Element Mesh Research Articles

Numerical Simulation of Free Surface Deformation and Melt Stirring in Induction Melting Using ALE and Level Set Methods.

This study investigates fixed and moving mesh methodologies for modeling liquid metal-free surface deformation during the induction melting process. The numerical method employs robust coupling of magnetic fields with the hydrodynamics of the turbulent stirring of liquid metal. Free surface tracking is implemented using the fixed mesh level set (LS) and the moving mesh arbitrary Lagrangian-Eulerian (ALE) formulation. The model's geometry and operating parameters are designed to replicate a semi-industrial induction melting furnace. Six case studies are analyzed under varying melt masses and coil power levels, with validation performed by comparing experimentally measured free surface profiles and magnetic field distributions. The melt's stirring velocity and recirculation patterns are also examined. The comparative analysis determines an improved performance of the ALE method, convergence, and computational efficiency. Experimental validation confirms that the ALE method reproduces the free surface shape more precisely, avoiding unrealistic topological changes observed in LS simulations. The ALE method faces numerical convergence difficulties for high-power and low-mass filling cases due to mesh element distortion. The proposed ALE-based simulation procedure is a potential numerical optimization tool for enhancing induction melting processes, offering scalable and robust solutions for industrial applications.

MESHING TRANSFERS IN AUTODESK INVENTOR

In order to improve the execution of drawings of gear elements in the Autodesk Inventor package, an approach to the presentation of geometric information in accordance with the requirements of current standards is proposed, based on the use of developed three-dimensional models of assembly units of gear elements in parametric shells. The basis for the development of the sketch geometry of parametric shells were the basic geometric parameters of the tooth crowns of the elements, since when making drawings of gear meshing elements, the images of the tooth crowns are made in violation of the requirements of current standards. In order to simplify the construction of drawings of gear elements in the Autodesk Inventor package, an algorithm was developed to provide geometric information through the developed three-dimensional models of the parametric shells of the gear crowns of their elements. That is, the geometric information is embedded in the parametric assembly units "gearing in shells". The algorithm is based on working with the parametric shells of the elements of the constituent units, where all the necessary geometric information is represented by a function of the main geometric parameters of real gear crowns. The method of parametric shells considers the issues of touching, implementation, methods of formation of such shells with detailed coverage of their properties and geometric parameters. The rigorous mathematical theory of parametric shells, which involves the joint processing of analytical and geometric information obtained on the basis of the geometry of the gear elements as forming elements, is characterized by generalization in approach and mathematical rigor. At the same time, the presence of toothed crowns of three-dimensional models of gear elements by meshing is ignored. The algorithm for simplified creation of gearing drawings involves making cuts based on sketches, adjusting contour lines and changing the properties of areas in accordance with the requirements of current standards. The library of parametric shells and the algorithm for creating working drawings of both elements and gearing are implemented in the educational process.

COMPUTING THE LOCAL QUALITY CHARACTERISTIC OF TETRAHEDRAL MESH ELEMENTS AS A SOLUTION EXTREME TASK

The paper discusses the problem of calculating the quality characteristic of elements of a triangulation grid (in multidimensional space). We call quality the degree of difference between a mesh element in a sense critical. For example, the difference between a triangle and a degenerate triangle. To calculate this value, the following construction is used. Mesh element vertices are treated as a numbered set of 𝑋 — points point family. In the space of such sets, the metric proposed in early works is introduced. As a result, the problem boils down to calculating the value of dist(𝑋,𝒴) — the distance between a set 𝑋 and a set 𝒴 defined by critical elements. In early works, the problem was solved through the empirical classification of families 𝑌 ∈ 𝒴 and excluding those that are not known to be closest to 𝑋. Namely, such that the offset some point in the 𝑌 family is given by the 𝑌 ′ ∈ 𝒴 family, which is closer to 𝑋. At the same time, empirical classification led to a large amount of calculations. This work gives a standardized classification of the families of the set 𝒴, allowing you to accurately describe the set of 𝒴− ⊂ 𝒴 of such families for which The specified conversion is not possible. That is, 𝒴− is approved dist(𝑋,𝒴) = dist(𝑋,𝒴−) . In addition, a diagram is given for constructing families of the set 𝒴− — analogues of the points of the assumed extremum in the extremum research problem of the function of numerical variables.

