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THE SOLUTION OF RECTANGULAR PLATES WITH LARGE DEFLECTION BY SPLINE FUNCTIONS 认领 引用
1
作者 潘立宙 陈为众 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第5期429-439,共11页
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 bein... 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. 展开更多
关键词 Li THE SOLUTION OF RECTANGULAR PLATES WITH LARGE DEFLECTION BY SPLINE FUNCTIONS Chen mode
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THE APPLICATION OF SPLINE FUNCTION IN THE GEOMETRIC REPRODUCTION OF LOG SHAPE 认领 引用 被引量：1
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作者 于龙梅 《Journal of Northeast Forestry University》 1994年第3期75-78,共4页
The paper introduces a method to get three-dimensional reproduction of log shape by adopting Spline Function in fitting the curve of the finite log data. The method has ad-vantages of higher accuracy, less acquired da... The paper introduces a method to get three-dimensional reproduction of log shape by adopting Spline Function in fitting the curve of the finite log data. The method has ad-vantages of higher accuracy, less acquired data, easier to use, etc. Making use of high-precision drawing function of computer, the graphs of log geometric shape in different visual angles can be achieved easily with this method. It also provided a firm foundation for the determination of optimum saw cutting scheme. 展开更多
关键词 Computer Spline function Three-dimensional reproduction Log shape Optimum saw cutting
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Solutions of Seventh Order Boundary Value Problems Using Ninth Degree Spline Functions and Comparison with Eighth Degree Spline Solutions 认领 引用 被引量：1
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作者 Parcha Kalyani Mihretu Nigatu Lemma 《Journal of Applied Mathematics and Physics》 2016年第2期249-261,共13页
In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems ... In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems at different step lengths. The approximate solution is compared with the solution obtained by eighth degree splines and exact solution. It has been observed that the approximate solution is an excellent agreement with exact solution. Low absolute error indicates that our numerical method is effective for solving high order linear boundary value problems. 展开更多
关键词 Seventh Order Boundary Value Problem Boundary Value Problem Ninth Degree Spline Function Absolute Error
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Numerical Solution of System of Fractional Delay Differential Equations Using Polynomial Spline Functions 认领 引用
4
作者 Mahmoud N. Sherif 《Applied Mathematics》 2016年第6期518-526,共9页
The aim of this paper is to approximate the solution of system of fractional delay differential equations. Our technique relies on the use of suitable spline functions of polynomial form. We introduce the description ... The aim of this paper is to approximate the solution of system of fractional delay differential equations. Our technique relies on the use of suitable spline functions of polynomial form. We introduce the description of the proposed approximation method. The error analysis and stability of the method are theoretically investigated. Numerical example is given to illustrate the applicability, accuracy and stability of the proposed method. 展开更多
关键词 Fractional Differential Equation Spline Functions Taylor Expansion Stability
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MIRROR EXTENDING AND CIRCULAR SPLINE FUNCTION FOR EMPIRICAL MODE DECOMPOSITION METHOD 认领 引用
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作者 ZHAO Jin-ping HUANG Da-ji 《Journal of Zhejiang University Science》 2001年第3期8-13,共6页
