Finite Element Mesh Density Research Articles

Compressive strength of cylindrical specimens generated by topology optimization: influence of finite element mesh refinement

ABSTRACT Topology optimization (TO) is a mathematical method that optimizes a part’s layout, maintaining the project’s spatial constraints, considering loads, boundary conditions, and manufacturing to maximize its performance. Through mesh analysis, non-essential areas in the structure are identified, allowing efficient material removal without compromising its integrity. However, it is not usual to use TO without changing the part layout, focusing only on removing its internal mass, as is done in this paper. Therefore, two sets of cylindrical ABS samples were generated: one with an internal structure obtained by TO, varying the density of finite element mesh through the SolidWorks Software, and another with an internal structure chosen in the slicing stage before 3D printing. Then, the samples were subjected to the same compression tests. According to the results, all models support loads above the 10 kN specified. Unlike theoretical expectations, the best performance was from the coarse mesh TO, which was statistically equivalent to the tri-hexagonal and grid infill patterns. However, TOs made with medium and fine mesh pushed the limit of the piece shape, making the wall very thin and reducing its resistance. Using the infill pattern proved to be simpler to execute and less time-consuming to manufacture.

Experimental and computational models for simulating the oral breakdown of food due to the interaction with molar teeth during the first bite

The first bite involves the structural breakdown of foods due to the interaction with teeth and is a crucial process in oral processing. Although in vitro experiments are useful in predicting the oral response of food, they do not facilitate a mechanistic understanding of the relationship between the intrinsic food mechanical properties and the food behaviour in the oral cavity. Computer simulations, on the other hand, allow for such links to be established, offering a promising design alternative that will reduce the need for time consuming and costly in vivo and in vitro trials. Developing virtual models of ductile fracture in soft materials, such as food, with random and non-predefined crack morphology imposes many challenges. One of the most important is to derive results that do not depend on numerical parameters, such as Finite Element (FE) mesh density, but only physical constants obtained through independent standard mechanical tests, such as fracture strain and/or critical energy release rate. We demonstrate here that this challenge can be overcome if a non-local damage approach is used within the FE framework. We develop a first bite FE modelling methodology that provides mesh independent results which are also in agreement with physical first bite experiments performed on chocolate. The model accounts for key features found in chocolate and a wide range of compliant media, such as rate dependent plasticity and pressure dependent fracture initiation strain. As a result, our computational methodology can prove valuable in studying food structure-function relationships that are essential in product development.

Sensitivity analysis of numerical model parameters for optimized PEH responses

With the increasing popularity of wearable devices, typically employed in fitness and health monitoring, there is an evident need to extend their autonomy and replace the conventional power sources with environmentally friendly alternatives. Piezoelectric energy harvesting systems, optimized for collecting kinetic energy from random human motion and transduce it into electrical energy, represent a viable option for powering autonomous wearables. Since established analytical methods are unable to model the behaviour of piezoelectric harvesters with complex optimized geometries, suitable numerical models need to be employed for their design. This implies the need of a thorough study focused on the mechanical engineering design optimization purposes of how the finite element type and mesh density affect the uncoupled modal and coupled transient responses of a new class of optimised design configurations of the studied devices.

3D Finite Element Analysis of a Concrete Dam Behavior under Changing Hydrostatic Load: A Case Study.

In this study, a large arch-gravity Moste Dam was analyzed, where an automated system for the measurements of horizontal displacements of the upper part of the dam was established. Two-dimensional (2D) and three-dimensional (3D) analyses of dam behavior, taking into account the earth pressures and the hydrostatic load, using the finite element method (FEM)-based computer program DIANA, were performed. The influence of lowering the water level of the reservoir by 6.2 m, on the horizontal displacements of the upper part of the dam, at stationary temperature conditions, was investigated. It was found that the results of the performed 2D and 3D FEM analyses fitted in very well with the result of experimentally determined measurement of horizontal displacements (which was 0.48 mm in the upstream direction) that was obtained using a hanging pendulum. An additional comparison of the results of 3D calculations showed that the finite element mesh density had a small effect on the calculated horizontal displacements.