Nonlinear structural strength of steel chain contacted with knuckle-shaped plate under lifting conditions

ABSTRACT The study focuses on evaluating the nonlinear structural strength of steel chains in lifting operations, particularly in contact with knuckle-shaped plates, under various loading conditions. Using finite element analysis (FEA), the research examines how different contact angles (0°, 45°, 90°) and materials (SS400, HT32, HT36, ASTM A356) influence the chain’s performance under tensile loading. The analysis categorises four main loading conditions, referred to as 0 degree through 45 degrees to symmetric direction, each representing different orientations of the chain relative to the lifted object. Among these, lifting at 90 degrees consistently showed the lowest ultimate strength across all materials and chain sizes. The primary cause of this weakness was identified as significant stress concentration at the central link, where the loading angle of 90 degrees led to early yielding. This critical loading condition not only reduced the chain’s load-bearing capacity but also increased the risk of premature failure due to localised stress buildup. The study further highlights that as the yield strength of the material increases, the difference in load capacity between non-symmetric 45 and 90 degrees becomes more pronounced, with 90 degrees lifting exhibiting lower strength across the board. For instance, ASTM A356, although generally stronger than SS400, still demonstrated a notable reduction in load capacity under 90 degrees lifting. Mesh convergence tests were performed to ensure the accuracy of the FEA results, confirming that 12 mesh elements were sufficient to accurately model stress distributions. The results also indicated that increasing the chain diameter could improve load-bearing capacity under most loading conditions, but even larger chains were still vulnerable under 90 degrees lifting. In conclusion, 90 degrees lifting presents a critical design challenge due to its inherent weakness, and mitigating stress concentration at the central link is key to improving chain durability and safety. This study’s findings offer valuable insights for engineers, particularly in the shipbuilding and offshore industries, on how to optimise chain design and improve safety in hoisting operations.

Stress distribution and shear lag effect of composite steel plate girder bridges based on spatial fine mesh elements

Stress distribution and shear lag effect of composite steel plate girder bridges based on spatial fine mesh elements

Resistance Welding Joints of CF/PEEK Orthogonal Laminates Strengthened by in situ Grafting of ZnO‐Nanowires: Preparation, Properties, and Mechanism

ABSTRACTA high strength bonding interface by resistance welding has always been a goal for the production of highly reliable resin‐based composite joints. In this work, SS mesh element with grafted ZnO nanowires (SSM@ZnO) was developed for resistance welding of CF/PEEK composite laminates to improving interfacial strength. First, the surface of stainless‐steel mesh (SSM) was modified by in Situ grafting of zinc oxide (ZnO) nanowires via hydrothermal growth method and the as‐obtained product (SSM@ZnO) used to the resistance welding of carbon fiber/polyether ether ketone (CF/PEEK) orthogonal laminates. The dependance of the SSM@ZnO microstructure, heating properties, wettability and interfacial adhesion on the growth time was investigated. The electrical heating rate under constant input power is increased from 4.8°C/s to 7.12°C/s, and IFSS between SSM@ZnO and PEEK resin is increased from original 45 MPa to 61 MPa. The mechanical properties and failure mode of CF/PEEK resistance welding joints were characterized by single lap shear stress (SLSS) and SEM, respectively. At SSM@ZnO growth time of 8 h, the SLSS reaches the maximum value of 52.8 MPa, and the failure mode was shifted from interfacial peeling between CF/PEEK laminate and adhesion layer to fiber tearing of CF/PEEK laminate surface.

