NURBS-Enhanced Finite Element Method (NEFEM)

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.     

Automated low-order to high-order mesh conversion

An algorithm is presented for the CAD-free conversion of linear unstructured meshes into curved high-order meshes, which are necessary for high-order flow simulations. The algorithm operates via three steps: (1) autonomous detection of feature curves along the mesh surface, (2) reconstruction of the surface curvature from the combination of surface node positions and feature curve positions, and (3) alignment of the mesh interior to the newly curved surface. The algorithm is implemented in our freely available cross-platform graphical software program meshCurve, which transforms existing linear meshes into high-order curved meshes

     

High-Order Mixed Current Basis Functions for Electromagnetic Scattering of Curved Surfaces

We construct high-order mixed current vector basis (unctions on an arbitrary curved surface which can be subdivided as a union of curved triangles and quadrilaterals. The objective is to construct vector basis (a) which consists of high-order polynomials of the surface parameterization variables on triangles and quadrilaterals, (b) part of the basis will have vanishing moments on the triangles and quadrilaterals. The first property will enable us to represent the current distribution over scatter surface with much less number of unknowns and larger patches of either triangular or quadrilateral shapes. The second property will achieve what wavelet basis does on an interval, but on a more general domain, namely, a sparse matrix representation for some integral operators.     

Two optimization methods for complicated structures with multiparameter elements based on generalized condensation

A high-order condensation expression is proposed to generalize Duffin's condensation formula. Based on the higher-order condensation expression, two primal algorithms of the second-order are constructed to solve GGP (generalized geometric programming) problems. To overcome the difficulty of solving the structural optimization with multiparameter elements, two methods are proposed and implemented in a computer program. The first method takes one geometrical property of the cross-section as one component of the design variables for each element and adopts SQP (sequential quadratic programming) to solve the optimization model. The second method takes geometrical sizes of the cross-section as the design variables for each element and adopts primal algorithms of GGP problems to solve the optimization model.     

Optimization techniques for curved path computing

Participating media with an inhomogeneous index of refraction make light follow curved paths. Simulating this in a global illumination environment has usually been neglected due to the complexity of the calculations involved, sacrificing accurate physical simulations for efficient visual results. This paper aims to simulate non-linear media in a more reasonable time than previous works without losing physical correctness. Accuracy is achieved by solving the Eikonal equation of geometrical optics, which describes the path followed by a light beam that traverses a non-linear medium. This equation is used in the context of a photon mapping extension.     

反向工程中NURBS曲面CAD重构技术研究

CAD几何模型重构技术是反向工程RE(Reverse Engineering)技术的核心,NURBS(Non-Uniform Rational B-Splines)方法因其表示法的形状控制灵活性,在曲面造型和曲面重构中具有重要作用.针对CAD曲面重构技术进行研究,并对NURBS曲面重构提出一种新的构建方法,将每个数据点相对应的有理基函数的参数值最大化,所得函数值作为数据点的参数值来构造NURBS参数曲面.最后通过实例证明了该方法的有效性.     

A virtual punching method for shape optimization of openings on curved panels using CAD-based Boolean operations

This paper aims at developing new methodologies for shape optimization of openings on three-dimensional curved panels that are used widely in aeronautical and aerospace engineering. To circumvent the difficulties associated with the hole boundary shape parameterization, a virtual punching method that exploits Boolean operations of the CAD modeler is proposed for the definition of shape design variables. Compared with the parametric mapping method developed previously, the virtual punching method is shown to be an implicit boundary representation for this specific kind of structure. Instead, the parametric mapping method is based on the explicit boundary representation.A zero-order genetic algorithm (GA) is correspondingly implemented into the design procedure of the virtual punching method to execute the optimization process for two reasons. First, it makes it possible to avoid sensitivity analysis that is relatively difficult due to the implicit boundary representation formulation and the use of an unstructured mesh. Second, the computing cost of the GA is practically affordable in shape optimization because often only a small number of design variables are involved. Numerical tests are carried out for typical examples of the stress concentration minimization around openings on the curved panels.     

