This paper presents a finite element approach for modelling three-dimensional crack propagation in quasi-brittle materials, based on the strain injection and the crack-path field techniques. These numerical techniques were already tested and validated by static and dynamic simulations in 2D classical benchmarks [Dias et al., in: Monograph CIMNE No-134. International Center for Numerical Methods in Engineering, Barcelona, (2012); Oliver et al. in Comput Methods Appl Mech Eng 274:289–348, (2014); Lloberas-Valls et al. in Comput Methods Appl Mech Eng 308:499–534, (2016)] and, also, for modelling tensile crack propagation in real concrete structures, like concrete gravity dams [Dias et al. in Eng Fract Mech 154:288–310, (2016)]. The main advantages of the methodology are the low computational cost and the independence of the results on the size and orientation of the finite element mesh. These advantages were highlighted in previous works by the authors and motivate the present extension to 3D cases. The proposed methodology is implemented in the finite element framework using continuum constitutive models equipped with strain softening and consists, essentially, in injecting the elements candidate to capture the cracks with some goal oriented strain modes for improving the performance of the injected elements for simulating propagating displacement discontinuities. The goal-oriented strain modes are introduced by resorting to mixed formulations and to the Continuum Strong Discontinuity Approach (CSDA), while the crack position inside the finite elements is retrieved by resorting to the crack-path field technique. Representative numerical simulations in 3D benchmarks show that the advantages of the methodology already pointed out in 2D are kept in 3D scenarios.

New approach for getting better accuracy with mesh dependent material properties

Based on the relationship between finite element (FE) solution and mesh size, a new approach based on mesh depending on the material properties is proposed to make the finite element analysis results more efficient and more close to the optimal solution. This optimal solution is often evaluated either by experiment or by finite element method (FEM). At the opposite of the accuracy obtained by sensitivities analysis of the FEM which requires time-consuming, our approach allows getting the optimal meshing based on the material properties.

An h-adaptive thermo-mechanical phase field model for fracture

In this work, brittle fracture and thermo-mechanical induced cracks are simulated using a phase field model in 2D and 3D continua in homogeneous and heterogeneous materials. The phase field model for fracture has specific regulations regarding the finite element mesh size. Therefore, a mesh refinement algorithm by adopting a predictor-corrector mesh refinement strategy is used in both applications of mechanical and thermo-mechanical fracture models. Several mechanical and thermo-mechanical examples are presented in this work to prove the capability of the proposed numerical implementation. The multi-field problems are solved using a staggered solution algorithm with and without the parallelization of the system equations. The simulation times of the tested specimens are compared for different meshing criteria, adaptive refinement, pre-refinement of the expected crack path, and the global refinement of the specimen.

Hareketli Ve Sabit Cisimler İçin Ağ Yama Yöntemi

An efficient and versatile mesh method is suggested and implemented for problems involving individual overlapping mesh blocks around moving objects. The overlapped mesh blocks are combined using a stitching stripe, which considers smooth transition of the mesh element size between the blocks. Interpolation of the flow values between the mesh blocks is not needed. This is considered as a relative advantage of this method compared to the overset mesh method. Unsteady flow around an oscillating body test case is used to demonstrate applicability of this method. Other test cases include hypothetical multiple flapping airfoils in relative motion and store separation from a store bay.

Implementation of the Theory of Critical Distances using mesh control

The Theory of Critical Distances (TCD) is a method for predicting fatigue and fracture at stress concentration features. It is extensively used in the design of engineering components, being a relatively simple approach based on post processing of finite element analysis (FEA). It requires only one additional material parameter, the so-called critical distance, L. However its implementation for engineering components of complex shape can be difficult because of the need to use a fine mesh and the requirement to obtain stress/distance path information for the feature being investigated. In this paper we propose a new approach by which predictions can be made more easily through control of the size and type of mesh used. We found that by setting the element size to be a simple multiple of L and by using certain other mesh controls which are generally available in commercial software such as ANSYS, fatigue behaviour could be predicted by simply using the “hot spot stress”, i.e. the maximum stress at the notch root. With this approach the user avoids excessive mesh refinement and does not need to obtain the stress at the critical distance in order to make the prediction. We tested eight different stress concentration features including cracks, sharp notches, blunt notches and V-shaped notches, along with an example component (a welded joint). We found that the error in using this approach, compared with that of the usual implementation of the TCD (Point Method) was acceptably small (less than 20%) in the great majority of cases. A few cases in which larger errors arose were found to be due to particular combinations of mesh element size, feature size and component size which caused difficulties for the automatic mesh generation software. This new approach will allow the TCD to be used more easily, for a wider range of industrial components, structures and materials.

