Finite Element Mesh Generation Research Articles

Numerical computation of cut off wave number in polygonal wave guide by eight node finite element mesh generation approach

This study proposes a two-dimensional, eight-noded automated mesh generator for precise and efficient finite element analysis (FEA) in microwave applications. The suggested method for solving the Helmholtz problem employs an optimal domain discretization procedure. MAPLE-13 software's advanced automatic mesh generator was developed specifically for this work. To demonstrate the effectiveness of the approach, three distinct waveguide structures are analyzed, with the results compared to the best available analytical or numerical solutions. The findings indicate that the proposed method yields highly accurate and efficient finite element results, particularly for waveguide structures containing singularities. In microwave applications, this method can significantly enhance energy transmission efficiency.

Wave Propagation for Structural Health Monitoring (WaveProSHM): open software with GUI

Guided wave–based SHM methods have been explored extensively in recent decades. The wave propagation modelling including piezoelectric transducers and various damage types helps understand intricacies of guided wave behavior and for designing a robust SHM system. However, modelling aspects are still challenging. Moreover, commercially available software for the modelling of guided waves often lacks appropriate high-order elements and code optimization for fast GPU computations. This research aimed to develop and disseminate to the SHM community the open software based on highly efficient vectorised code of the time domain spectral element method which can be run on GPU. The developed code is written in MATLAB with Graphical User Interface (GUI) and communicates with GMSH – open source finite element mesh generator. It can model signals of propagating guided waves in structures which are excited and registered by an array of piezoelectric transducers. The capabilities of the software are shown in an example of a large-scale problem of interacting guided waves with delamination.

An efficient finite element mesh generation methodology based on μCT images of multi-layer woven composites

High-fidelity models are essential for accurate finite element (FE) simulations of composite material behavior. This paper proposes an efficient meshing methodology based on micro-Computed Tomography (μCT) images. U-Net convolutional neural network was used for image segmentation. Connected yarns were then separated using an improved procedure based on watershed algorithm and geometric transformations. The proposed Constrained Delaunay-Advancing Front Technique (CD-AFT) surface reconstruction algorithm extracts point cloud of yarns from segmented images and outputs high-quality and smooth orientable manifold watertight triangulated surface. Intersecting meshes of yarns are separated through node position detection and Laplacian moving. Experimental results show that proposed methodology is capable of accomplishing mesh generation for different mesh sizes. Compared with commercial software, it has obvious advantages in mesh quality and size control. Since the proposed method operates independently of commercial software and manual operation, it facilitates the automated generation of numerous high-fidelity models from μCT images for FE simulations.

Generation of 3D finite element mesh of layered geological bodies in intersecting fault zones.

As the geological fault surface divides the 3D space of stratified ores and rocks into complex spatial surface domains, it is necessary to fully consider the spatial relationship between intersecting fault zones and geological bodies in the process of 3D modeling, and how to accurately establish the 3D finite element mesh of geological bodies in intersecting fault zones is a difficult point in modeling complex geological structure. The laminated geological body in intersecting fault zone is a multifaceted domain grid model consisting of a ground-level grid, a geological fault plane grid, and a range grid. By analyzing the spatial relationship between the geological interfaces of the intersecting fault zones, a closed manifold processing method is proposed to establish the closed manifold spatial surface model of the intersecting fault zones, based on which the closed spatial surface model is tetrahedrally divided to establish a 3D solid model. Finally, the 3D solid model is imported into Ansys to generate a 3D finite element mesh. VC++ is used as the development platform for programming, to realize the generation and closed manifold processing of ground level and geological fault surfaces, and use TetGen library to generate finite element mesh based on irregular tetrahedron. Taking an intersecting fault zone in an open-pit mine as an example, the 3D finite element mesh of laminated geological bodies in the intersecting fault zone is established successfully. This method provides an effective and feasible solution for generating accurate 3D finite element meshes in complex stratigraphic spaces based on closed manifold processing.