基于高阶结构约束的稀疏人脸识别算法

为了挖掘人脸稀疏表示的高阶结构信息,从而获得更精确的人脸分类判别信息,提出一种新的基于高阶结构约束的稀疏表示的人脸识别算法。在提取人脸图像的Gabor特征后,选取适当的训练样本构建稀疏线性编码模型,利用样本特征间的高阶结构信息约束和最优化求解测试样本的稀疏系数,将稀疏系数作为最终特征对人脸进行识别,实验结果表明,与结构约束稀疏表示和非结构约束稀疏表示的方法比较,人脸的高阶结构稀疏表示能显著提高人脸的识别准确率。     

Computation of medial axis and offset curves of curved boundaries in planar domain

In this paper, we begin our research from the generating theory of the medial axis. The normal equidistant mapping relationships between two boundaries and its medial axis have been proposed based on the moving Frenet frames and Cesaro’s approach of the differential geometry. Two pairs of adjoint curves have been formed and the geometrical model of the medial axis transform of the planar domains with curved boundaries has been established. The relations of position mapping, scale transform and differential invariants between the curved boundaries and the medial axis have been investigated. Based on this model, a tracing algorithm for the computation of the medial axis has been generated. In order to get the accurate medial axis and branch points, a Two_Tangent_Points_Circle algorithm and a Three_Tangent_Points_Circle algorithm have been generated, which use the results of the tracing algorithm as the initial values to make the iterative process effective. These algorithms can be used for the computation of the medial axis effectively and accurately. Based on the medial axis transform and the envelope theory, the trimmed offset curves of curved boundaries have been investigated. Several numerical examples are given at the end of the paper.     

一种基于平面对称群的对称图案生成方法

织物图案中包含着各类蜿蜒曲线、规则与不规则的复杂元素。虽然剪纸图案和分 形图案的生成方法已有大量研究工作,但是面向新疆织物图案特点的计算机自动生成方法仍然 存在许多挑战性难题。针对新疆织物图案风格化建模难度大的问题,提出图案对称性作为图案 生成关键指标,构造循环群和二面体群等变映射与不变映射,研究图案对称性的表征方式,利 用对称图案探讨群的映射空间与对称图形之间的关联。通过群映射的仿真实验,绘制混沌吸引 子得到群对称图案,有效提高图案的对称性,丰富织物图案的花型设计。     

Array-based,parallel hierarchical mesh refinement algorithms for unstructured meshes

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE’s using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in-memory refinement). We also describe a high-order boundary reconstruction capability that can be used to project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework “Mesh Oriented dAtaBase” (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. We also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.     

Application of natural approach to non-linear analysis of sandwich and composite plates and shells

The natural approach is used to construct a curved triangular shell element for analysis of sandwich and composite shells. The shells can be either symmetric or unsymmetric and the in-plane shear relation can be linear or non-linear. The attention is centered on the transverse shear treatment, the local rigid movement representation and the development of the geometrical stiffness matrix.     

并联机器人曲面汉字雕刻刀路规划算法研究

解决了并联机器人在空间曲面上雕刻汉字时所遇到的相关问题,包括平面刀路向曲面刀路的映射方法、曲线插补计算及刀具姿态实时规划算法等,给出了算例并以6-PUS并联机器人为模型进行了实验,实验结果验证了所提方法的有效性和可行性,这些方法理论上适用于任意种类的文字及空间曲面,也适用于雕刻之外的其它加工领域.     

Environment Mapping and Other Applications of World Projections

Various techniques have been developed that employ projections of the world as seen from a particular viewpoint. Blinn and Newell introduced reflection mapping for simulating mirror reflections on curved surfaces. Miller and Hoffman have presented a general illumination model based on environment mapping. World projections have also been used to model distant objects and to produce pictures with the fish-eye distortion required for Omnimax frames. This article proposes a uniform framework for representing and using world projections and argues that the best general-purpose representation is the is projection onto a cube. Surface shading and texture filtering are discussed in the context of environment mapping, and methods are presented for obtaining diffuse and specular surface illumination from prefiltered environment maps. Comparisons are made with ray tracing, noting that two problems with ray tracing?obtaining diffuse reflection and antialiasing specular reflection?can be handled effectively by environment mapping.     