К вопросу моделирования высоковольтного изолятора в программном комплексе COMSOL Multiphysics 5.6

The article discusses the main aspects of modeling suspended polymer high-voltage insulation of overhead power lines (PTL) in the COMSOL Multiphysics 5.6 software package. Analytical expressions of the mathematical model of the electromagnetic field around the insulator are given, on the basis of which a numerical solution is formed within the software package that allows you to build a model of the electric field in two-dimensional and three-dimensional space. There are three main stages of working with the program interface. At the first stage, the task of the geometric dimensions of the model and the surrounding area is considered, attention is paid to the formation of the design features of polymer insulators. In the second stage, the physical properties of the structural materials of the insulator, as well as the surrounding space, are described. The third stage is reduced to the determination of boundary conditions for solving the Poisson differential equation. Recommendations for finite element mesh density are given. A gradient picture of the distribution of the electric potential near the surface of the insulator is presented. The graphs of the distribution of the normal component of the electric field strength along the surface of the insulator are also plotted. On the basis of the obtained results, the influence of external factors on the properties of the polymer insulator is studied. A possible variant of modeling influencing factors, such as pollution and moisture, by making changes in the description of the physical properties of the insulator surface, namely by including a uniform and continuous layer with a given conductivity, is described. The distribution of the normal component of the electric field strength along the surface of the insulator with contamination is obtained. The results of modeling the electric field distribution with the presence of contamination on the surface of the insulator and its absence are summarized in the table where the electric field strength is indicated depending on the distance to the traverse. Based on the analysis of the results obtained, an assumption is made about the overestimated level of the maximum electric field on the insulators recommended by the manufacturers. The convergence of the considered models with the experimental data obtained in the course of long-term observation of the dynamics of the degradation and aging processes of the surface of polymer suspended insulators of overhead transmission lines is discussed.

Fatigue Strength of an Aircraft Wing Panel with a Repair Patch Based on the Filled Hole at Various Values of Interference Fit

The main goal of the present paper is a numerical study of the fatigue strength indicators in filled holes using the example of a repair patch on an aircraft panel. The stress state characteristics of the first hole were considered in most detail being the most load-bearing and therefore the most susceptible to the formation of fatigue cracks. The analysis of the finite element mesh density in the calculated holes was carried out to stabilize the obtained values of the equivalent stresses in the contact elements. The acquired data was further processed to obtain the dependencies of the fatigue safety margins reduced to a symmetric cycle in normal and shear stresses for a filled hole with a clearance fit, an interference fit and for a mixed type of bolt setting. The results were used to determine a preferable type of fit for the bolted joint of the first hole in the patched panel for the compressed and tensioned zone.

Concise Data Set Formulation for Dynamically Loaded Conformal Elastohydrodynamic Lubrication Problems

AbstractThis paper introduces a concise data set formulation for efficient modeling of dynamically loaded conformal elastohydrodynamic lubrication (EHL) problems. The data set represents the structural elasticity of the bearing members and is constructed independently of the lubricant film model. Data set construction involves modification of a previously published mode-based EHL formulation such that the resulting structural information is insensitive to changes in finite-element mesh density and thus to the modeling process itself. Curve-fitted expressions of modal information are introduced for elastic structures, which otherwise would normally be represented by large structural matrices. A data set is formulated for the sample case of a dynamically loaded big-end connecting-rod bearing, and the resulting bearing performance agrees well with previously published node- and mode-based EHL methods.

Numerical Analysis of Stress Concentration in Non-uniformly Corroded Small-Scale Specimens

A numerical evaluation of stress concentrations of corroded plate surfaces of small-scale corroded steel specimens is compared with the experimentally estimated ones. Eleven specimens were cut from a steel box girder, which was initially corroded in real seawater conditions. The surface of all corroded specimens was analysed applying photogrammetry techniques, and a statistical description of an idealised corroded surface of each specimen was established. Fatigue lives of specimens are determined from the fatigue tests. Based on experimentally obtained fatigue lives, the stress concentration factors are calculated concerning the ideally smooth specimens. The correlation between the statistical parameters of the corroded specimen surfaces and the estimated stress concentration factors is analysed. Idealised corroded surfaces, converted in graphical format, are then used for the finite element modelling in ABAQUS software, and stress concentration factors are estimated from the finite element results. A convergence study is performed to determine the appropriate finite element mesh density. Comparison between experimentally obtained and numerically estimated stress concentration factors is performed as well as correlation analysis between actual and finite element predicted crack locations.

