Automatic Mesh Generation Research Articles

A fast and robust patient specific Finite Element mesh registration technique: Application to 60 clinical cases

Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially digitized at intraoperative stage, and 50 CT volumes of patients' heads. In the latter case, both skin and bone surfaces were taken into account by the mesh registration process in order to model the face muscles and fat layers. The MMRep algorithm succeeded in all 60 cases, yielding for each patient a hex-dominant, Atlas based, Finite Element mesh with submillimetric surface representation accuracy, directly exploitable within a commercial FE software.

三次元き裂進展自動解析システムの構築 : 第1報,き裂解析システムの概要と有限要素法モデル生成

Although three-dimensional finite element analysis has become a common tool in the industries to perform their design analyses, there still exist some difficulties in performing three-dimensional fracture analyses. One of them is that although automatic mesh generation techniques are available for tetrahedral finite elements, hexahedral finite elements are commonly used in three-dimensional crack analyses. The other is that the analysis models tend to be large in their scales. Therefore performing a three-dimensional fracture analysis takes much manual labor in the analysis model generation processes and computational time. In present research, the authors have been developing a fracture mechanics analysis system that minimizes the manual labor. The key components in the analysis system are a mesh generation software and the virtual crack closure-integral method (VCCM) for the second-order tetrahedral finite element to evaluate the crack parameters (the energy release rates and the stress intensity factors). Based on them, the software system was carefully designed to handle large scale analysis model. In this paper, as the first report, the outlines of the system and the finite element model procedures are described.

Automated hexahedral mesh generation of complex biological objects

This paper describes the development of a new automatic mesh generator for complex biological objects based on voxel hexahedral meshing (VHM). The system produces hexahedral meshes with multiple material classifications from three-dimensional (3D) computed tomography (CT) datasets. The quality of the VHM meshes is improved using a series of mesh connectivity improvement algorithms, leading to the application of a new and novel boundary smoothing algorithm. The boundary smoothing algorithm classifies boundary nodes into different groups based on the configuration of their neighbouring elements: this provides a varying compromise between smoothness and element distortion. The high anatomic detail of which the method is capable is shown for meshes of single and mixed material types. This system illustrates how to harness the speed and simplicity of VHM as an initial mesh generator while simultaneously improving the quality of those meshes with additional meshing techniques. MATLAB code for this software is freely available for research purposes upon request.

Effect of Diameter and Length on Stress Distribution of the Alveolar Crest around Immediate Loading Implants

Many clinical observations have shown that immediate loading is indicated when the stabilization of the bone/implant is optimal and when the estimated loads are not excessively high. Nonetheless, more experimental studies are needed to consider the immediate loading protocol as a safe procedure. Mechanical analysis using the finite element (FE) method analysis has been employed by many authors to understand the biomechanical behavior around dental implants. This study was to evaluate the effect of the diameter and length on the stress and strain distribution of the crestal bone around implants under immediate loading. By an ad hoc automatic mesh generator, high-quality FE models of complete range mandible was constructed from computer tomography, with three Straumann (Straumann Institute, Waldenburg, Switzerland) implants of various sizes embedded in the anterior zone. The implant diameter ranged from 3.3 to 4.8 mm, and length ranged from 6 to 14 mm, resulting in seven designs. The implant-bone interface was simulated by nonlinear frictional contact algorithm. For each design, vertical and oblique loadings of 150 N were applied, respectively, to each implant, and stresses and strains in the surrounding cortical bone were evaluated. The biomechanics analysis provided results that the oblique loading would induce significantly higher interfacial stresses and strains than the vertical loading, while the intergroup stress difference significant levels was evaluated using t-tests method and the level of significance (.05) that was accepted for significance. Under both loadings, the maximal values were recorded in the 3.3 (diameter) x 10 (length) mm implant configuration, whose mean and peak values were both higher than that of others with significant statistical differences. The second maximal one is 4.1 x 6 mm configuration, and the minimal stresses were recorded in 4.8 x 10 mm configuration, whose strains were also near to lowest. Increasing the diameter and length of the implant decreased the stress and strain on the alveolar crest, and the stress and strain values notably increased under buccolingual loading as compared with vertical loading, but diameter had a more significant effect than length to relieve the crestal stress and strain concentration.