Local remesh procedure to model reaming in vertical oil wells drilled through salt rocks

This paper presents an alternative methodology, based on cutting and adjusting finite elements, to model reaming of salt rocks during vertical wells drilling. The developed strategy ensures that the stress, deformation, and displacement fields are maintained after the remesh. To reach the pre-salt hydrocarbon reservoirs it is necessary to pass through thick layers of salt rocks. The mobility of these salt rocks can cause serious operational problems, such as the imprisonment of the drill string, casing collapse and annular entrapment of columns, compromising the casing integrity. Therefore, adequate monitoring of the well diameter must be done constantly throughout the entire drilling process. Thus, reaming procedures may be required to recondition the diameter of the well to its original state. The reaming strategy presented in this work is based on removing and adjusting mesh elements reestablishing the initial radius of the well in specific regions. This procedure improves the precision and realism of the simulations, avoiding the appearance of a gap between the mesh and drill bit passage. Stress graphs along the wellbore and comparisons with real wells data are used to enhance the phenomena understanding and validate the proposed methodology

A novel approach for large-scale hybrid mesh generation on distributed systems

This study presents an approach for the generation of a large-scale viscous mesh using a parallel advancing layer method based on distributed systems with multi-cores. A triangular surface mesh that conforms with the original geometrical model is prepared as input and decomposed into multiple subdomains. A coarser background mesh with high-quality viscous elements from the same model is employed for parallel computation. Instead of using a conventional approach to generate layer-wise prismatic elements, a normal calculation through linear interpolation is implemented to overcome the boundary problems arising in distributed systems. A novel strategy to deal with cross-processor transition elements is proposed to reduce frequent communications during viscous mesh generation. To improve the parallel efficiency, a fast domain decomposition method is introduced to speed up the parallel meshing procedure of tetrahedral elements. Numerical experiments are performed on high-performance computing systems with billions of mesh elements to demonstrate the effectiveness and efficiency of the proposed approach and numerical simulation results represent a promising applicability.

Bayesian mesh optimization for graph neural networks to enhance engineering performance prediction

Abstract In engineering design, surrogate models are widely employed to reduce the computational costs of simulations by approximating design variables and geometric parameters from computer-aided design (CAD) models. However, traditional surrogate models often lose critical information when simplified to lower dimensions, and face challenges in handling the complexity of 3D shapes, especially in industrial datasets. To address these limitations, we propose a Bayesian graph neural network (GNN) framework that directly learns geometric features from CAD mesh representations for accurate engineering performance prediction. Our framework leverages Bayesian optimization (BO) to dynamically determine the optimal mesh element size, significantly improving model accuracy while balancing computational efficiency. This approach addresses the challenge of mesh quality by optimizing mesh resolution, ensuring that critical geometric features are preserved in 3D deep-learning-based surrogate models. Unlike existing models that rely on static or predefined mesh resolutions, our method adapts mesh size based on the task, making it highly flexible for a wide range of engineering applications. Experimental results demonstrate that mesh quality directly impacts prediction accuracy, and the proposed BO-EI GNN model outperforms state-of-the-art models such as 3D CNN, SubdivNet, GCN, and GNN in predicting mass, rim stiffness, and disk stiffness. Our method also significantly reduces the computational costs compared to traditional optimization techniques. The proposed framework shows promising potential for application in finite element analysis (FEA) and other mesh-based simulations, enhancing the utility of surrogate models across various engineering fields.

Simulation of the Collapse Mechanism of a Minaret under the Effect of Strong Wind

In this study, the collapse mechanism of a destroyed minaret under strong wind influence was simulated to understand such structural interactions and identify potential risky regions. Wind profiles were defined according to Eurocode and Turkish Standards and were used in Computational Fluid Dynamics analyses. The pressure and suction stresses obtained with these wind analyses were applied on the minaret’s surface with Abaqus and the nonlinear finite element analyses were performed. As a result of the numerical analyses, displacements, stresses, plastic strains, and damages were obtained and results were comparatively presented. The results obtained with both standards are quite close and top displacements exceed the limit value specified in the Italian Building Code and Eurocode 8. Besides, many mesh elements in the minaret’s transition segment were damaged with tension stresses in nonlinear finite element analyses. Finally, the minaret’s failure behaviour was successfully simulated with the used methods.

