引进综采设备常用渐开线花键的标准及计算

根据煤矿引进的综采设备中采用不同标准渐开线花键的特点 ,提出了综采设备常用渐开线花键的测量与计算     

保单调插值的奇异混合三角/双曲B样条

为了使得插值曲线保单调,设计了两类新的平面参数曲线及其保单调插值算法.计算奇异混合函数,把三角/双曲多项式B样条曲线与奇异多边形通过奇异混合函数混合,无需解方程组或繁琐的迭代,得到自动插值给定平面点列且C2(或G1)连续的带形状参数的复合曲线,尤其能得到摆线、螺旋线、双曲线、悬链线等各类超越曲线.通过把插值曲线的导矢分量转化为类Bernstein多项式,并且利用Bernstein多项式非负的充要条件,得到插值曲线单调的充要条件,获得形状参数合适的取值范围. 该方法简单方便,所得参数范围保证了插值曲线保单调.     

渐开线螺旋花键的滚压加工

阐述了渐开线螺旋花键的滚压原理、坯料计算、工装设计及材料的选择，对滚压加工进行了很好的研究。实践表明，采用滚压技术加工的渐开线螺旋花健，不仅极大地提高了生产效率，且制件的质量也大为提高。     

基于静力测试的三维曲面结构测点优化配置

传感器测点优化配置在结构健康监测系统中具有重要作用。针对结构健康监测中静力作用下三维曲面结构变形状况进行了研究,提出了三维曲面结构的测点优化配置方法。首先,对三维曲面结构进行测点组合选取,根据已知测点的响应值采用三维超曲面样条函数插值估计未布置测点的响应值,然后建立适应度函数,对未布置测点的估计值与实际值的误差进行判定,最后通过二重结构编码遗传算法对测点组合进行优化,选取适应度函数值最小的测点配置方案,从而实现了传感器测点优化配置的目的。应用该方法对简支的圆柱壳弯曲变形进行了测点优化配置,得到的适应度函数值最小的测点配置方案中,未布置测点的估计值与实际值的误差为1.10％,从而验证了该方法的可行性和有效性。     

Generating planar spiral by geometry driven subdivision scheme

Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a new iterative subdivision scheme for generating planar spiral segments from two points and their tangent vectors. The subdivision process consists of two main steps, computing new points and adjusting tangent vectors adaptively for each iteration. We categorize this iterative scheme as geometry...     

Powell–Sabin B‐splines and unstructured standard T‐splines for the solution of the Kirchhoff–Love plate theory exploiting Bézier extraction

The equations that govern Kirchhoff–Love plate theory are solved using quadratic Powell–Sabin B‐splines and unstructured standard T‐splines. Bézier extraction is exploited to make the formulation computationally efficient. Because quadratic Powell–Sabin B‐splines result in ‐continuous shape functions, they are of sufficiently high continuity to capture Kirchhoff–Love plate theory when cast in a weak form. Unlike non‐uniform rational B‐splines (NURBS), which are commonly used in isogeometric analysis, Powell–Sabin B‐splines do not necessarily capture the geometry exactly. However, the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to NURBS, as no bending strip method for joined NURBS patches is needed. This paper further illustrates how unstructured T‐splines can be modified such that they are ‐continuous around extraordinary points, and that the blending functions fulfil the partition of unity property. The performance of quadratic NURBS, unstructured T‐splines, Powell–Sabin B‐splines and NURBS‐to‐NURPS (non‐uniform rational Powell–Sabin B‐splines, which are obtained by a transformation from a NURBS patch) is compared in a study of a circular plate. Copyright © 2015 John Wiley & Sons, Ltd.     

Invariant image reconstruction from irregular samples and hexagonal grid splines

We present an algorithm for the reconstruction of images from irregularly placed samples, using linear splines with control points on a hexagonal grid. Several spline approximations are computed for different transformations of the control point grid (e.g. translations and rotations). These approximations are then merged together after compensation of the transformations, yielding a high-quality invariant image reconstruction. Evaluations show that the use of hexagonal grids of the “invariance by integration” principle improves reconstruction quality. An application to image coding is also presented.     

The thin plate spline robust point matching (TPS-RPM) algorithm: A revisit

This paper reviews the TPS-RPM algorithm (Chui and Rangarajan, 2003) for robustly registering two sets of points and demonstrates from a theoretical point of view its inherent limited performance when outliers are present in both point sets simultaneously. A double-sided outlier handling approach is proposed to overcome this limitation with a rigorous mathematical proof as the underlying theoretical support. This double-sided outlier handling approach is proved to be equivalent to the original formulation of the point matching problem. For a practical application, we also extend the TPS-RPM algorithms to non-rigid image registration by registering two sets of sparse features extracted from images. The intensity information of the extracted features are incorporated into feature matching in order to reduce the impact from outliers. Our experiments demonstrate the double-sided outlier handling approach and the efficiency of intensity information in assisting outlier detection.     

Modelling solitary waves of a fifth-order non-linear wave equation

A numerical solution of a fifth-order non-linear dispersive wave equation is set up using collocation of seventh-order B-spline interpolation functions over finite elements. A linear stability analysis shows that this numerical scheme, based on a Crank–Nicolson approximation in time, is unconditionally stable. The method is used to model the behaviour of solitary waves.     

Unconditionally stable C1-cubic spline collocation method for solving parabolic equations

This article aims to present a new approach based on C¹-cubic splines introduced by Sallam and Naim Anwar [Sallam, S. and Naim Anwar, M. (2000). Stabilized cubic C¹-spline collocation method for solving first-order ordinary initial value problems, Int. J. Comput. Math., 74, 87–96.], which is A-stable, for the time integration of parabolic equations (diffusion or heat equation). The introduced method is an example of the so-called method of lines (the solution is thought to consist of space discretization and time integration), which is an extension of the 1/3-Simpson's finite-difference scheme. Our main objective is to prove the unconditional stability of the proposed method as well as to show that the method is convergent and is of order O (h ²)?+?O (k ⁴) i.e. it is a fourth-order in time and second-order in space. Computational results also show that the method is relevant for long time interval problems.