き裂メッシュ自動生成手法と四面体二次要素用VCCMを用いた三次元き裂（進展）解析

き裂メッシュ自動生成手法と四面体二次要素用VCCMを用いた三次元き裂（進展）解析

Fatigue study of partially overlapped circular hollow section K-joints. Part 1: Geometrical models and mesh generation

In this study, a set of consistent geometrical models is developed for fatigue assessment of partially overlapped circular hollow section K-joint. To accomplish the fatigue assessment, an accompanying set of automatic finite element mesh generation procedures is developed. These mesh generation procedures are able to discretize the geometrical models into different types of meshes for fatigue assessments of uncracked and cracked joints. The presentation of the work is divided into two parts. In Part 1, descriptions of the geometrical models and the mesh generation procedures are given. In Part 2, attention is focused on the validation of the numerical results.

Die surface design optimization accommodating springback assisted by an automatic surface generator

One of manufacturing problems in sheet metal forming is springback. This elastic recovery occurs when unloading the formed part off the tooling dies, resulting in shape inaccuracies. Optimizing the geometry surfaces of the tools can be used to accommodate the springback, so that after the unloading process, the formed part meets the target shape. This paper presents an optimization method to modify the geometry surfaces of the tooling dies based on springforward simulations assisted by an automatic surface generator during the process. In the optimization cycle, new sets of upper and lower die surfaces are required. An automatic surface generation method based on normal vector has been developed to create new finite elements of the new surfaces. The normal vector calculation of the deformed elements after springback generates new upper and lower surfaces with uniform gaps. The new generated elements can be used directly during the optimization cycle. For testing and verification purposes, the method is applied in various complicated surfaces. The test results show that this method is able to generate a uniform gap in a corner with 90 degrees angle, without discontinuity in any elements. The application in optimization to minimize the springback is conducted in hat- shape problem. The result shows that the automatic mesh generator works effectively during the optimization cycle. The distortion error after springback can be significantly minimized.

Automatic and topology-preserving gradient mesh generation for image vectorization

Gradient mesh vector graphics representation, used in commercial software, is a regular grid with specified position and color, and their gradients, at each grid point. Gradient meshes can compactly represent smoothly changing data, and are typically used for single objects. This paper advances the state of the art for gradient meshes in several significant ways. Firstly, we introduce a topology-preserving gradient mesh representation which allows an arbitrary number of holes . This is important, as objects in images often have holes, either due to occlusion, or their 3D structure. Secondly, our algorithm uses the concept of image manifolds, adapting surface parameterization and fitting techniques to generate the gradient mesh in a fully automatic manner. Existing gradient-mesh algorithms require manual interaction to guide grid construction, and to cut objects with holes into disk-like regions. Our new algorithm is empirically at least 10 times faster than previous approaches. Furthermore, image segmentation can be used with our new algorithm to provide automatic gradient mesh generation for a whole image . Finally, fitting errors can be simply controlled to balance quality with storage.

An automatic 3D mesh generation method for domains with multiple materials

This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided.

Design of HTS Magnets for a 2.5 MJ SMES

A 600 kJ HTS SMES system has been developed for power system stabilization as a national project in Korea. Successful operating tests of the 600 kJ were recently completed. In this paper, a 2.5 MJ class SMES with HTS magnets of single solenoid, multiple solenoid and modular toroid type were optimized using a recently developed multi-modal optimization technique named multi-grouped particle swarm optimization (MGPSO). The objective of the optimization was to minimize the total length of HTS superconductor wires satisfying some equality and inequality constraints. The stored energy and constraints were calculated using 3-D magnetic field analysis techniques and an automatic tetrahedral mesh generator. Optimized results were verified by 3D finite element method (FEM).

Optimal design of HTS magnets for a modular toroid-type 2.5 MJ SMES using multi-grouped particle swarm optimization

Superconducting magnetic energy storage (SMES) is one of the promising power system applications of superconducting technology and has been actively researched and developed worldwide. Generally, there are three types of SMES-solenoid, multiple solenoid, and toroid. Among these types, toroid type seems to require more wires than solenoid type and multiple solenoid type at the same operating current. However toroid type reduces normal field in the wire and stray field dramatically because magnetic field is confined inside the coil. So, the total length of wire in the toroid type can be reduced in comparison with that in the solenoid type by increasing operating current. In this paper, a 2.5 MJ class SMES with HTS magnets of single solenoid, multiple solenoid and modular toroid type were optimized using a recently developed multi-modal optimization technique named multi-grouped particle swarm optimization (MGPSO). The objective of the optimization was to minimize the total length of HTS superconductor wires satisfying some equality and inequality constraints. The stored energy and constraints were calculated using 3D magnetic field analysis techniques and an automatic tetrahedral mesh generator. Optimized results were verified by 3D finite element method (FEM).

