Surface Modellinhg and Mesh Generation for Simulating Superplastic Forming

This paper presents an approach which enables surface modelling,mesh generation and the Finite Element(FE) analysis to be integrated together to simulate superplastic forming process for complex shaped components.Techniques have been developed to generate an FE mesh over non-four-sided surface areas,the boundaries of which are Bezier curves of arbitrary degree,using a consistent expression.Theoretical evidence is given to determine the number of Bezier triangular patches required for accurately re-constructing die surfaces within a commercial FE solver.The developed techniques have been successfully used in determining the process parameters for forming a 3D rectangular box.     

Process monitoring in stamping operations through tooling integrated sensing

This paper introduces a new sensing method for stamping process monitoring based on the measurement of contact pressure distribution across the sheet metal-tooling interface, by means of an array of tooling-integrated force sensors. The role of numeric surface methods in estimating the contact pressure distribution on the sheet metal-tooling interface has been studied through finite element analysis and experiments. A finite element model is set up to model the contact interactions, based on the geometry of a customized stamping test fixture. Discrete samples of contact pressure taken from the FE model have been used to recreate continuous-pressure surfaces based on the Thin Plate Splines (TPS) and Bezier surface algorithms. It is shown that the temporal–spatial contact pressure distribution across the sheet metal-tooling interface can be effectively reconstructed through interpolation using spatially discrete sensor data. Comparison of surface-based pressure estimates with the FEA field solution indicates that the TPS-based method is more accurate than the Bezier method. The effectiveness of the surface modeling scheme is also evaluated experimentally by comparing the net press force calculated from numerical integration of the TPS surfaces with the experimentally measured value under different press speeds. The effectiveness of the new sensing method is further demonstrated by detection of slide misparallelism through analysis of the tooling interface pressure distribution. The study presents a new approach to enhancing process observability in manufacturing operations.     

Bezier参数曲面快速拟合及其光顺性分析

本文从具有Ｂｅｚｉｅｒ性质的一般性参数曲线着手，推导出导关系数为４的另一种变形Ｂｅｚｉｅｒ曲线，由它生成的双三次Ｂｅｚｉｅｒ曲面具有拟合速度快、精度高的特点，同时还可用于对控制点的拟合。为减少拟合时间、较快地生成自由曲面提出了一种策略。     

从点集重构曲面网格方法综述

本文主要对三维数据点重构曲面网格模型方法进行了综述。从三维数据点集重构曲面一般遵循以下三个步骤:1)重构曲面网格模型;2)网格简化;3)拟合曲面(通常为Bezier,NURBS),其中重构曲面网格为关键的一步;三维数据点集由三维数字化仪采集得到,不同的数字化设备,得到的三维数据点集可能会有差别,重构曲面网格的算法也不尽相同。本文介绍了几种对于不同数据形式、有代表性的重构曲面网格算法。     

Volume of Solid (VOS) and surface tracking method for metal forming applications

The adaptation of the Volume of Fluid (VOF) method to solid mechanics (VOS) is presented with the focus on metal forming applications. The method is discussed for a general non-uniform mesh with Eulerian FE formulation. The discussion in this paper focuses on the modeling of the contact between the tool and the workpiece, and the connectivity of the free surface during the whole process. Improvement on the connectivity of the free surface and the representation of curves is achieved by considering the mechanics of these processes. Three applications are discussed and used to highlight different aspects of the VOS method.     

Polynomial surfaces interpolating arbitrary triangulations

Triangular Bezier patches are an important tool for defining smooth surfaces over arbitrary triangular meshes. The previously introduced 4-split method interpolates the vertices of a 2-manifold triangle mesh by a set of tangent plane continuous triangular Bezier patches of degree five. The resulting surface has an explicit closed form representation and is defined locally. In this paper, we introduce a new method for visually smooth interpolation of arbitrary triangle meshes based on a regular 4-split of the domain triangles. Ensuring tangent plane continuity of the surface is not enough for producing an overall fair shape. Interpolation of irregular control-polygons, be that in 1D or in 2D, often yields unwanted undulations. Note that this undulation problem is not particular to parametric interpolation, but also occurs with interpolatory subdivision surfaces. Our new method avoids unwanted undulations by relaxing the constraint of the first derivatives at the input mesh vertices: The tangent directions of the boundary curves at the mesh vertices are now completely free. Irregular triangulations can be handled much better in the sense that unwanted undulations due to flat triangles in the mesh are now avoided.     