The Mirror Extending(ME)approach is proposed in this paper for solving the end extending issue in the Empirical Mode Decomposition(EMD)method.By this approach,the data is extended into a closed circuit without end.The... The Mirror Extending(ME)approach is proposed in this paper for solving the end extending issue in the Empirical Mode Decomposition(EMD)method.By this approach,the data is extended into a closed circuit without end.The derivatives on ends are not necessary any more for Spline fitting.The approach eliminates the possible problems in reliability and uniqueness in the original extending approach of the EMD method.In the ME approach only one extending is necessary before the data analysis.A theoretical criterion is proposed here for checking the extending approach.ME approach has been proved to satisfy the theoretical criterion automatically and permanently.This approach makes the EMD method reliable and easy to follow. 展开更多
关键词 empirical mode decomposition mirror extension circular Spline function time series analysis time-frequency domain
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APPLICATIONS OF SURFACE SPLINE FUNCTIONS TO STRUCTURAL ANALYSIS IN COAL GEOLOGY 认领 引用
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作者 韩金炎 余志伟 《Journal of China University of Mining and Technology》 1996年第1期9-14,共6页
A surface spline function is used to fit a coal seam surface in structural anal ysis in coal geology. From the surface spline function, the first and second partial derivatives can also be derived and used to structur... A surface spline function is used to fit a coal seam surface in structural anal ysis in coal geology. From the surface spline function, the first and second partial derivatives can also be derived and used to structural analysis, especially for recogni tion of the concealed structures. The detection of structures related to faulting is em phasized. 展开更多
关键词 surface spline function structural analysis recognition of concealed structures
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OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1) 认领 引用
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作者 Ye Maodong Zhejiang University,China 《Analysis in Theory and Applications》 1993年第4期46-54,共9页
In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
关键词 As OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS 十义 义人
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Modeling the Dynamic Gravity Variations of Northeastern Margin of Qinghai-Xizang (Tibet) Plateau by Using Bicubic Spline Interpolation Function 认领 引用
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作者 Zhu Yiqing Hu Bin +1 位作者 Li Hui Jiang Fengyun 《Earthquake Research in China》 2005年第4期346-353,共8页
In this paper, the spatial-temporal gravity variation patterns of the northeastern margin of Qinghal-Xizang （Tibet） Plateau in 1992 - 2001 are modeled using bicubic spline interpolation functions and the relations o... In this paper, the spatial-temporal gravity variation patterns of the northeastern margin of Qinghal-Xizang （Tibet） Plateau in 1992 - 2001 are modeled using bicubic spline interpolation functions and the relations of gravity change with seismicity and tectonic movement are discussed preliminarily. The results show as follows： ① Regional gravitational field changes regularly and the gravity abnormity zone or gravity concentration zone appears in the earthquake preparation process; ②In the significant time period, the gravity variation shows different features in the northwest, southeast and northeast parts of the surveyed region respectively, with Lanzhou as its boundary;③The gravity variation distribution is basically identical to the strike of tectonic fault zone of the region, and the contour of gravity variation is closely related to the fault distribution. 展开更多
关键词 Northeastern margin of Qinghai-Xizang （Tibet） Plateau Gravity variation Bicubic spline interpolation function Tectonic deformation
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Optimization of Quantizer’s Segment Threshold Using Spline Approximations for Optimal Compressor Function 认领 引用
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作者 Lazar Velimirovic Zoran Peric +1 位作者 Miomir Stankovic Jelena Nikolic 《Applied Mathematics》 2012年第10期1430-1434,共5页