An Improved Strategy of Automatic Triangular Mesh Generation over 3D Surface

A quadratic mapping method based on curvature for mesh generation is presented in this paper. The method starts from the triangulation of 2D parametric surface by applying the Advancing Front Technique (AFT) and Delaunay Triangulation (DT) together with 3D feature information. Then 3D surface mapping from 2D elements is realized by quadratic mapping method with curvature measure information. After that, triangular mesh over 3D surface is automatically generated. Besides, graded mesh control strategy is discussed in the paper for the sake of generating mesh with higher quality. Finally, several application examples are given to show the characteristics of the presented method.

피지이론과 버블기법을 이용한 3차원 구조물의 유한요소해석을 위한 요소생성기법

본 논문은 3차원구조물의 유한요소해석을 위한 자동 유한요소 생성에 관한 것으로 퍼지이론과 버블요소 생성기법, 상용 솔리드모델러로 구성되어진다. 새로운 요소생성과정은 (a) 해석모델인 형상모델링 정의, (b) 버블생성, 그리고 (c) 요소생성으로 이루어진다. 형상모델링에는 상용 솔리드모델러를 이용하였으며 버블은 각 지점에서의 버블간격함수에 의해 생성되어진다. 버블간격 함수는 지식처리수법에 의해 조절되어 진다. 요소생성을 위해서는 기본적으로 데로우니방법을 도입하였다. 이러한 3차원 구조물에 대한 유한요소의 자동생성은 해석을 위해 큰 잇점이 있다. 실제적인 현 시스템의 효용성을 검증하기위해 3차원 형상에 대한 예를 제시하였다. This paper describes an automatic finite element mesh generation for finite element analysis of three-dimensional structures. It is consisting of fuzzy knowledge processing, bubble meshing and solid geometry modeler. This novel mesh generation process consists of three subprocesses: (a) definition of geometric model, i.e. analysis model, (b) generation of bubbles, and (c) generation of elements. One of commercial solid modelers is employed for three-dimensional solid structures. Bubble is generated if its distance from existing bubble points is similar to the bubble spacing function at the point. The bubble spacing function is well controlled by the fuzzy knowledge processing. The Delaunay method is introduced as a basic tool for element generation. Automatic generation of finite element for three-dimensional solid structures holds great benefits for analyses. Practical performances of the present system are demonstrated through several mesh generations for 3D geometry.

Three-dimensional automatic mesh generation for hybrid electromagnetic simulations

Hybrid mesh generation is required for finite-difference time-domain/finite-element time-domain (FDTD/FETD) hybrid simulations. A combined approach is presented to automatically generate Cartesian/tetrahedral hybrid meshes for open and closed structures. This approach first generates a buffer zone that surrounds a target with specified tightness. The advancing-front technique with ldquosweep-and-retryrdquo is subsequently applied to generate an initial tetrahedral mesh that fills the buffer zone. Finally, the tetrahedral mesh undergoes a combined quality improvement procedure. Due to the low profile of the resulting tetrahedral mesh, the sparse Cholesky decomposition can be applied effectively to solve the resulting FETD matrix. Several examples are provided to demonstrate the main features and the performance of the proposed automatic mesh-generation method.

Advanced Numerical Simulation of Metal Forming Processes Using Adaptive Remeshing Procedure

This paper presents an advanced numerical methodology which aims to improve virtually any metal forming processes. It is based on elastoplastic constitutive equations accounting for non-linear mixed isotropic and kinematic hardening “strongly” coupled with isotropic ductile damage. During simulation of metal forming processes, where large plastic deformations with ductile damage occur, severe mesh distorsion takes place after a finite number of incremental steps. Hence an automatic mesh generation with remeshing capabilities is essential to carry out the finite element analysis. Besides, when damage is taken into account a kill element procedure is needed to eliminate the fully damaged elements in order to simulate the growth of macroscopic cracks. The necessary steps to remesh a damaged structure in finite element simulation of forming processes including damage occurrence (initiation and growth) are given. An important part of this procedure is constituted by geometrical and physical error estimates. The meshing and remeshing procedures are automatic and are implemented in a computational finite element analysis package (ABAQUS/Explicit solver using the Vumat user subroutine). Some numerical results are presented to show the capability of the proposed procedure to predict the damage initiation and growth during the metal forming processes.

