Automatic Mesh Generation Research Articles

Subdivision-based digital geometry processing as a fundamental building block of digital manufacturing

Digital manufacturing relies on geometric modelling techniques, virtual environments, and a solid common platform that can support multiple disciplines and applications. Subdivision methods offer powerful computational representations and algorithms for digital geometry processing (DGP) and can create a common model and unified representation for geometric design, numerical analysis, and numerical control (NC) machining. Subdivision-based digital geometry processing can be a fundamental building block of digital manufacturing. In this paper, models for geometric design, finite/boundary element analysis (FEA/BEA), and NC machining are created using subdivision surfaces. Automatic mesh generation for the FEA of sheet metal structures and for the BEA of general three-dimensional structures is fulfilled through subdivision-based digital geometry processing. Models with progressive refinement for progressive transmission are created. Subdivision-based digital geometry processing for NC machining is discussed.

Non-locking Tetrahedral Finite Element for Surgical Simulation.

To obtain a very fast solution for finite element models used in surgical simulations low order elements such as the linear tetrahedron or the linear under-integrated hexahedron must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper we extend the average nodal pressure tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way, with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing TLED (Total Lagrangian Explicit Dynamics) algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared to the average nodal pressure element in case of models consisting of multiple materials.

Measurement and interpretation of long-term deformation of a rock slope at the Ikura limestone quarry, Japan

More than 10 years of displacement measurements at the Ikura limestone quarry in Japan have clarified aspects of rock slope deformation arising from excavation in the quarry. Although the cause of most deformations can be explained theoretically, those occurring in a rock slope just behind the Tarumi working face proved perplexing. Contraction continued to occur on the rock slope although excavation of limestone had ceased at this face. The cause of this continuous deformation was evaluated through numerical analysis employed to assess the stability of the rock slope. An automatic 3D mesh generation technique was used to model the complex topography of the quarry resulting from the excavation and a finite element mesh model was rendered for each of the successive excavation stages. Elastic analysis then allowed the resulting rock slope deformation to be predicted. The calculated results reveal that the rock slope continued to deform elastically after excavation had ceased on the Tarumi face and that the on-going excavation at the Kawamukai working face, located 400 m away from the rock slope, was the probable cause. The calculated results using appropriate elastic moduli were in good agreement with measured results. The rock slopes are assessed as stable and the continuous deformation is believed to be elastic.

Multidisciplinary Design Exploration for a Winglet

In this paper, we describe a multidisciplinary design exploration technique with a high-fidelity analysis applied to the winglet design for a commercial jet aircraft. The minimization of the block fuel at a fixed aircraft operating range and a maximum takeoff weight were selected as design objectives. Both objective functions were estimated from a computational fluid dynamics based aerodynamic drag and a finite element method based structural weight. Various computational fluid dynamics and optimization techniques, such as the midfield drag decomposition method, the automatic computational fluid dynamics mesh generation, the kriging surrogate model, and multi-objective genetic algorithms, were integrated and applied to the detail design exploration. Computational fluid dynamics with the midfield drag decomposition method showed the effect on wave, induced, and profile drag components due to different winglet defining parameters. Practical design decision was explored based on the Pareto front and some design criteria that were uncovered within the numerical optimization. Finally, the design process was validated through the validation of the kriging approximation and aerodynamic characteristics based on the wind-tunnel test.

One-dimensional finite element heat transfer solution of a fin with triangular perforations of bases parallel and towered its base

Heat transfer dissipation from a horizontal rectangular fin embedded with equilateral triangular perforations is computed numerically using one-dimensional finite element technique. The bases of the triangles are parallel and toward the fin base. The body of the fin is discretized into a number of subdivisions (finite elements). The number of these elements can be altered as required according to the automatic mesh generation. The heat dissipation of the perforated fin is computed and compared with that of the solid one of the same dimensions and same thermal properties. The comparison refers to acceptable results and heat dissipation enhancement due to certain perforation.