DFNMesh: Finite element meshing for discrete fracture matrix models

This paper presents a novel methodology for robust Finite Element (FE) mesh generation of Discrete Fracture Matrix (DFM) models. The method can handle the complete multi-dimensional domain from the tridimensional porous rock matrix, through fracture surfaces, down to open curves for fracture–fracture intersections. The accompanying open-source code is written in modern C++ with a JSON interface and largely relies on two state-of-the-art FE libraries: NeoPZ and Gmsh. Starting from a user-defined coarse mesh, fractures are sequentially read as convex polygons and introduced without distortions to the coarse geometry. The main steps involve: intersect edges by checking for nodes on opposite sides of the fracture plane, extend intersections from edges to faces, coalesce intersections to closest existing nodes (given a tolerance), refine interface elements to conform to the fracture, identify subsets of fracture surface, mesh the surface, and locate boundaries and intersections where they arise. Finally, the space around fractures is filled with the fine-scale unstructured mesh, which is kept conformal. The robustness of the implementation is derived from the consistent background of well-defined and simple premises like convexity and side-specific element neighborhood. Results show that the proposed technique can construct adequate 3D DFM grids, while still giving users freedom to adjust between geometrical fidelity and mesh quality through more aggressive feature rejection.

Multi-compartment head modeling in EEG: Unstructured boundary-fitted tetra meshing with subcortical structures.

This paper introduces an automated approach for generating a finite element (FE) discretization of a multi-compartment human head model for electroencephalographic (EEG) source localization. We aim to provide an adaptable FE mesh generation tool for EEG studies. Our technique relies on recursive solid angle labeling of a surface segmentation coupled with smoothing, refinement, inflation, and optimization procedures to enhance the mesh quality. In this study, we performed numerical meshing experiments with the three-layer Ary sphere and a magnetic resonance imaging (MRI)-based multi-compartment head segmentation which incorporates a comprehensive set of subcortical brain structures. These experiments are motivated, on one hand, by the sensitivity of non-invasive subcortical source localization to modeling errors and, on the other hand, by the present lack of open EEG software pipelines to discretize all these structures. Our approach was found to successfully produce an unstructured and boundary-fitted tetrahedral mesh with a sub-one-millimeter fitting error, providing the desired accuracy for the three-dimensional anatomical details, EEG lead field matrix, and source localization. The mesh generator applied in this study has been implemented in the open MATLAB-based Zeffiro Interface toolbox for forward and inverse processing in EEG and it allows for graphics processing unit acceleration.

Development of a Tetrahedral Mesh Generator Based on Constrained Delaunay Triangulation

The article describes the basic principles of operation of the finite element mesh generator SMCMGrid, which is an integral part of the SMCM software package designed to solve problems in the mechanics of composite materials and structures, which was developed at the Scientific-educational center on supercomputer modeling and software engineering of Bauman Moscow State Technical University (BMSTU SIMPLEX CENTER). The paper describes a software pipeline for constructing high-quality tetrahedral unstructured meshes for arbitrary shape B-rep models based on constrained Delaunay triangulation. We have presented the main algorithms for generating meshes on the edges and surfaces of the model, which make it possible to create the so-called simplicial complex, for which it is then possible to construct a constrained Delaunay triangulation and create the final tetrahedral mesh of the required quality. The mesh is generated in a Riemannian space with a given metric that takes into account the required characteristics of the mesh at each point of the geometric model. We gave examples of finite element meshes for various geometric models of engineering structure elements, including composite materials, and also demonstrated the adequacy of the results of solving the elasticity problem on a mesh built using the SMCMGrid generator. The results of the work led to the conclusion that the presented generator can be used to solve problems of engineering analysis and modeling.