Mesh optimization for the virtual element method: How small can an agglomerated mesh become?

We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups of elements are agglomerated to optimize the global mesh quality. A user-set parameter regulates the percentage of mesh elements, and consequently of faces, edges, and vertices, to be removed. This significantly reduces the total number of degrees of freedom associated with a discrete problem defined over the mesh with the VEM, particularly for high-order formulations. We show how the VEM convergence rate is preserved in the optimized meshes, and the approximation errors are comparable with those obtained with the original ones. We observe that the optimization has a regularization effect over low-quality meshes, removing the most pathological elements. In such cases, these “badly-shaped” elements yield a system matrix with very large condition number, which may cause the VEM to diverge, while the optimized meshes lead to convergence. We conclude by showing how the optimization of a real CAD model can be used effectively in the simulation of a time-dependent problem.

Evaluating the Accuracy of the COMSOL-Based Finite-Element Method for Simulating Plasmon-Modified Fluorescence.

Accurately modeling plasmon-modified fluorescence is important for understanding and guiding the design of experimental nanostructures that reliably enhance fluorescence. They are of particular interest due to their potential to allow localized "hot spots" of high fluorescence enhancement in a reproducible manner. Given the increasingly prevalent use of the COMSOL Multiphysics software package for simulating these phenomena, we investigate its accuracy using an analytically tractable model consisting of a gold nanosphere interacting with either a plane wave or a radiating point dipole. COMSOL simulation results were compared with a formally exact analytical theory. It was found that simulation parameters commonly used for plane-wave scattering do not necessarily produce accurate results for the nanoparticle-plasmon-coupled dipole emission case. Instead, user-input adaptive meshing parameters were found to be helpful in achieving quantitative agreements between COMSOL and analytical theory results for plasmon-modified fluorescence. Our studies suggest convergence to analytically calculated values when a minimum of two additional user-input mesh elements separate the point-dipole position and the nanoparticle surface. This practical insight is expected to aid in the application of COMSOL simulations to planning and interpreting fluorescence modification experiments.

Mesh Refinement for Dynamics Airflow in Health Care

This studyexplores using computational fluid dynamics(CFD) tooptimize ventilation in healthcare, with a focus on mesh refinement for accurate airflow analysis. The goal is to reduce airborne contaminant spread, which is crucial during COVID-19. Ventilation in healthcare ensures air quality and minimizes pathogen transmission. The research analyzer analyzes mesh element size's impact on airflow accuracy in simulated hospital wards with two coughing patients. The optimal mesh size is determined for reliable predictions. Mesh refinement enhances accuracy in critical zones. The k-epsilon turbulence model is chosen for low error. Experimental validation shows temperature discrepancies, likely due to simulated manikins lacking clothing insulation. Air velocity measurements show minor variations within an acceptable range. Further research on various ventilation configurations and airflow rates in real hospital conditions is crucial. Addressing these limitations optimizer optimizeshealthcare ventilation, enhancing safety and infection control.

Multifunctional Double Band Mesh Antenna with Solar Cell Integration for Communications Purposes

A dual band flexible antenna based on a circularly polarized modified meshed patch antenna design. This article focuses on some of the most pressing issues in small satellite applications. The antenna optimization and improvement of antenna performance, such as radiation efficiency. As is well known, circular polarization is immune to the Faraday rotation effect in the ionosphere and can thus prevent a 3-dB loss in geo-satellite communication. With the use of the software program Computer Simulation Technology (CST), the proposed circularly polarized modified meshed patch antenna has been created. Therefore, this article also presents a modified design of a circularly polarized meshed patch antenna to reduce the complexity of the antenna and decrease the size as much as it is capable. However, a meshed patch antenna can support a high communication data rate. The antenna architecture will theoretically be consistent with the installation of solar panels. The antenna utilizes a conductive copper as the core material and the substrate using flexible polyimide. The design antenna is very small, having an overall size of 30 * 30 mm when compared to other conventional non-transparent antenna operating at the same frequencies of 2.6, 3.5 GHz. The antenna that is proposed involves two meshed patch elements of same size but in various shapes. Finally, the proposed antenna is integrated into a solar cell by using the amorphous silicon thin film.

