Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness

The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.

ANALYSIS OF BENDING, VIBRATION AND STABILITY FOR THIN PLATE ON ELASTIC FOUNDATION BY THE MULTIVARIABLE SPLINE ELEMENT METHOD

In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.

A Study on Precipitation Products with High Resolution in Anhui Province Based on Thin Plate Smoothing Spline

In order to achieve refined precipitation grid data with high accuracy and high spatial resolution,hourly precipitation grid dataset with 1 km spatial resolution in Anhui Province from May to September (in the rainy season) in 2016 and from August 2017 to July 2018 was established based on thin plate smoothing spline (TPS),which meets the needs of climate change research and meteorological disaster risk assessment.The interpolation errors were then analyzed.The grid precipitation product obtained based on thin plate smoothing spline,CLDAS-FAST and CLDAS-FRT were evaluated.The results show that the interpolated values of hourly precipitation by thin plate smoothing spline are close to the observed values in the rainy season of 2016.The errors are generally below 0.9 mm/h.However,the errors of precipitation in the mountainous areas of eastern Huaibei and western Anhui are above 1.2 mm/h.On monthly scale,the errors in June and July are the largest,and the proportion of absolute values of the errors ≥2 mm/h is up to 2.0% in June and 2.2% in July.The errors in September are the smallest,and the proportion of absolute values of the errors ≥2 mm/h is only 0.6%.The root mean square (RMSE) is only 0.37 mm/h,and the correlation coefficient (COR) is 0.93.The interpolation accuracy of CLDAS-FRT is the highest,with the smallest RMSE (0.65 mm/h) and mean error ( ME =0.01 mm/h),and the largest COR (0.81).The accuracy of the precipitation product obtained by thin plate smoothing spline interpolation is close to that of CLDAS-FAST.Its RMSE is up to 0.80 mm/h,and its ME is only -0.01 mm/h.Its COR is 0.73,but its bias (BIAS) is up to 1.06 mm/h.

Development of quadrilateral spline thin plate elements using the B-net method

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

COMPACT SUPPORT THIN PLATE SPLINE ALGORITHM

Common tools based on landmarks in medical image elastic registration are Thin Plate Spline (TPS) and Compact Support Radial Basis Function (CSRBF). TPS forces the corresponding landmarks to exactly match each other and minimizes the bending energy of the whole image. However, in real application, such scheme would deform the image globally when deformation is only local. CSRBF needs manually determine the support size, although its deformation is limited local. Therefore, to limit the effect of the deformation, new Compact Support Thin Plate Spline algorithm (CSTPS) is approached, analyzed and applied. Such new approach gains optimal mutual information, which shows its registration result satisfactory. The experiments also show it can apply in both local and global elastic registration.

CUBLIC SPLINE SOLUTIONS OF AXISYMMETRICALNONLINEAR BENDING AND BUCKLING OFCIRCULAR SANDWICH PLATES

Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.

THz time domain monostatic radar cross section measurement of metallic plates and dihedrons

THz Radar Cross Section(RCS)measurement setup based on THz Time Domain Spectroscopy(TDS)is built to provide large scaled targets test ability in recent years.As calibrations,the metal plates and dihedrons are used in our experiments.The measurements are performed in a monostatic terahertz time-domain setup.The author proposed time domain and frequency domain calibration methods for angular RCS of calibrations,comparing the measurements with the theory to verify the ability of the time domain measurement setup.

ISOTROPICALIZED SPLINE INTEGRAL EQUATION METHOD FOR THE ANALYSIS OF ANISOTROPIC PLATES

In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotrqpic plates are utlized for the spline integral equation analysis of anisotropic plates.Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.

THE SOLUTION OF RECTANGULAR PLATES WITH LARGE DEFLECTION BY SPLINE FUNCTIONS

In this paper, Von Karman's set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection being taken as a perturbation parameter. These sets of linear equations are solved by the spline finite-point (SFP) method and by the spline finite element (SFE) method. The solutions for rectangular plates having any length-to-width ratios under a uniformly distributed load and with various boundary conditions are presented, and the analytical formulas for displacements and deflections are given in the paper. The computer programs are worked out by ourselves. Comparison of the results with those in other papers indicates that the results of this paper are satisfactorily better.

Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

基于薄板样条径向基函数的复合材料层合板自由振动分析

基于复合材料层合板的三角剪切变形理论,推导了对称复合材料层合板的控制微分方程。利用基于薄板样条径向基函数的无网格配置方法离散的控制微分方程,预测了对称复合材料层合板的自由振动行为。计算了不同材料参数和层合板几何参数的固有频率,并与文献结果进行了比较。还研究了节点排布、模量比和边厚比对固有频率的影响。结果表明,本文结果与文献结果具有较好的一致性,节点数量越大,无量纲频率对网格分布越不敏感,固有频率随着边厚比和模量比的增加而增加。通过数值实验,证明了用薄板样条径向基函数离散的三角剪切变形理论对对称复合材料层合板的自由振动分析具有较高的数值精度和良好的收敛性。

花键约束下变形摩擦片角向摆动的数值分析

为了揭示离合器分离状态下摩擦元件变形前后的动力学特性差异,本文研究了花键约束下不同变形程度摩擦片的角向摆动特性,分析了花键界面和翘曲变形对摆动的影响。本文对平直摩擦片进行了力学分析,并建立了平直片角向摆动的动力学模型。在此基础上,对平直片引入薄板的变形函数,考虑几何差异推导出了变形摩擦片的摆动模型。同时,与经典边界条件对比,在摩擦片内径的花键约束处采用了摩擦边界,并且基于几何结构推导出了最大允许摆动角。通过数值仿真,在时域和频域分析了各影响因素对摆动的影响。结果表明:旋转的摩擦片受扰动后,角向摆动频率随转速的增加而增加,而翘曲变形会降低摆动频率。此外,最大摆动角度在低转速时会延长摩擦片摆动的时间,摩擦力则会降低摆动的时间。

基于改进薄板样条运动模型的人脸动画算法

面部动画在电影、游戏、虚拟现实等领域起着关键作用,对于实现逼真、生动的人脸动画和情感传达至关重要。当面临面部形状、姿态、表情等多个变化因素时,虽然通过薄板样条非线性变换可以获得较好的运动估计结果,但在处理面部复杂纹理和嘴部运动时存在运动估计不精细的问题,需要更强大的图像修复能力。因此,提出一种基于改进薄板样条运动模型(TPSMM)的人脸动画算法。首先,在TPSMM的基础上引入一种Farneback光流金字塔算法,通过与薄板样条变换和背景仿射变换相结合,使得人脸局部运动估计更精准;其次,为了更真实地恢复缺失区域的细节纹理信息,提出一种多尺度细节感知网络,该网络在编码器中通过嵌入通道注意力(ECA)模块减少源图像因多层下采样而导致的人脸细节信息丢失,在解码器中利用坐标注意力(CA)模块来有效捕获运动估计特征图中不同位置的重要特征,提高人脸图像的生成质量。实验结果表明,相比一阶段运动模型(FOMM)、关节动画的运动表示法(MRAA)、TPSMM等,该算法在MUG、UvA-Nemo和Oulu-CASIA数据集上的L1、平均关键点距离(AKD)、平均欧氏距离(AED)数值均达到最优,平均分别为0.0129、0.923、0.00099。

基于小波分析的智能电能表动态测试信号模型与误差分析

针对电能表动态误差测试问题,文章采用小波分析对采集到的加热炉负载等三种实际工况信号进行了分解,提取了时域及时频域的特征,从幅值和频率两个维度总结提取了包括幅值变化、低频稳态、高频稳态、高频暂态在内的四类测试信号,能够全面表征多种动态信号的特性,并且采用薄板样条插值建立了包络信号,幅值上升、下降、中断、谐波、间谐波、冲击的七种单一测试信号模型,在搭建好的动态信号测试平台上实验并分析了单一测试信号的参数对误差的影响,结果表明幅值变化和包络、间谐波对电能表计量误差影响较大。通过单一测试信号的参数调整以及多种信号的复合进一步建立了复合测试信号模型,可逼近现实工况信号,遍历各种工作模态,对采集到的激光切割机负荷进行误差预测与补偿,模型预测误差的结果验证了复合测试信号模型的正确性,可为电能表动态误差研究提供依据。