Automated Finite Element Mesh Generation for Integrated Structural Systems

Automated Finite Element Mesh Generation for Integrated Structural Systems

Rigid-Block DEM Modeling of Mesoscale Fracture Behavior of Concrete with Random Aggregates

The mesoscale structure generated in concrete plays a significant role in the mechanical properties and local failure behavior of mesoscale concrete. This work proposes a novel rigid-block discrete-element method (RB-DEM) for concrete modeling with random mesoscale structure. The results of the uniaxial compression using the RB-DEM demonstrated satisfactory agreement with experimental data. The RB-DEM does not only show satisfactory performance in simulation but also it is simple to use. The RB-DEM model can be built from any finite-element mesh generator, either open source codes or commercial software, which are readily available. The interfacial transition zone (ITZ) is modeled directly by assigning the weakened contact model or parameter at the interface between aggregate and mortar. The effects of ITZ parameters, aggregate volume fraction, and geometric shape on the stress–strain curve and crack propagation are discussed. This work provides a novel and efficient tool for the mesoscale fracture simulation of concretelike material considering the relatively large time-step of the DEM.

Finite element analysis of floor slabs by means of visual programming in SAPFIR-3D

To calculate analytical model of buildings and receive stress-strain state results, triangulation of structural elements is required. Great attention should be paid to reinforced concrete multi-span floor slabs at the joints with vertical elements. Due to unevenness and complexity in form, the finite element mesh of slab in such places can become more concentrated, which leads to an increase in stress values and inadequately elements design. To prevent such negative consequences and create an even mesh all over the slab, additional mesh generation in such places is required. To simplify such problem and reduce human costs, adjustment of finite element (FE) mesh can be obtained by means of visual programming. The purpose of this paper is to obtain and compare the results of finite element analysis (FEA) of reinforced concrete floor slab in residential building and to adjust generated mesh at the joints with vertical elements by means of visual programming in SAPFIR-3D. The scientific and practical importance of the work stands in the describing of the method of adjustment of FE mesh generation of floor slabs at the joints with vertical elements by means of visual programming. The results of the research are based on the results of calculation in programming complexes SAPFIR-3D and LIRA-SAPR, also analysis of literary sources and practical experience of the authors. The article revealed the possibility usage of visual programming to adjust FE mesh of floor slab with aim to simplify its shape at the joints with vertical structural elements. There is considered method and options for visual programming in the SAPFIR-3D. In this paper, results of the 8-storey skeleton reinforced concrete residential building with basement, have been analyzed and compared. The practical importance of the results of this paper lies in the presentation of the proposed method to adjust FE mesh of floor slab by means of visual programming.

Direct generation of finite element mesh using 3D laser point cloud

An approach for the finite element (FE) mesh generation of tunnel structures considering the lack of detail, low automation, and intermediate link transformation in the FE mesh generation of tunnels based on the 3D laser point cloud is presented in this paper. To this end, we acquired the tunnel point cloud model using terrestrial laser scanning or mobile laser scanning, and uniform nodes from the raw point cloud using a clock simulation extraction algorithm we developed. In addition, we assign topology information to these nodes. Further, we generated an FE model of the tunnel structure suitable for numerical simulation analysis using Abaqus. We applied the developed method to three types of tunnels; the mesh satisfied the evaluation standards of practical engineering applications. We examined the impact of mesh size and used an engineering example to confirm the method's accuracy. Finally, we provide recommendations for future research considering the future trend of FE mesh generation based on the 3D laser point cloud and its improvements.

2D Digital Reconstruction of Asphalt Concrete Microstructure for Numerical Modeling Purposes.

In this paper, we deal with the issue of asphalt concrete microstructure recognition for further numerical analysis. An efficient reconstruction of the underlying microstructure makes the composite analysis more reliable. We propose for this purpose a methodology based on the image processing and focus on a two-dimensional case (it can be easily used as a part of the 3D geometry reconstruction, however). Initially obtained geometry of the inclusions is further simplified to reduce the cost of the finite element mesh generation. Three straightforward geometry simplification algorithms are used to perform this process in a controlled way. Subsequently, we present the solutions of two problems, i.e., heat flow and elasticity (plane strain), in order to illustrate the effectiveness of the whole elaborated methodology. The numerical results were obtained using the finite element method. Consequently, an error analysis is demonstrated in order to refer the overkill mesh solutions to the ones presented in this study. The main finding of this paper is the efficient methodology dedicated to a digital reconstruction of the asphalt concrete microstructure by the image processing. It can be also extended to other materials exhibiting similar microstructure.