An Optimized Generator of Finite Element Meshes Based on a Neural Network

An automatic mesh generator of triangular finite elements, based on an artificial neural network, is optimized by means of Design of Experiments techniques and Genetic Algorithms. The optimization concerns the various parameters which are defined in the mesh generator, whereas the objective function is related to the mesh quality. By means of this optimization the generator allows us to obtain very high-quality meshes.

A strategy of automatic hexahedral mesh generation by using an improved whisker-weaving method with a surface mesh modification procedure

One of the demands for three dimensional (3D) finite element analyses is the development of an automatic hexahedral mesh generator. For this problem, several methods have been proposed by many researchers. However, reliable automatic hexahedral mesh generation has not been developed at present. In this paper, a new strategy of fully automatic hexahedral mesh generation is proposed. In this strategy, the prerequisite for generating a hexahedral mesh is a quadrilateral surface mesh. From the given surface mesh, combinatorial dual cycles (sheet loops for the whisker-weaving algorithm) are generated to produce a hexahedral mesh. Since generating a good quality hexahedral mesh does not depend only on the quality of quadrilaterals of the surface mesh but also on the quality of the sheet loops generated from it, a surface mesh modification method to remove self-intersections from sheet loops is developed. Next, an automatic hexahedral mesh generator by the improved whisker-weaving algorithm is developed in this paper. By creating elements and nodes on 3D real space during the weaving process, it becomes possible to generate a hexahedral mesh with fewer bad-quality elements. Several examples will be presented to show the validity of the proposed mesh generation strategy.

A virtual crack closure-integral method (VCCM) to compute the energy release rates and stress intensity factors based on quadratic tetrahedral finite elements

This paper proposes a new virtual crack closure-integral method (VCCM) for quadratic tetrahedral finite element to compute the energy release rates/stress intensity factors. The formulations, numerical implementations and some numerical results of proposed VCCM are presented in this paper. Proposed VCCM enables us to adopt the tetrahedral finite element in 3D crack problems and us to use automatic mesh generation programs. Therefore process time to perform 3D crack analysis drastically reduces compared with the case of hexahedral elements.

Three-Dimensional Crack Propagation Analysis Based on VCCM (Virtual Crack Closure-Integral Method) for Tetrahedral Finite Element

This paper describes the development of a software to perform three-dimensional crack propagation analyses. The software is based on the conventional finite element method with second order tetrahedral element and an automatic mesh generation software. Hexahedral finite elements have historically been used in fracture analyses and methodologies to compute the crack parameters have been developed for the hexahedral elements. In present research, the authors have developed a VCCM (virtual crack closure-integral method) for the second order tetrahedral finite element. Use of the tetrahedral element allows us to utilize an automatic mesh generation software. The direction and rate of crack propagation are predicted based on the stress intensity factors and the shape of crack is updated. Hence, a software package containing the modules for mesh generation, for finite element analysis, for stress intensity factor evaluation, for predicting the rate and the direction of crack propagation and for updating crack configuration, can be developed.

English

Quasi-static axial and lateral compression tests were conducted on aluminium tubes of circular,rectangular, and square cross sections on a universal testing machine (Instron model 1197).During the compression process, different tubes were collapsed in different modes of collapse.These compression processes were also modelled using FORGE2 finite element code. The codehas the capabilities of automatic mesh generation, modelling of die, creation of material data file,carrying out the finite element computations, and post-processing of results. The deformingtube material was modelled as rigid-visco-plastic. Development of different modes of collapsewas investigated experimentally and computationally. The experimental load-compression curvesand deformed shapes are compared with the computed results and found in good agreement.It is found that the proposed finite element models of the different compression processes arecapable of predicting the modes of collapse.

Design sensitivity and shape optimization of geometrical nonlinear structure

This paper presents the structural shape optimization with linear elastic material, large displacement and small strains. The whole shape optimization process is carried out by coupling a closed geometric shape in R 2 with boundaries defined by B-splines curves, automatic mesh generation at each iteration, exact sensitivity analysis and mathematical programming method (SQP: Sequential Quadratic Programming). The design variables are the control point's coordinates which minimize the Von-Mises criteria, with a constraint that the total material volume of the structure remains constant. In this work the sensitivity analysis is performed using two methods: numerically by an efficient finite difference scheme and by the new method called exact Jacobian method. The feasibility of the proposed method is carried out for two numerical examples.