A Mesh Convergence Study for 2D Axisymmetric Pipe Wall Thickness

A meshing size study is essential for any simulation, as it affects the accuracy of the results by approximating the real-world geometry. This paper presents a detailed mesh convergence study for a 2D axisymmetric pipe model. The model incorporates a one-quarter cross-section due to the axisymmetric nature of the pipe. Four pipe wall thicknesses were investigated: 3.40 mm, 7.11 mm, 10.97 mm, and 18.26 mm. The results revealed a significant advantage for simulations involving thin pipes. They achieved convergence, a state with stable solution values, by utilizing a less dense mesh, leading to reduced computational time. This trend was exemplified by the fact that a thinner pipe with thickness, t = 3.40 mm has converged with only 8 mesh elements, whereas a significantly thicker pipe, t = 18.26 mm necessitated 14 elements for convergence. This suggests that more complex geometries, with intricate details, may require a larger and denser mesh for convergence, leading to increased computational time. In conclusion, the mesh convergence study confirms that the finite element analysis (FEA) model has achieved a converged solution.

A Monte-Carlo approach for crack initiation modeling of cast superalloys informed by crystal plasticity

Crystal plasticity simulations of materials to assess the fatigue response on the microscale are becoming increasingly popular in industrial application. However, in the case of parts made from cast Ni-base superalloys, the amount of pores in a part combined with the fine spatial discretization around the pores needed due to strong mechanical gradients quickly leads to a computationally impractical number of mesh elements. In this paper we show an alternative to explicit crystal plasticity modeling of part-scale porosity by introducing a Monte-Carlo submodel that recombines the fatigue response of single pores predicted by crystal plasticity into the fatigue response of the pore agglomerate. The model can be applied in realtime due to the use of precomputed crystal plasticity results. We demonstrate that fatigue indicator parameters predicted by the Monte-Carlo submodel agree well with those predicted by explicit crystal plasticity simulations. Lastly, we apply the proposed model to study the influence of different porosity volume percentages, pore sizes and pore morphologies on the fatigue indicator parameters of a cast MAR-M247 superalloy.

Aging evaluation of fuse holders of BWR nuclear power plant

The aging evaluation of a typical fuse holder, which is used in a BWR-5 nuclear plant, is discussed in this paper. This evaluation considered the guidelines of the NUREG-1760. A fuse holder, class R, has been considered. It has a wire gauge in the 500 kcmil – 4 Cu/Al range. It is used for a nominal current between 201 A and 400 A. It has 3 poles with a box-type terminal and a reinforcing clip, for blade-type fuses. The evaluation was carried out in two steps using the ANSYS® code. In the first, the operation of the fuse holder without aging was simulated. A three-dimensional model was used. The numerical solution requires the coupling of electrical, thermal, and mechanical analyses. It can be done with a single model. The mesh elements are Solid 232, Solid 291, and Solid 187. The model was refined at the clip holder and connector terminals. The model has 3,379,780 nodes and 2,387,463 elements. Its natural frequencies and the distribution of temperature, voltage, and stresses were obtained. The aging analysis was carried out in the second step after sixty years of operation. The loss of 1 mm in the thickness of the fastener, caused by corrosion or wear in the fuse assembly, was considered. The results showed that the vibration modes occurred with lower natural frequencies when inadequate contact occurred. Besides, changes in the other operating parameters were observed.