基于部件组合的连衣裙款式图快速生成研究

款式图作为真实服装的一种平面表达方式,在服装生产过程中起着重要的作用。为了简化服装款式设计过程,提高款式设计的效率与服装信息表达的准确率,并针对不同体型生成个性化的款式图,以连衣裙为对象,基于部件数字化对款式图快速生成进行了研究。首先,采用薄板样条插值算法以使服装款式图拟合不同人体体型,使衣身能够快速达到满足特定体型的尺寸;其次,通过基于关键点的矩阵变形实现部件之间的自适应组合;最后,选用参数驱动和交互式修正关键点2种方法实现对服装款式细节的调整。以连腰鱼尾裙为例,阐述并实现了连衣裙款式图快速生成过程,验证了基于部件组合的款式图快速生成的可行性,为个性化定制和智能化款式设计提供理论支持。

R^n上Plate方程全局吸引子的正则性和有限维性

研究了无界区域Rn上Plate方程全局吸引子的正则性和有限分形维性.该方程的全局吸引子在相空间H2(Rn)×L2(Rn)的存在性已在先期文章建立,现在进一步证明该全局吸引子具有更好的正则性,即它是H4(Rn)×H2(Rn)的有界集并具有有限分形维数.

基于姿势引导下的虚拟试穿网络

针对现有的基于姿势引导下的虚拟试穿方法存在着服装纹理过度变形、生成的图像出现遮挡等问题,提出了一种基于姿势引导下的虚拟试穿网络(pose-guidedvirtualtry-on network,PG-VTON).首先,使用基于U-Net的网络对人物图像进行姿势转换,生成目标姿势下的人物解析图,引入信息增强模块提高解析图的准确性,减少试穿中的错误遮挡;然后,通过薄板样条变换(thin platespline,TPS)方法将目标服装变形为与人物身体相贴合的形状,引入网格变形约束项来保留目标服装的纹理和细节特征;最后,将解析图和变形服装结合起来,生成最终的虚拟试穿图像.实验结果表明,该方法不仅比Downto(downtothelast detail)网络试穿图像的平均结构相似性(structural similarity,SSIM)提高了2.83%,初始得分(inception score,IS)提高了6.74%,与其他最新的虚拟试穿方法相比减少了试穿过程中的错误遮挡,能生成更加清晰真实的结果.

既有网架受拉球节点托板加固技术试验研究

针对既有网架结构下弦受拉球节点加固问题,提出一种基于临杆焊接托板的加固方法。该方法综合考虑了受拉球节点与杆件的材质、空间结构以及尺度效应的影响,通过将球节点周围相邻杆件焊接托板进行加固,使得该方法便于施工,且能够普遍适用于各类受拉球节点的加固工程,并通过模型试验验证和仿真研究,焊接托板后的节点域承载能力大幅提升,加固效果良好,为既有网架受拉球节点加固提供了新思路。

既有网架受拉球节点托板加固技术试验研究

针对既有网架结构下弦受拉球节点加固问题,提出一种基于临杆焊接托板的加固方法。该方法综合考虑了受拉球节点与杆件的材质、空间结构以及尺度效应的影响,通过将球节点周围相邻杆件焊接托板进行加固,使得该方法便于施工,且能够普遍适用于各类受拉球节点的加固工程,并通过模型试验验证和仿真研究,焊接托板后的节点域承载能力大幅提升,加固效果良好,为既有网架受拉球节点加固提供了新思路。

二次B-Spline时域基函数的TDFEM的应用

提出了时域有限元法(TDFEM)的一种新的基函数—二次B-spline时域基函数.首先简述了时域有限元法的原理和基本公式;然后提出了新型的基于B-spline函数的条件稳定和无条件稳定的时域有限元法方案,并应用于三维电磁辐射问题.通过典型的算例对这两种方案的精度、运算时间进行了比较,证实了基于二次B-spline函数的时域有限元法的有效性.通过稳定性理论分析得出该算法的精确稳定性,并且通过数值计算的结果得到验证.