Subdivision-based integration of geometric design and finite element mesh generation for sheet metal structures

Subdivision methods have been mainly used in computer graphics. This paper extends their applications to the integration of geometric design and Finite Element Analysis (FEA) for sheet metal structures, and fulfils the seamless integration of geometric design and FEA in the model and representation. A common model or a unified representation for geometric design and FEA was created with subdivision surfaces for sheet metal structures. Automatic mesh generation for geometric design and FEA was fulfilled through subdivision methods. The seamless integration can improve the accuracy in numerical analysis and shorten the cycle for the geometric design and the FEA of sheet metal structures.

Analytical Shape and Thickness Sensitivities of Linear Shells

This paper describes an efficient method to calculate sensitivity of shell structures. Sensitivity parameters of interest are shape and thickness of shell structures. An 18-node hexahedral shell is used in element formulation with inclusion of proposed methodologies to alleviate various locking phenomena. Automatic mesh generation scheme using the design element concept and isoparametric technique is employed to avoid re-meshing structures every iteration of optimization process. Numerical examples are performed and compared with exact solutions and forward finite differences to investigate the accuracy of proposed element formulation and sensitivity analysis.

병렬 컴퓨팅 환경 하에서 인공위성 어댑터 가상최적설계

연구는 병렬 컴퓨팅 기반에서 자동화된 격자 생성 기법과 입자 군집 최적화(PSO) 알고리즘을 적용한 최적 설계 프레임워크를 개발하여 이를 인공위성 어댑터 모듈의 구조 최적 설계에 적용하였다. 자동화된 격자 생성 기법을 적용하여 구조 형상 변화를 가능하게 함으로써 폭넓은 범위에서 최적 형상 모델을 도출할 수 있었다. 또한 최적화 알고리즘인 PSO 알고리즘을 병렬 계산환경과 접목하고, 계산 성능을 최대화하기 위해 비동기식 PSO 알고리즘을 개발하였다. 그 결과 최적화에 걸리는 계산 시간을 줄일 수 있었다. 최적화 작업에서 제한 조건으로는 고유진동수와 어댑터에 발생하는 최대 응력 값을 고려하였다. 결과적으로 인공위성 어댑터 모듈의 최적 설계를 통해 인공위성 구조 질량 감소를 유도해 내었다. In this paper, optimal design framework is developed by automatic mesh generation and PSO(Particle Swarm Optimization) algorithm based on parallel computing environment and applied to structural optimal design of satellite adapter module. By applying automatic mesh generation, it became possible to change the structural shape of adapter module. PSO algorithm was merged with parallel computing environment and for maximizing a computing performance, asynchronous PSO algorithm was developed and could reduce the computing time of optimization process. As constraint conditions, eigen-frequency and maximum stress was considered. Finally using optimal design framework, weight reduction of satellite adapter module is derived with satisfaction of structural safety.

Optimization of arches using genetic algorithm

An optimization procedure is presented for the minimum weight and strain energy optimization for arch structures subjected to constraints on stress, displacement and weight responses. Both thickness and shape variables defining the natural line of the arch are considered. The computer program which is developed in this study can be used to optimize thick, thin and variable thickness curved beams/arches. An automated optimization procedure is adopted which integrates finite element analysis, parametric cubic spline geometry definition, automatic mesh generation and genetic algorithm methods. Several examples are presented to illustrate optimal arch structures with smooth shapes and thickness variations. The changes in the relative contributions of the bending, membrane and shear strain energies are monitored during the whole process of optimization.