Integration of CAD and boundary element analysis through subdivision methods

Subdivision methods have been mainly used in computer graphics. This paper extends their applications to mechanical design and boundary element analysis (BEA), and fulfills the seamless integration of CAD and BEA in the model and representation. Traditionally, geometric design and BEA are treated as separate modules requiring different representations and models, which include continuous parametric models and discrete models. Due to the incompatibility of the involved representations and models, the post-processing in geometric design or the pre-processing in BEA is essential. The transition from geometric design to BEA requires substantial effort and errors are inevitably introduced during the transition. In this paper, a framework of realizing the integration of CAD and BEA was first presented based on subdivision methods. A common model or a unified representation for geometric design and BEA was created with subdivision surfaces. For general 3D structures, automatic mesh generation for geometric design and BEA was fulfilled through subdivision methods. The seamless integration improves the accuracy of numerical analysis and shortens the cycle of geometric design and BEA.

F1-1 三次元複雑形状き裂解析のための四面体自動メッシュ生成について(F-1 構造物の健全性評価と計算力学技術,フォーラム)

F1-1 三次元複雑形状き裂解析のための四面体自動メッシュ生成について(F-1 構造物の健全性評価と計算力学技術,フォーラム)

Identification of the heat fluxes and thermal resistance on the ingot-mould surface in continuous casting of metals

Identification of thermal resistance of the gas-gap between the ingot and mould, as well as the heat flux distribution on the phase change from the solid side during continuous casting of metals is the subject of this article. Analysed parameter estimation problems of the steady-state heat conduction belong to the group of inverse problems. The presented work shows the possibility of applying the least square adjustment method with a priori data for the identification of thermal resistance, the interphase location as well the heat flux distribution on the phase change from the solid side and the temperature field within the ingot and mould. The most important feature of the approach is that the unknown thermal resistance of the gas-gap is obtained from the temperature measurements at a number of sensors located in the wall of the mould, and some sensors located in the ingot, by solving the appropriate inverse problem. The validity of the solution of the inverse problem is checked by comparison with the results of direct problem. In this work, a front-tracking method with an automatic mesh generation finite element technique (so called deforming or moving finite-elements) for steady-state equation conduction-advection problems is developed. Such an approach makes it possible to find the exact solid-liquid interface location, because it is the integral part of the solution. Due to the strong convective nature of the problem (casting velocity, thermal parameters) the special up-wind technique is applied.

A three-dimensional inverse geometry problem in estimating the space and time-dependent shape of an irregular internal cavity

A three-dimensional inverse geometry problem (or shape identification problem) to estimate the unknown space and time-dependent irregular shape of internal cavity by utilizing the gradient-based steepest descent method (SDM) and a general purpose commercial code CFD-ACE+ is considered in the present study. The validity of the present inverse algorithm is examined based on the simulated measured temperature distributions on the outer surface by an imaginary infrared scanner. The advantage of calling CFD-ACE+ as a subroutine in this shape identification problem lies in its characteristics of automatic mesh generation since this function of CFD-ACE+ enables the easily-handling of the moving boundary problem. Two numerical test cases are performed to test the validity and accuracy of the present shape identification algorithm by using different types of cavity shapes, initial guesses and measurement errors. Results show that excellent estimations on the unknown geometry of the internal cavity can be obtained.

Validation of BS7910:2005 failure assessment diagrams for cracked square hollow section T-, Y- and K-joints

This paper describes the usage of finite element (FE) analyses results to validate the standard BS7910 assessment procedure for the safe design of cracked square hollow section (SHS) T-, Y- and K-joints. In the study, the actual 3D surface cracks obtained from previous fatigue tests have been included in the FE models. An automatic mesh generation program is then developed and used to produce the failure assessment diagram (FAD) through the J-integral method. The ultimate strength of uncracked SHS joints with reduced load bearing areas have been referenced to derive the plastic collapse loads of cracked SHS joints for the development of FAD. These loads have been validated against the previous experimental results. In comparison with the existing standard BS7910 Level 2A/3A FAD curve and the proposed assessment procedure for circular hollow section joints, it is found that a plastic collapse load with a penalty factor of 1.05 will be sufficient for the safe assessment of cracked SHS T, Y, and K-joints under brace end axial loading.