A Tensile Criterion to Minimize FE Mesh-Dependency in Concrete Beam under Blast Loading

This paper focuses on the mesh-size dependency in numerical simulations of reinforced concrete (RC) structures subjected to blast loading. A tensile failure criterion that can minimize the mesh-dependency of simulation results is introduced based on the fracture energy theory. In addition, conventional plasticity based damage models for concrete such as the CSC model and the HJC model, which are widely used for blast analyses of concrete structures, are compared with the orthotropic model that adopts the introduced tensile failure criterion in blast tests to verify the proposed criterion. The numerical predictions of the time-displacement relations at the mid-span of RC beams subjected to blast loading are compared with experimental results. The analytical results show that the numerical error according to the change in the finite element mesh size is substantially reduced and the accuracy of the numerical results is improved by applying a unique failure strain value determined by the proposed criterion.

Dynamic 2.5-D Green's function for a point load or a point fluid source in a layered poroelastic half-space

The complete dynamic two-and-a-half-dimensional (2.5-D) Green's function for an internal point load or fluid source buried in a layered poroelastic half-space is derived and applied to the 2.5-D boundary element method (BEM) in this paper. Based on Biot's theory, the general solutions are derived using the potential decomposition method and the Fourier transform. Utilizing the boundary conditions of the free surface, interfaces and bottom half-space, as well as the general solutions, the complete 2.5-D Green's function for a layered poroelastic half-space is obtained using the transmission and reflection matrix (TRM) method. The solutions presented in this paper are free of numerical instability for the high frequency and large layer thickness. The proposed 2.5-D Green's function is verified by comparison with the existing solutions. A case study of calculating vibrations from a semi-circular tunnel embedded in a layered poroelastic half-space is presented using the 2.5-D BEM along with the proposed 2.5-D Green's function. The layer interfaces and the surface of the poroelastic half-space no longer have to be meshed, avoiding spurious reflections at mesh truncations. The boundary element mesh can be limited to the surface of the tunnel, significantly reducing the size of the boundary element mesh.

FEM simulation research of natural frequency vibration of crankshaft from internal combustion engine

The article presents vibration simulation studies of a crankshaft used in internal combustion engine. The simulation was performed using FEM method. The study was conducted in Abaqus software, and a shaft model was implemented in Catia v5. The influence of a mesh element size on the results of obtained calculations was analysed. A shaft which will be used in the ultralight aircraft engine was the subject of research. Results show the first 10 frequency modes and 12 grid examples for various element sizes, from 9 to 1.3 mm. Moreover, the effect of mesh size on the obtained results is presented. It has been proven that the maximum error for two extreme results (the densest and sparsest grid) is approximately 1.4%; therefore, it is justified to carry out calculations of own vibration on a fatal grid. Results presented herein will be used in the future work on the crankshaft geometry modifications.

Modeling of Hydraulic Fracture of Concrete Gravity Dams by Stress-Seepage-Damage Coupling Model

High-pressure hydraulic fracture (HF) is an important part of the safety assessment of high concrete dams. A stress-seepage-damage coupling model based on the finite element method is presented and first applied in HF in concrete dams. The coupling model has the following characteristics: (1) the strain softening behavior of fracture process zone in concrete is considered; (2) the mesh-dependent hardening technique is adopted so that the fracture energy dissipation is not affected by the finite element mesh size; (3) four coupling processes during hydraulic fracture are considered. By the damage model, the crack propagation processes of a 1 : 40 scaled model dam and Koyna dam are simulated. The results are in agreement with experimental and other numerical results, indicating that the damage model can effectively predict the carrying capacity and the crack trajectory of concrete gravity dams. Subsequently, the crack propagation processes of Koyna dam using three notches of different initial lengths are simulated by the damage model and the coupling model. And the influence of HF on the crack propagation path and carrying capacity is studied. The results reveal that HF has a significant influence on the global response of the dam.

Numerical and Experimental Investigations on a Three-Dimensional Rod-Plate Impact

There are a few numerical simulation methods available for impact problems. However, most numerical results are not validated experimentally. The goal of this paper is to examine how well the simulation results correspond to the physical reality. In this work, normal and oblique impacts of a hemispherical-tip rod on a square plate are investigated both numerically and experimentally. In the numerical approach, finite element method is used to discretize the contact bodies to describe the deformation precisely combined with the floating reference frame method to describe the rigid motion. In the experimental study, strain gauges and Laser Doppler Vibrometers are employed to measure the high-frequency impact responses. Detailed comparative studies between numerical and experimental results are performed. In the case of normal impact, great attention is given to investigate the influence of finite element mesh size on the simulation accuracy and a “Prediction-Refinement” discretization strategy is proposed for obtaining a mesh which is optimal for impact dynamics. In the case of oblique impact, the influence of Coulomb’s friction coefficient is investigated additionally. It shows that the numerical results are in good agreement with the experimental results for both normal and oblique impacts.