一种基于图卷积网络的文本多标签学习方法

多标签学习广泛应用于文本分类、标签推荐、主题标注等.最近,基于深度学习技术的多标签学习受到广泛关注,针对如何在多标签学习中有效挖掘并利用高阶标签关系的问题,提出一种基于图卷积网络探究标签高阶关系的模型TMLLGCN.该模型采用GCN的映射函数从数据驱动的标签表示中生成对象分类器挖掘标签高阶关系.首先,采用深度学习方法提...     

Studied X-FEM enrichment to handle material interfaces with higher order finite element

An approach to improve the geometrical representation of surfaces with the eXtended Finite Element Method is proposed. Surfaces are implicitly represented using the level set method. The finite element approximation is enriched by additional functions through the notion of partition of unity, to track material interfaces. Optimal rate of convergence is achieved with curved geometries, using linear elements and linear level set in elements. In order to accelerate the convergence, the order of approximation shape functions is increased, while keeping the same computational mesh. The level set is represented on a finer sub-mesh than the finite element mesh. A special attention to integration procedure is necessary. A new enrichment function is introduced to represent the behavior of curved material interfaces. Numerical examples including free surfaces and material interfaces in 2-D linear elasticity are presented to study convergence rates.     

Normal Distributions Transform Traversability Maps: LIDAR‐Only Approach for Traversability Mapping in Outdoor Environments

Safe and reliable autonomous navigation in unstructured environments remains a challenge for field robots. In particular, operating on vegetated terrain is problematic, because simple purely geometric traversability analysis methods typically classify dense foliage as nontraversable. As traversing through vegetated terrain is often possible and even preferable in some cases (e.g., to avoid executing longer paths), more complex multimodal traversability analysis methods are necessary. In this article, we propose a three‐dimensional (3D) traversability mapping algorithm for outdoor environments, able to classify sparsely vegetated areas as traversable, without compromising accuracy on other terrain types. The proposed normal distributions transform traversability mapping (NDT‐TM) representation exploits 3D LIDAR sensor data to incrementally expand normal distributions transform occupancy (NDT‐OM) maps. In addition to geometrical information, we propose to augment the NDT‐OM representation with statistical data of the permeability and reflectivity of each cell. Using these additional features, we train a support‐vector machine classifier to discriminate between traversable and nondrivable areas of the NDT‐TM maps. We evaluate classifier performance on a set of challenging outdoor environments and note improvements over previous purely geometrical traversability analysis approaches.     

Nonlinear analysis of size-dependent frequencies in porous FG curved nanotubes based on nonlocal strain gradient theory

A nonlocal strain gradient model is developed in this research to analyse the nonlinear frequencies of functionally graded porous curved nanotubes. It is assumed that the curved nanotube is in contact with a two-parameter nonlinear elastic foundation and is also subjected to the uniform temperature rise. The non-classical theory presented for curved nanotubes contains a nonlocal parameter and a material length scale parameter which can capture the size effect. A power law distribution function is used to describe the graded properties through the thickness direction of curved nanotubes. The even dispersion pattern is used to model the porosities distribution. The high-order shear deformation theory and the von Kármán type of geometric non-linearity are utilized to obtain the nonlinear governing equations of the structure. The size-dependent equations of motion for the large amplitude vibrations of curved nanotubes are obtained by employing Hamilton’s principle. The analytical solutions are extracted for the curved nanotube with immovable hinged-hinged boundary conditions. Size-dependent frequencies of the curved nanotube exposed to thermal field are obtained using the two-step perturbation technique and Galerkin procedure. The effects of important parameters such as nonlocal and length scale parameters, temperature field, elastic foundation, porosity, power law index and geometrical parameters are studied in detail.

     

基于Log-Gabor和正交等度规映射的人脸识别

针对人脸识别中的特征提取问题,提出一种基于Log-Gabor和正交等度规映射(Orthogonal IsoProjection,OIsop)的人脸识别算法.算法首先采用Log-Gabor小波对图像进行滤波来提取高阶非线性统计信息.然后,在原始的优化问题中增加正交约束条件,推导出能得到一组具有正交性最优映射向量的迭代公式...