CAD／CAM中曲面光滑拼接的研究

本文讨论了CAD／CAM软件系统中复杂曲面的光滑拼接问题。提出了对曲面光滑接接的磨光法和覆合法。利用这些方法对一些机械零件进行了行造型和控具加工，取得了令人满意的效果。     

用局部阻尼波形法的自连贯网格生成法

介绍将生成或已有的有限元规则六面体单元改变成形状复杂且光滑的六面体单元的一种新技术——波形法．简单建立了波形法的数学模型并编程进行了网格生成．实验结果表明,只要把复杂外部形状按波的形式传输给指定的规则六面体单元模型,就可以得到具有复杂外部形状的六面体单元网格模型,且网格生成速度快、不出现单元或节点漏洞、欠缺等问题,同时不受单元类型的限制。     

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.     

B-SPLINE SURFACE SMOOTH JOINING

Ｂ－ＳＰＬＩＮＥＳＵＲＦＡＣＥＳＭＯＯＴＨＪＯＩＮＩＮＧＮｉｎｇＴａｏＪｉｎｇＬｉｎｇＧｕａｎＺｈｉｄｏｎｇＴａｎｇＲｏｎｇｘｉＡｂｓｔｒａｃｔＯｐｔｉｍｉｚａｔｉｏｎｔｅｃｈｎｉｑｕｅｓａｒｅｂｅｉｎｇａｐｐｌｉｅｄｔｏｓｏｌｖｅｔｈｅｐｒｏｂｌｅ...     

优化技术在B样条曲面拼接中的应用

只要选用相应的目标函数，曲面插值、逼近、拼接和光顺都可以使用优化技术统一处理，本文讨论用优化技术构造Ｂ样条网络曲面，着重解决角点和Ｇ＾１、Ｇ＾２协调与边界上的Ｇ＾１拼接。关于角点处网格曲面的Ｇ＾２协调，本文针对退化和非爱化两种情况进行讨论。本文算法允许共边曲面沿公共边界具有不同的参数化，在理论上允许曲面在角点处退化。     

复杂曲面混合网格的生成算法

有限元网格质量的好坏对金属成形模拟的精度和效率有很大影响。提出了一种复杂曲面混合网格自动生成算法，该算法根据所要划分的网格密度形成初始化边界节点，逐步向内铺砌混合网格，直至布满整个区域。应用实践表明．该算法具有稳定、准确和速度快的特点，生成的网格在相邻曲面边界处不会产生裂缝与覆盖，很好地满足了金属成形模拟分析软件对网格划分的要求。     

Template-based finite-element mesh generation from medical images

The finite-element (FE) method is commonly used in biomedical engineering to simulate the behaviour of biological structures because of its ability to model complex shapes in a subject-specific manner. However, generating FE meshes from medical images remains a bottleneck. We present a template-based technique for semi-automatically generating FE meshes which is applicable to prospective studies of individual patients in which FE meshes must be generated from scans of the same structure taken at different points in time to study the effects of disease progression/regression. In this "template-based" meshing approach, the baseline FE (tetrahedral) volume mesh is first manually aligned with the follow-up images. The triangulated surface of the mesh is then automatically deformed to fit the imaged organ boundary. The deformed surface nodes are then smoothed using a Laplacian smoothing algorithm to correct triangle (surface nodes) distortion and thus preserve triangle quality. Finally, the internal mesh nodes are smoothed to correct distorted tetrahedral elements and thus preserve tetrahedral element quality. This template-based approach is shown to be as accurate and precise as the previous technique used by our group, while preserving element quality and volume.     

Mesh generation and mesh refinement procedures for the analysis of concrete shells

In this paper, a mesh generation and mesh refinement procedure for adaptive finite element (FE) analyses of real-life surface structures are proposed. For mesh generation, the advancing front method is employed. FE meshes of curved structures are generated in the respective 2D parametric space of the structure. Thereafter, the 2D mesh is mapped onto the middle surface of the structure. For mesh refinement, two different modes, namely uniform and adaptive mesh refinement, are considered. Remeshing in the context of adaptive mesh refinement is controlled by the spatial distribution of the estimated error of the FE results. Depending on this distribution, remeshing may result in a partial increase and decrease, respectively, of the element size. In contrast to adaptive mesh refinement, uniform mesh refinement is characterized by a reduction of the element size in the entire domain. The different refinement strategies are applied to ultimate load analysis of a retrofitted cooling tower. The influence of the underlying FE discretization on the numerical results is investigated.     