In this paper, the optimization of quantizer’s segment threshold is done. The quantizer is designed on the basis of approximative spline functions. Coefficients on which we form approximative spline functions are cal... In this paper, the optimization of quantizer’s segment threshold is done. The quantizer is designed on the basis of approximative spline functions. Coefficients on which we form approximative spline functions are calculated by minimization mean square error (MSE). For coefficients determined in this way, spline functions by which optimal compressor function is approximated are obtained. For the quantizer designed on the basis of approximative spline functions, segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). Thus, quantizer with optimized segment threshold is achieved. It is shown that by quantizer model designed in this way and proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved. 展开更多
关键词 Optimization of Quantizer’s Segment Threshold Mean Square Error Second-Degree Spline Functions Compressor Function
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The G^3 spline basis functions 认领 引用
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作者 Diao Luhong Cao Huan +1 位作者 Zhang Zhenmeng Lu Xiaoyan 《Computer Aided Drafting,Design and Manufacturing》 2016年第1期41-46,共6页
The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equ... The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters＇ values. It makes the equation＇s solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented. 展开更多
关键词 geometric continuity G3 spline basis functions splines B6zier representation matrix decomposition
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ELASTIC ANALYSIS OF ORTHOTROPIC PLANE PROBLEMS BY THE SPLINE FICTITIOUS BOUNDARY ELEMENT METHOD 认领 引用
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作者 SU Cheng +1 位作者 HAN Da-jian 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第4期446-453,共8页
Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious... Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method. 展开更多
关键词 orthotropic plane problem spline function boundary element method
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一种多参数G3高精度的八次Hermite插值样条 认领 引用
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作者 谢进 尹行 《浙江大学学报（理学版）》 CAS CSCD 北大核心 2026年第1期78-87,共10页
为解决工程计算中的连续性和精度问题,提出了一种具有高阶连续性、高精度且带多个参数的八次Hermite插值样条。首先,在多项式空间,利用高阶连续性条件,通过解方程组,给出一种带多个参数的Hermite型基函数的构造方法,并定义了相应的高阶... 为解决工程计算中的连续性和精度问题,提出了一种具有高阶连续性、高精度且带多个参数的八次Hermite插值样条。首先,在多项式空间,利用高阶连续性条件,通过解方程组,给出一种带多个参数的Hermite型基函数的构造方法,并定义了相应的高阶插值样条;其次,给出了最优插值的参数选择方法;最后,讨论了插值余项和最优插值函数的确定方法,并通过实例验证了该插值样条的有效性和高精度。与现有的带参数的分段Hermite插值样条相比,提出的八次Hermite插值样条无需增加任何条件即可自动满足G3连续,且兼备形状可调性与高阶连续性,应用前景广阔。 展开更多
关键词 G3连续性 高精度 八次Hermite样条 最优参数 最优插值函数
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Quintic spline smooth semi-supervised support vector classification machine 认领 引用 被引量：4
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作者 Xiaodan Zhang Jinggai Ma +1 位作者 Aihua Li Ang Li 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2015年第3期626-632,共7页
A semi-supervised vector machine is a relatively new learning method using both labeled and unlabeled data in classifi- cation. Since the objective function of the model for an unstrained semi-supervised vector machin... A semi-supervised vector machine is a relatively new learning method using both labeled and unlabeled data in classifi- cation. Since the objective function of the model for an unstrained semi-supervised vector machine is not smooth, many fast opti- mization algorithms cannot be applied to solve the model. In order to overcome the difficulty of dealing with non-smooth objective functions, new methods that can solve the semi-supervised vector machine with desired classification accuracy are in great demand. A quintic spline function with three-times differentiability at the ori- gin is constructed by a general three-moment method, which can be used to approximate the symmetric hinge loss function. The approximate accuracy of the quintic spiine function is estimated. Moreover, a quintic spline smooth semi-support vector machine is obtained and the convergence accuracy of the smooth model to the non-smooth one is analyzed. Three experiments are performed to test the efficiency of the model. The experimental results show that the new model outperforms other smooth models, in terms of classification performance. Furthermore, the new model is not sensitive to the increasing number of the labeled samples, which means that the new model is more efficient. 展开更多