Study on calculation methods for acoustic radiation of axisymmetric structures in finite water depth

In this paper, a kind of FEM–WSM (Finite Element Method–Wave​ Superposition Method) is used to calculate the acoustic radiation of axisymmetric structures in finite water depth. FEM is used to solve the dry modes of axisymmetric structures, and WSM is applied along with the dry mode method to consider fluid–structure interaction effects and calculate the acoustic radiated field. This method combines the advantages of FEM and WSM. On one hand, it is suitable for complex or large axisymmetric structures on the one hand. On the other hand, it has higher computational efficiency than the FEM, and the computational domain size for the water is not limited. As long as the Green’s function is tailored for the boundary condition, the acoustic radiated field of axisymmetric structures in more complex ocean acoustic environments can be calculated by using this method. Besides, a least-square method is used to reduce the distortion resulting from computational errors of the modal estimates. The influence of the number of source and field points and the finite element mesh density on the calculation accuracy are discussed, eliciting some disciplinary conclusions. Using a spherical shell and a capsule shell as models, the results from the present approach, a semi-analytical method, and the crude FEM are compared to verify the correctness and efficiency. Based on numerical examples, the influence of the sea surface and the seafloor on the acoustic radiated field of structures in finite water depth is also analyzed.

Effects of algorithmic simulation parameters on the prediction of extreme value fatigue indicator parameters in duplex Ti-6Al-4V

Fatigue Indicator Parameters (FIPs) serve as surrogate measures of the driving force to form and grow transgranular fatigue cracks in metals and alloys. FIPs are volume averaged over sub-grain regions using a crystal plasticity finite element method (CPFEM) model of polycrystalline microstructures. Questions naturally arise regarding the ability to computationally simulate a sufficient volume of microstructure samples to objectively build a converged estimate of the distribution of maximum FIPs above some threshold, referred to as an Extreme Value Distribution (EVD). A reliable EVD can be estimated by considering FIPs computed from samples comprised of a sufficient number of grains. A recently developed statistical technique is exploited in this work to predict the maximum FIPs in a large volume of duplex Ti-6Al-4V. Effects of several crucial algorithmic parameters in the CPFEM simulations are explored, including the sub-grain FIP averaging volume, the statistical volume element (SVE) size of each microstructure instantiation, number of SVEs necessary to project extreme value FIPs for larger volumes, and finite element mesh density. The SVE size defines the number of grains in a single simulation and therefore controls the number of nearest and second nearest neighbor grain interactions that dominate FIP EVDs. This interplays closely with the number of SVEs needed to establish reliable estimates of FIP EVDs for larger volumes of microstructure. We demonstrate that the number of grains sampled is a critical consideration in these types of CPFEM simulations aimed at EVDs. The statistical technique for estimation of EVD FIPs is relatively insensitive to both the SVE size and mesh density of a single simulation, provided a sufficient number of individual grains are sampled to capture dominant effects of microstructure heterogeneity. Furthermore, averaging FIPs over different sub-grain volumes results in consistent predictions of the maximum FIPs.

Experimental and numerical dataset of Microbond test using optical fibres for strain.

This data article provides useful information often required for numerical modeling of the so-called microbond tests. It includes the experimental and simulation data of the microbond testing using Fibre Bragg Grating (FBG) fibres for optical strains. Microbond testing was performed on five different droplets of varying embedded length and diameter to collect the data. Finite element simulation was carried out and modelling was validated, by using two variables force and strain, to collect the data. The output data of the fitted models is given and is also visualized via graphs of force-strain derivative curves. The data of the simulations is provided for different finite element mesh densities. Here, to clarify the type and form of the data for the use by readers, the energy distribution curves describing various functionalities of the droplet, fibre and interface are presented. For further reading, the interpretation and analysis of this data can be found in a research article titled “3D interfacial debonding during microbond testing: Advantages of local strain recording” (R. Dsouza et al., 2020) [1].