ReMo3D – an open-source Python package for 2D and 3D simulation of normal and lateral resistivity logs

An open-source Python package is presented, ReMo3D, which allows the generation of synthetic normal and lateral resistivity logs for 2D and 3D models. The package is built around a finite element mesh generator Gmsh and a high-performance multiphysics finite element software Netgen/NGSolve and supports distributed-memory parallel computation. The examples included in the paper show that the developed software can accurately simulate the measurement process and produce detailed synthetic normal and lateral resistivity logs. In addition, basic information about normal and lateral tools such as tool configurations, measurement principles, nomenclature and a brief history of utilization is included in the paper.

Tight bounds for the dihedral angle sums of a pyramid

We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval (3π, 5π). Moreover, for any number in (3π, 5π) there exists a pyramid whose dihedral angle sum is equal to this number, which means that the lower and upper bounds are tight. Furthermore, the improved (and tight) upper bound 4π is derived for the class of pyramids with parallelogramic bases. This includes pyramids with rectangular bases, often used in finite element mesh generation and analysis.

Human-Autonomous Devices for Finite Element Discrete Element Analysis of Geo Material Based on Digital Image Technology

Based on the theory of digital image processing, geometric vector transformation and the principle of automatic generation of finite element meshes, a finite element-discrete element analysis method for digital image of geotechnical engineering materials is proposed. Combining the digital image technology with the finite element-discrete element method (FDEM) coupling analysis method proposed by Munjiza, a FDEM analysis system is developed to characterize the real heterogeneity of rock mass, which provides a new way to model rock mass and study the fracture mechanism of rock mass from a meso-scopic point of view. With the help of digital image technology, the system obtains the real meso-structure of rock material from the image of rock section. With the help of mature mesh generation technology, it maps it to the FDEM computational grid, thus overcoming the shortcomings of the original FDEM in considering material heterogeneity. Using this system, the Brazilian disk splitting test is simulated numerically, and the real fracture process of granite under load is reproduced. And we examined how transparency and task type influence trustfulness, perceived quality of work during human-autonomous system interaction. The numerical simulation results show that the stress distribution of rock samples considering heterogeneity is asymmetric, and the micro-structure of rock has an important influence on the crack propagation and stress distribution in rock.

Comparison and Verification of Dynamic Simulations and Experiments for a Modified Spur Gear Pair

In this study, static and dynamic analyses of a spur gear pair with linear tip relief and longitudinal crowning were performed. Dynamic experiments were conducted to compare and verify the dynamic analysis results. On the basis of the theory of gearing, the mathematical model of a modified spur gear pair was established. In addition, a finite element mesh generation program was developed according to the mathematical model. Finite element analysis was applied to calculate the contact stress, contact patterns, and mesh stiffness of the gear pair. Moreover, a dynamic analysis was performed to predict the dynamic transmission error (DTE) at various speeds and loads. Dynamic experiments were performed on the spur gear pair by using a gear dynamic tester. Accelerometers were mounted on the gear pair to record the vibrations during gear meshing. The experimental DTE was calculated and compared with the simulated DTE to verify the prediction of the vibration performance of the spur gear pair under different rotational conditions.

BLOOD FLOW IN ARTERIAL BIFURCATION CALCULATED BY TURBULENT FINITE ELEMENT MODEL

In this paper, turbulent fluid flow is analyzed using a two-equation turbulent finite element model that can calculate values in the viscous sublayer. Implicit integration of the equations is used for determining the fluid velocity, fluid pressure, turbulence, kinetic energy, and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of the incremental-iterative procedure. Developed turbulent finite element model, with the customized generation of finite element meshes, is used for calculating complex blood flow problems. Analysis of results shows that a cardiologist can use the proposed tools and methods for investigating the hemodynamic conditions inside the bifurcation of arteries.