Finite element mesh deformation with the skeleton-section template

To develop fast finite element (FE) adaptation methods for simulation-driven design optimization, we propose a radial basis functions (RBF) method with a skeleton-section template to globally and locally deform FE meshes of thin-walled beam structures.The skeleton-section template is automatically formulated from the input mesh and serves as a hierarchical parameterization for the FE meshes. With this hierarchical parameterization, both the global and the local geometries of a thin-walled beam can be processed in the same framework, which is of importance for designing engineering components. The curve skeleton of the mesh is constructed with Voronoi decomposition, while the cross-sections are extracted from the mesh based on the curve skeleton.The RBF method is employed to locally and globally deform the mesh model with the cross-sections and the skeleton, respectively. The RBF method solves the spatial deformation field given prescribed deformations at the cross-sections. At the local scale, the user modifies the cross-sections to deform a region of the surface mesh. At the global level, the skeleton is manipulated and its deformation is transferred to all cross-sections to induce the mesh deformation.In order to handle curved mesh models and attain flexible local deformations, the input mesh is embedded into its skeleton frame field using an anisotropic distance metric. In this way, even strip-like features along arbitrary directions can be created on the mesh model using only a few cross-sections as the deformation handles. In addition, form features can be rigidly preserved at both deformation levels.Numerical examples demonstrate that intuitive and qualified FE mesh deformations can be obtained with manipulation of the skeleton-section template.     

Expert system to predict forging load and axial stress

Finite element (FE) analysis of forging process generally takes a long time to carry out. Sometimes, it might be required to predict the results of FE analysis as accurately as possible in a less processing time. A pre-analysis prediction of the results could also be helpful in some cases. Soft computing-based expert system has been developed in the present work, to predict forging load and axial stress developed. Forging load and axial stress have been calculated for an axi-symmetric part by varying the values of maximum contact friction stress and normal contact stiffness factor in ANSYS FE package. Data generated in the process have been utilized for developing a fuzzy logic-based expert system, on the basis of the authors’ knowledge, which has been optimized subsequently using a genetic algorithm (GA). Two other expert systems (ESs) have been developed automatically using the GA, without taking any aid from the manually-designed fuzzy logic system. It has been found that the expert systems are able to make predictions of forging load and axial stress as accurately as the FE package can do. Results of the ESs have also been seen to be comparable with the experimental results reported in the available literature. Instantaneous prediction capability of the developed expert systems proves their suitability for on-line implementations.     

Generation of Smooth Surfaces by Controlling Curvature Variation

To satisfy a designer's intention for constructing aesthetic shapes such as automotive bodies, we propose a surface generation method. In the surface design process, designers determine shapes according to their great concern for the reflected images of vehicle surroundings, shade lines and highlight lines. Since reflection and shading are affected by changes of surface normal, the curvature variation of the surface, which represents the change of the surface normal, should be smooth and distributed as designers want. The proposed method controls curvature distribution directly by determining a surface shape from an evolute, which is a locus of the curvature center of the generatrix and moves along directrices to form the surface. It first generates evolutes of boundary curves to be generatrices as rational Bezier curves, then interpolates their shapes with the Bezier polygons, and locates the interpolated shape to the corresponding position of the directrices. By applying this method, we have confirmed that a smooth shape is generated from four boundary curves.     

G2 quasi-developable Bezier surface interpolation of two space curves

Surface development is used in many manufacturing planning operations, e.g., for garments, ships and automobiles. However, most freeform surfaces used in design are not developable, and therefore the developed patterns are not isometric to the original design surface. In some domains, the CAD model is created by interpolating two given space curves. In this paper, we propose a method to obtain a G² quasi-developable Bezier surface interpolating two arbitrary space curves. The given curves are first split into a number of piecewise Bezier curves and elemental Bezier patches each of which passes through four splitting points are constructed. All neighboring elemental patches are G² connected and they are assembled optimally in terms of the degree of developability (the integral Gaussian curvature). Experiments show that the final composite Bezier surface is superior to a lofted one which is defined regardless of the final surface developability.     

Jacobian-based repair method for finite element meshes after registration

Registration methods are used in the meshing field to “adapt” a given mesh to a target domain. Finite element method (FEM) is applied to the resulting mesh to compute an approximate solution to the system of partial differential equations (PDE) representing the physical phenomena under study. Prior to FE analysis the Jacobian matrix determinant must be checked for all mesh elements. The value of this Jacobian depends on the configuration of the element nodes. If it is negative for a given node, the element is invalid and therefore the FE analysis cannot be carried out. Similarly, some elements, although valid, can present poor quality regarding Jacobian-based indicator values, such as the Jacobian ratio. Mesh registration procedures are likely to produce invalid and/or poor quality elements if the Jacobian parameter is ignored. To repair invalid and poor quality elements after mesh registration, we propose a relaxation procedure driven by specific validity and quality energy formulations derived from the Jacobian value. The algorithm first recovers mesh validity and further improves elements quality, focusing primarily on nodes that make the elements invalid or of poor quality. Our novel approach has been developed in the context of non-rigid mesh registration and validated on a data set of 60 clinical cases in the context of orthopaedic and orthognathic hard and soft tissues modelling studies. The proposed repair method achieves a valid state of the mesh and also raises the quality of the elements to a level suitable for commercial FE solvers.