Image-based mesh generation for constructing a virtual representation of engineered wood product samples

The complex structure of timber has traditionally been difficult to model as it is a highly heterogeneous material. The density and material properties for structural species such as Pinus radiata (radiata pine) can vary greatly across the growth rings. Numerical simulation methods are becoming more prevalent as a method of predicting moisture migration, stress and strain distributions, and fungal/rot intrusion in engineered wood products (EWPs). All these applications require a computational mesh that captures the growth ring structure to facilitate an accurate assessment of the performance of EWPs. In this work, a low-cost image-based algorithm is developed for generating a virtual representation of a small cross laminated timber panel sample. Specifically, the proposed method results in a virtual description of an EWP sample comprised of a triangular prismatic mesh where the nodes are aligned on the growth rings of each individual timber component of the EWP, with specific wood material properties allocated to each mesh element. Each small component is treated individually and we assume there is no longitudinal variation in the density, pith location, and pith angle within the mesh structure. The initial step involves analysing an image of the end grain pattern of a single clear wood sample to identify the growth rings using a spectral clustering algorithm. Next, the centre of the tree (pith) is located through an iterative constrained least-squares algorithm to determine the pith angle. Image analysis of an anatomical image combined with the pith location allows for a constant density value to be assigned to each mesh element. The capability of this framework is then demonstrated by simulating the moisture migration and heat transfer throughout a CLT sample under atmospheric and saturating boundary conditions. Furthermore, the virtual representation provides the basis for simulating additional physical and biological phenomena, such as moisture-induced swelling, decay and fungal growth.

A multiscale steel–concrete interface model for structural applications

In this paper, a new multiscale macro-element formulation for the steel–concrete interface modeling is proposed. This element allows for the representation of the behavior of steel and the interface zone surrounding it. It can also model the interfacial bond stresses in between. Compared to conventional interface models of the literature, which employ separate mesh elements for the steel and the interface, utilizing a macro-element to model both components simplifies the creation of a reinforced concrete structure mesh. Moreover, the macro-element equilibrium is solved using a sub-structuring method that aims to reduce the computational cost. At the global level, it is considered as a four-node element linked to two-dimensional and three-dimensional concrete elements. At the local level, an assembly of multiple three-node bar elements with bond stresses is performed. An inner mesh discretization is therefore possible at the local level independently of the global level. The coupling between the two modeling scales is done using a static condensation technique. The formulation of the macro-element is presented in this paper. A selection of numerical examples is provided. The presented applications demonstrate the robustness of the proposed interface model and its capacity to reproduce the experimental behavior of reinforced concrete structural elements.

Free and forced vibration analysis of piezolaminated plates via an isogeometric layerwise finite element

Isogeometric layerwise finite element (L-IGA) formulation is a recent state-of-the-art approach integrating Non-Uniform Rational B-spline (NURBS) basis functions into the quasi-static solution process of piezolaminated composite plates. This study extends the application of the L-IGA framework to encompass free, forced vibration, and displacement control analyses of laminated composite plates with straight/curvilinear fibers and piezoelectric layers. To this end, the NURBS basis functions, utilized in geometry definition, are employed to solve electromechanically coupled differential equations following Hamilton’s variational principle. The adoption of high-order continuous NURBS shape functions throughout the IGA discretization span both in-plane and through-thickness laminate dimensions. This effectively facilitates precise geometry representation directly from Computer-Aided Design (CAD). Besides, such a discretization accelerates the convergence of displacement and electric potential solution fields toward exact results. Various benchmark problems have been solved to verify the robustness and high accuracy of the proposed dynamic L-IGA method. These include comparative analyses between L-IGA dynamic solutions (i.e. employing the Newmark-Beta method), analytical solutions, and ANSYS-Solid 226 finite element results. All the results are compared across various span-to-thickness ratios, mechanical-potential loading scenarios, and fiber orientation angles. Remarkably, the L-IGA method attains almost excellently accurate time response of various fields (displacement, stress, electric potential) and modal results, with considerably fewer mesh elements than Solid 226 solutions. Overall, such an outcome reveals the high potential and practical merits of the proposed L-IGA formulation as a proficient finite element approach for the dynamic analysis of piezolaminated plates.