Modeling porosity migration in LWR and fast reactor MOX fuel using the finite element method

An engineering-scale finite element simulation of pore migration in oxide fuel is presented. The porosity field is governed by an advection-diffusion equation which is coupled to the fuel temperature and stress fields through the thermal conductivity and volumetric heat source term. The engineering-scale porosity equation models the microscopic process of vapor transport of fuel across pores, taking into account thermal and vapor pressure gradients within the fuel. In the simulations, the porosity is initialized to a constant value at every point in the domain, and as the temperature gradient is increased by application of a heat source, the pores move up the thermal gradient and accumulate at the center of the fuel in a time frame that is consistent with experimental observations. Results from representative simulations are provided to demonstrate the new capability, and we show that a sufficiently high power ramp rate limits restructuring and leads to a corresponding increase in fuel temperature. We also discuss the finite element mesh density required to compute pore migration and present multidimensional results.

FREE VIBRATION ANALYSIS OF CURVILINEARLY STIFFENED KIRCHHOFF-MINDLIN PLATES

Compared with traditional stiffened plates, curvilinearly stiffened plates can deliver the mechanical properties of materials more adequately. In mechanical analysis of stiffened thick plates, Reissner-Mindlin theory is usually adopted. However, difficulties are encountered in connection with shear locking when the plate thickness approaches zero. In order to avoid the above problem, the discrete Kirchhoff-Mindlin theory was investigated by employing the assumption of shear strain field. An efficient finite element approach for free vibration analysis of curvlinearly stiffened KirchhoffMindlin plates is presented in this paper. The discrete Kirchhoff-Mindlin triangular (DKMT) element and the Timoshenko curved beam element are employed for modeling the plate and the stiffeners, respectively. The finite element equation is established through the displacement interpolation function of plate and the displacement compatibility conditions at the plate-stiffener interfaces. In order to verify the efficiency and accuracy of the present method, linearly stiffened thin plate and curvilinearly stiffened thin and thick plates are used as numerical examples. The reasonable finite element mesh density is selected by convergence and accuracy analysis. The first 20 natural frequencies of the linearly stiffened plate are in good agreement with the literature. In the examples of the curvilinearly stiffened plate, the number of plate elements satisfying the convergence condition is 2469, while the number in Nastran model is 6243. The maximum error of the natural frequency between the present method and Nastran is 3.4%. Results show that present approach can guarantee the accuracy of calculation with less number of elements. The present method can be applied to the free vibration analysis of both stiffened thin and thick plates.

Modeling of Cementitious Representative Volume Element with Additives

CEMHYD3D has been employed to simulate the representative volume element (RVE) of cementitious systems (Type I cement) containing fly ash (Class F) through a voxel-based finite element analysis (FEA) approach. Three-dimensional microstructures composed of voxels are generated for a heterogeneous cementitious material consisting of various constituent phases. The primary focus is to simulate a cementitious RVE containing fly ash and to present the homogenized macromechanical properties obtained from its analysis. Simple kinematic uniform boundary conditions as well as periodic boundary conditions were imposed on the RVE to obtain the principal and shear moduli. Our current work considers the effect of fly ash percentage on the elastic properties based on the mass and volume replacements. RVEs with lengths of 50, 100 and 200[Formula: see text][Formula: see text] at different degrees of hydration are generated, and the elastic properties are modeled and simulated. In general, the elastic properties of a cementitious RVE with fly ash replacement for cement based on mass and volume differ from each other. Moreover, the finite element (FE) mesh density effect is studied. Results indicate that mechanical properties decrease with increasing mesh density.

Three dimensional crack propagation through mesh-based explicit representation for arbitrarily shaped cracks using the extended finite element method

In this study a three-dimensional extended finite element modeling work is developed for crack propagation analysis of arbitrarily shaped crack(s) under mixed mode loading conditions. An explicit method is proposed for crack geometry characterizations, slicing of the enriched elements, and crack propagations. The method can be used to model multiple cracks propagation and allows for crack geometry transition from internal to surface, and further to through-thickness modalities under arbitrary loading conditions. Benchmark cases are studied and satisfactory agreement between theoretical and numerical results is observed. In addition, comparison between fully explicit and conventional implicit methods is made at different finite element mesh densities. The results show that compared to the conventional implicit method, there is a significant improvement in the obtained stress intensity factors for the fully explicit method at coarse linear hexahedral and quadratic tetrahedral meshes.