Biomechanical analysis of the cervical spine segment as a method for studying the functional and dynamic anatomy of the human neck

BackgroundTraditionally, dynamic and functional anatomy, in particular the dynamic anatomy of the neck, is studied on cadaveric material. However, the development of in vivo visualization technologies and in silico modeling has made it possible to expand these possibilities. Despite significant progress in the study of dynamic and functional anatomy of the neck by means of in silico methods, the issues of validating the developed models and taking into account the pronounced nonlinearity of soft tissues as well as local anisotropy remain open. The aim of this study was to develop a virtual dynamic anatomical model of the human neck and reproduce the dynamic processes in the cervical spine from this model using the finite element method. Materials and methodsReverse engineering was used to generate a dynamic anatomical model of the neck from CT data (both male, 24 and 22 years old). Two segments of the cervical spine (C3-C5, C2-T1) were isolated from the resulting model for finite element analysis. Finite element mesh generation and contact interactions were performed using the HyperMesh software (Altair Engineering Inc, Troy, Michigan, USA). The anisotropic hyperelastic Holzapfel-Gasser-Ogden model was used to describe the material behavior of the fibrous rings of the disc. Material modeling and finite element analysis were performed using Abaqus CAE 6.14 software (Simulia, Johnston, Rhode Island, USA). ResultsA technique for creating a virtual dynamic anatomical model of the neck was elaborated and implemented. The model includes 79 major anatomical structures of the neck segmented from radiological data. A finite element analysis of the cervical spine was performed. The results of finite element analysis of the C3-C5 segment under axial load were compared with in vitro data. The proposed model shows nonlinear deformation of the disc under static loading; the model predicted displacement values agree well with the experimental ones. The displacement of the С3-С5 central vertebra with an axial load of 800 N reaches a value of 0.65 mm. For the segment C2-T1, data on intradiscal pressure, stress plots and displacements during flexion were obtained. The maximum stress value of 10.036 MPa is observed in the C3-C4 disc. ConclusionSimulation results using the proposed methodology are in good agreement with experimental data. The generated biomechanical models allow describing dynamic phenomena in the cervical spine and obtaining a wide range of quantitative properties of anatomical objects, which are otherwise inaccessible to classical methods for studying dynamic and functional anatomy.

Analysis and Testing of the Dynamic Characteristics of Rotor Worktable

The finite element modelling, mesh generation and modal analysis of the rotor worktable are carried out by combining the analysis technology of finite element software in this paper. Then, the software analysis results and the actual experimental results are compared and analyzed, so as to get the causes of error, which can provide good basic data for the use of the rotor table in the future that could better meet the needs of scientific research and teaching.

Ground view factor computation model for bifacial photovoltaic collector field: uniform and non-uniform surfaces

The photovoltaic collectors in a field are subject to three types of solar radiation: direct, diffuse, and reflected irradiance. The reflected irradiance received by solar photovoltaic (PV) depends on the view factor from solar PV to the ground. This view factor component is dominant for bifacial PV due to additional reflected irradiance gain, which can be achieved from the module’s rear side.This paper proposes and verifies a finite element method based view factor computation model, which can handle both uniform and non-uniform ground surfaces. The unique contribution of this work is that it introduces a geometric progression based finite element mesh generation process that forms the quasi-uniform grid. The generated grid values are fitted into the computation model to calculate the view factor from bifacial photovoltaics to the ground, known as the ground view factor (GVF). The proposed computation model can achieve an accuracy of 99%. To keep accuracy at this level, the smallest element size of the coarse mesh should be within 0.1%–0.4% of surface width or length. Moreover, the geometric progression ratio of the fine and coarse mesh should be in the range of 1.001–1.002 and 1.01–1.04, respectively. The model is analysed under six different PV field variables: multiple reflective ground surfaces, the height of PV, tilted ground surface, PV position in the ground, length and width of the ground, and PV string length. For the different string sizes considered here, the view factor model’s computation time varies from 180 s to 257 min for the iteration size of 7.67 billion to 765 billion. The view factor computation model will contribute to analyse reflected irradiance at the rear side of bifacial PV, which is essential to predict the energy generation accurately. The proposed model is also beneficial for urban planning and addressing heat gain of the building-integrated PV system and energy usage.