Prediction of gas–liquid flow in an annular gap bubble column using a bi-dispersed Eulerian model

We present and discuss numerical results from simulations of the air–water flow in an annular gap bubble column of 0.24m internal diameter, at air superficial velocities ranging from 0.004m/s to 0.225m/s, covering the homogeneous and heterogeneous flow regimes. A bi-dispersed Eulerian model is implemented to account for both the stabilizing and destabilizing effects of small and large bubbles. Sensitivity studies on the mesh element size, time step size and number of outer iterations per time step are performed and most appropriate simulation parameters and mesh are used to predict the gas holdup curve. Comparison with two mono-dispersed models is provided to emphasize the necessity of a bi-dispersed approach for the accurate prediction of the homogeneous flow regime, given the poly-dispersed nature of the flow investigated. Two different approaches for the characterization of the small and large bubbles groups are also discussed. We found that the relative amount of small bubbles is an important input parameter for the present model and can be provided using available empirical correlations or experimental data. The results obtained from the simulations also demonstrated the necessity of a population balance model able to capture the bubbles coalescence and breakup phenomena for the correct prediction of the heterogeneous flow regime.

Bayesian-network-based system identification of spatial distribution of structural parameters

Structural deterioration or damage in civil infrastructures may results in severe losses of properties and human lives. To prevent such situations, structure health monitoring (SHM) technologies have been developed in recent decades. As one of the SHM technologies, so-called system identification (SI) methods aim to estimate structural parameters by minimizing an error function consisting of measured and calculated responses of a structure under the same loading condition. Such optimization-based SI algorithms may suffer from ill-posedness of the inverse problem, which may result in non-uniqueness of solutions or non-stability of the optimization process. In this paper, in order to avoid issues related to ill-posedness, an SI method based on the Bayesian Network (BN) technology is developed, especially for probabilistic identification of spatial distribution of structural parameters. Utilizing graph theories, a BN describes random variables by nodes connected by links, which represent conditional probability tables (CPT) explaining the probabilistic relationship between the linked nodes. For effective SI using BN, this study proposes a BN graph model, which employs a bi-variate Gaussian function as a shape function describing the spatial distribution of a structural parameter with a small number of parameters. The parameters of the Gaussian (shape) function are considered as nodes in the BN to describe various spatial distribution patterns using a small number of parent nodes. Using this modeling approach, the number of the BN nodes is not affected by the size of the finite element (FE) mesh. Thus, the approach prevents the BN graph from growing to an intractable size even if the FE analysis requires smaller meshes to improve the accuracy of the structural analysis. Using the constructed BN, information on applied loads, and observed structural responses, a BN inference algorithm effectively updates the prior distribution of spatial distribution parameters to the posterior distribution. The proposed method is tested and demonstrated by numerical examples. Using a variety of structural deterioration scenarios, the SI results by the proposed method are compared with those by maximum likelihood estimation (MLE), and an FE-updating method. During the test, the influences of measurement errors, and incomplete/missing data on the performance of the methods are also investigated. The results show that the proposed SI approach is more stable and robust than the other tested methods, and potentially has more merits that are worth investigating in future research.

A priori error estimates of the DtN-FEM for the transmission problem in acoustics

This paper is concerned with a variational approach solving the two-dimensional acoustic transmission problems. The original problem is reduced to an equivalent nonlocal boundary value problem by introducing an exact Dirichlet-to-Neumann (DtN) mapping in terms of Fourier expansion series on an artificial boundary. Uniqueness and existence of solutions in appropriate Sobolev spaces are established for the corresponding variational problem and its modification due to the truncation of DtN mapping. A priori error estimates containing the effects of both element meshsize and truncation order of series for the finite element approximation are derived. Numerical experiments are also presented to illustrate the efficiency and accuracy of the numerical scheme.

Solving steady incompressible Navier–Stokes equations by the Arrow–Hurwicz method

This article is devoted to analyzing an Arrow–Hurwicz type method for solving incompressible Navier–Stokes equations discretized by mixed element methods. Under several reasonable conditions, it is proved by a subtle argument that the method converges geometrically with a contraction number independent of the finite element mesh size h, even for regular triangulations. A series of numerical examples are provided to illustrate the computational performance of the method.

Sensitivity Analysis of the Tetrapolar Electrical Impedance Measurement Systems Using COMSOL Multiphysics for the non-uniform and Inhomogeneous Medium

One of the major problems with Electrical Impedance Tomography (EIT) is the lack of spatial sensitivity within the measured volume. In this paper, sensitivity distribution of the tetrapolar impedance measurement system was visualized considering a cylindrical phantom consisting of homogeneous and inhomogeneous medium. Previously, sensitivity distribution was analysed analytically only for the homogeneous medium considering simple geometries and the distribution was found to be complex1,2. However, for the inhomogeneous volume conductors sensitivity analysis needs to be done using finite element method (FEM). In this paper, the results of sensitivity analysis based on finite element method using COMSOL Multiphysics simulation software are presented. A cylindrical non-uniform, inhomogeneous phantom, which mimics the human upper arm, was chosen to do the experiments by varying different parameters of interest. A successful method for controlling the region of interest was found where the sensitivity was maximum. Refining the finite element mesh size and introducing multifrequency input current (up to 1 MHz) this simulation method can be further improved.Dhaka Univ. J. Sci. 64(1): 7-13, 2016 (January)