Adaptation of CAD model topology for finite element analysis

The preparation of a Finite Element Analysis (FEA) model from a Computer Aided Design (CAD) model is still a difficult task since its Boundary Representation (B-Rep) is often composed of a large number of faces, some of which may be narrow or feature short edges that are smaller than the desired FE size (for mesh generation). Consequently, these faces and edges are considered as geometric artefacts that are irrelevant for the automatic mesh generation process. Such inconsistencies often cause either poorly-shaped elements or meshes that are locally over-densified. These inconsistencies not only slow down the solver (using too many elements) but also produce poor or inappropriate simulation results. In this context, we propose a “Mesh Constraint Topology” ( MCT) model with automatic adaptation operators aimed at transforming a CAD model boundary decomposition into a FE model, featuring only mesh-relevant faces, edges and vertices, i.e., an explicit data model that is intrinsically adapted to the meshing process. We provide a set of criteria that can be used to transform CAD model boundary topology using MCT transformations, i.e., edge deletion, vertex deletion, edge collapsing, and merging of vertices. The proposed simplification criteria take into account a size map, a discretization error threshold and boundary conditions. Applications and results are presented through the adaptation of CAD models using the proposed simplification criteria.

Influence of anisotropy on peri-implant stress and strain in complete mandible model from CT

This paper reveals the influence of elastic anisotropy for the peri-implant stress and strain in personalized mandible. First, from CT data, the individual geometry of the complete range of mandible was well reproduced, also the separation between cortical and cancellous bone. Then, by an ad hoc automatic mesh generator integrated with anisotropic material assignment function, high quality anisotropic finite element model of the complete mandible was created, with two standard threaded implants embedded in posterior zone. The values of principal stress and strain in surrounding bone were evaluated under buccolingual oblique loading, and compared to that of the same FE model with equivalent isotropic material. Results of the analyses demonstrated that the percentage increase of stress and strain in anisotropic case reached up to 70%. It is concluded that anisotropy has significant effects on peri-implant stress and strain and careful consideration should be given to its use in biomechanical FE studies.

Numerical Model for Analyzing Slug Tests in Vertical Cutoff Walls

Analysis of a slug test estimating the hydraulic conductivity of a vertical cutoff wall is complicated by the high compressibility of backfill materials and by the proximity of a well to the edge of the cutoff wall. An implicit finite-difference program, named Slug_3, was developed to analyze results of slug tests in the vertical cutoff wall. The program uses block-centered mesh formulation, considers variable hydraulic conductivity and specific storage, and has automatic time-step control and mesh generation. The geometry and flux-boundary condition in the well-intake section is fully considered, and the interface between a cutoff wall and natural soil formation is modeled as a constant head-boundary condition. Also, a filter cake can be simulated in Slug_3. Slug_3 is verified by comparing results with an analytical solution for a partially penetrating well in aquifers and another numerical code, MODFLOW-96, for a vertical cutoff wall. The program provides a new analytic tool for analyzing slug-test results from vertical cutoff walls and is unique in the ability to simulate variable hydraulic properties, which can be particularly important for highly compressible materials such as soil-bentonite backfill in a cutoff wall.

Investigations into the applicability of adaptive finite element methods to two‐dimensional infinite Prandtl number thermal and thermochemical convection

An adaptive finite element procedure is presented for improving the quality of solutions to convection‐dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well‐known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation‐based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well‐established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid‐based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.

Finite element analysis for wavelike flow marks in injection molding

AbstractWavelike flow marks are a kind of surface defect that can arise during the filling stage of the injection molding process. In this study, we performed a numerical analysis using a finite element method to predict the conditions under which flow marks are generated. To simplify the analysis, a two dimensional flow through a channel between two parallel plates was considered. The viscosity of the polymer melt was modeled by the Cross‐WLF equation. For the finite element analysis, a velocity–pressure formulation was used to simultaneously solve the continuity and momentum equations. The calculation domain for the numerical analysis keeps changing with time due to the advancing melt front. To handle the free surface more accurately, a moving grid method was employed. A numerical mesh was generated at each time step using an automatic mesh generation scheme. An analytical model was developed to correlate the effects of process variables to the flow mark geometry. Results of the numerical analysis were compared with the available experimental data. The estimated geometry of the flow marks were in good qualitative agreement with experimental observations. Parametric studies have been performed to examine the effects of various processing conditions and the material properties on flow mark size. POLYM. ENG. SCI., 47:922–933, 2007. © 2007 Society of Plastics Engineers