Submicron size-scale mapping of carbonate effective elastic properties from FIB-SEM images and finite element method

In this paper, an automatic unstructured focused ion beam (FIB) and scanning electron microscopy (SEM) images induced representative volume element (RVE) finite element (FE) method is developed to predict submicron scale carbonate rock effective Young’s and bulk moduli and Poisson’s ratio on parallel CPU-GPU platform. Based on high resolution-contrast surface morphology and internal fabric-texture structure images from carbonate rock specimen (covered 0.12–64 μm2 area and 8000 μm3 domain), the cubic RVE FE models are constructed from different sites through Avizo with user-defined parameters Matlab coding. The effective Young’s and bulk moduli and Poisson’s ratio of the different RVEs and porosity and pore size are computed by using periodic boundary condition in the well-known FE software Abaqus. FE mesh sensitivity analysis has been conducted where all moduli converge to a certain constant value at larger FE mesh density. The effect of fabric-texture (pore size, shape, and distribution) on the elastic properties is discussed. The correlations between the computed effective elastic properties and pore size, porosity, RVE size have been established. The simulation results show that the effective Young’s and bulk moduli and Poisson’s ratio have strong anisotropic behavior and depend on RVE size, porosity and pore size. The RVE size, porosity and pore size are three independent factors in affecting of the effective elastic moduli, the effect mechanism of porosity and pore size is same while the effect mechanism of RVE size is difference.

Time-independent stochastic design sensitivity analysis of structural systems with second-order accuracy

In the paper, the static sensitivity of complex structures with respect to random design parameters is presented. Using the adjoint system method, based on the mean-point second-order perturbation method, the first two probabilistic moments of time-independent sensitivity are formulated with means and cross-covariances of random design parameters as the input data. It enables one to obtain the second-order accuracy of the solution. The presented formulations are illustrated by a number of numerical examples. The influence of finite element mesh density for the obtained results is discussed using the analysis of the spatial bar dome.

Application of the Value Optimization Model of Key Factors Based on DSEM

The key factors of the damping solvent extraction method (DSEM) for the analysis of the unbounded medium are the size of bounded domain, the artificial damping ratio, and the finite element mesh density. To control the simulation accuracy and computational efficiency of the soil-structure interaction, this study establishes a value optimization model of key factors that is composed of the design variables, the objective function, and the constraint function system. Then the optimum solutions of key factors are obtained by the optimization model. According to some comparisons of the results provided by the different initial conditions, the value optimization model of key factors is feasible to govern the simulation accuracy and computational efficiency and to analyze the practical unbounded medium-structure interaction.

An in-core grid index for transferring finite element data across dissimilar meshes

The simulation of a manufacturing process chain with the finite element method requires the selection of an appropriate finite element solver, element type and mesh density for each process of the chain. When the simulation results of one step are needed in a subsequent one, they have to be interpolated and transferred to another model. This paper presents an in-core grid index that can be created on a mesh represented by a list of nodes/elements. Finite element data can thus be transferred across different models in a process chain by mapping nodes or elements in indexed meshes. For each nodal or integration point of the target mesh, the index on the source mesh is searched for a specific node or element satisfying certain conditions, based on the mapping method. The underlying space of an indexed mesh is decomposed into a grid of variable-sized cells. The index allows local searches to be performed in a small subset of the cells, instead of linear searches in the entire mesh which are computationally expensive. This work focuses on the implementation and computational efficiency of indexing, searching and mapping. An experimental evaluation on medium-sized meshes suggests that the combination of index creation and mapping using the index is much faster than mapping through sequential searches.

Numerical analysis of the influence of number of grains, FE mesh density and friction coefficient on representativeness aspects of the polycrystalline digital material representation – Plane strain deformation case study

Investigation of the influence of digital material representation model parameters of a single phase polycrystalline unit cell on its behavior under loading conditions is the subject of the present paper. Firstly, investigation of the impact of the finite element mesh density on the quality of obtained results is conducted. However, the particular attention is put on the selection of the minimum amount of grains in the microstructure with periodic boundary conditions that can be considered as the representative volume element of a sample subjected to plastic deformation under plane strain. Finally, the influence of different friction coefficient values between tools and the sample, on deformation behavior of the unit cells is evaluated. Obtained data in the form of equivalent strain distributions and homogenized stress–strain curves for the analyzed case studies are presented and discussed within the paper.