关键词 semi-supervised support vector classification machine smooth quintic spline function convergence.
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基于三次样条非保守力建模方法的Swarm卫星时变重力场反演 认领 引用
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作者 陈鑑华 陈秋杰 +2 位作者 沈云中 张兴福 禤键豪 《地球物理学报》 SCIE EI CAS CSCD 北大核心 2026年第8期3472-3487,共16页
非保守力精确建模是影响低轨卫星时变重力场反演精度的关键因素之一.然而,大部分低轨卫星未搭载加速度计,为解决此类卫星非保守力建模问题,本文提出了一种无需外部物理模型输入的三次样条非保守力建模方法,同时基于优化短弧边值法,利用... 非保守力精确建模是影响低轨卫星时变重力场反演精度的关键因素之一.然而,大部分低轨卫星未搭载加速度计,为解决此类卫星非保守力建模问题,本文提出了一种无需外部物理模型输入的三次样条非保守力建模方法,同时基于优化短弧边值法,利用三颗Swarm卫星2016-07至2022-12时间段的运动学轨道数据反演了40阶次的Tongji-Swarm2025月时变重力场模型序列,结果表明:(1)三次样条建模结果成功刻画了非保守力变化的轨道周期特性与时间变化特征;(2)Tongji-Swarm2025与COSTG-Swarm、IGG-Swarm和ASU-Swarm在大地水准面阶方差的误差频谱特征表现一致;(3)Tongji-Swarm2025模型与其他Swarm模型均能有效探测大尺度区域的质量变化信号;在密西西比河、鄂毕河等流域,各Swarm模型与GLDAS地表水数据吻合,验证了其在陆地水储量监测中的可靠性;(4)四组Swarm模型估计的质量变化算术均值有效填补了GRACE/GRACE-FO间断期的质量变化信号(Tongji-Grace2022模型与四组Swarm均值联合估计的趋势及年振幅结果衔接良好),也表明了Tongji-Swarm2025模型在数据间断期的填补能力.本研究成果不仅可应用于如Sentinel等非专用重力卫星任务的重力场反演,还可进一步与国产重力卫星实测数据结合,进行重力场联合反演. 展开更多
关键词 非保守力建模 三次样条函数 Swarm 时变重力场反演
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牙科焦虑与下颌第三磨牙拔除手术时间的关联性 认领 引用
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作者 李蕾 白晓龙 +1 位作者 李佳晔 王维丽 《中国组织工程研究》 CAS 北大核心 2026年第35期9159-9164,共6页
背景:下颌第三磨牙拔除术患者的牙科焦虑水平显著高于其他口腔治疗,术前焦虑状态不仅可能延长手术时间,更会加重术后肿胀等不良反应。目的:探讨术前牙科焦虑与下颌第三磨牙拔除手术时间存在的关联性。方法:采用横断面观察性研究设计,收... 背景:下颌第三磨牙拔除术患者的牙科焦虑水平显著高于其他口腔治疗,术前焦虑状态不仅可能延长手术时间,更会加重术后肿胀等不良反应。目的:探讨术前牙科焦虑与下颌第三磨牙拔除手术时间存在的关联性。方法:采用横断面观察性研究设计,收集航天中心医院口腔科就诊拔除下颌第三磨牙的患者216例,采用改良的第三磨牙拔除牙科焦虑量表(Dental Anxiety Scale for Third Molar Surgery,DAS-TMS)评价术前焦虑水平,记录患者的人口学特征、手术和影像学特征。主要结局指标为手术持续时间。建立多重线性回归模型分析其影响因素,采用限制性立方样条函数评价其潜在的非线性关联。结果与结论:共有216例患者纳入研究,男性71例和女性145例;平均DAS-TMS为10.4分,其中32.4%为焦虑,8.8%为非常焦虑。在多变量调整后DAS-TMS每增加1个单位,手术时间增加1.1 min(β=1.10,P<0.001,95%CI:0.76-1.49)。限制性立方样条函数分析观察到非线性关联的证据(非线性的P=0.013)。结果说明,术前牙科焦虑对下颌第三磨牙拔除手术时间具有显著性影响。 展开更多
关键词 牙科焦虑 第三磨牙 拔除 改良牙科焦虑量表 手术时间 非线性 限制性立方样条函数 横断面观察性研究
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基于函数化重构算法的多区间水下航迹融合与应用 认领 引用
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作者 张旭 《中国舰船研究》 CSCD 北大核心 2026年第2期174-183,共10页
[目的]多区间观测的水下动态航行过程产生多源异类数据,因时间异步、系统误差未知等因素导致航迹交叉或分叉,造成连续变化过程难以刻画以及局部特征点难以识别。针对这一问题,提出一种基于函数化重构的水下数据融合算法。[方法]通过选... [目的]多区间观测的水下动态航行过程产生多源异类数据,因时间异步、系统误差未知等因素导致航迹交叉或分叉,造成连续变化过程难以刻画以及局部特征点难以识别。针对这一问题,提出一种基于函数化重构的水下数据融合算法。[方法]通过选取多项式函数与样条函数进行匹配分析、建模设计及系数辨识,实现水下全航段轨迹的一致性表达,解决高动态参数序列变化不连续以及重合段数据模糊的问题。[结果]数值分析结果表明,基于多项式函数和样条函数的融合结果比数据级融合结果更加光滑、连续,合理刻画了数据重合段的状态变化,并保留了非重合段的运动特征。经与滑动平均滤波算法比对,基于函数化重构的融合处理与滑动滤波处理均能够提供准确、平滑的参数序列,但在速度与加速度的一致性表达方面,前者相对于后者更有优势。经海上实验验证,综合运用多项式函数与样条函数融合方法,在有观测数据航段获得了特征点速度精度优于5%的再分析航迹,在后续无观测数据航段获得了特征点速度精度优于15%的预测航迹。[结论]所提方法对于水下复杂动态航行的多源、多区间数据的处理与分析有一定应用价值,也适用于航行状态的短时估计。 展开更多
关键词 水下动态航迹 多区间观测 融合处理 多项式约束融合 样条函数融合
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Cubic Algebraic Spline Curves Design 认领 引用 被引量：1
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作者 XU Chen-dong CHEN Fa-lai +1 位作者 DENG Jian-song YANG Zhou-wang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第2期213-229,共17页
In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 cont... In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves. 展开更多
关键词 CAGD piecewise algebraic curve functional spline geometric continuity.
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B-Spline高阶元方法在三维水弹性力学中的应用 认领 引用 被引量：4
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作者 杜双兴 殷学文 李琪华 《船舶力学》 EI 2000年第1期17-23,共7页
本文简要叙述了B－Spline样条函数的基本性质；将二元高阶B－Spline函数与Galerkin方法相结合，形成了任意光滑空间曲面的二元高阶 B－ Spline函数簇解析表达方法； 讨论了 B－ Spline函数在三维水弹性力学边界积分方程中应用的一些数... 本文简要叙述了B－Spline样条函数的基本性质；将二元高阶B－Spline函数与Galerkin方法相结合，形成了任意光滑空间曲面的二元高阶 B－ Spline函数簇解析表达方法； 讨论了 B－ Spline函数在三维水弹性力学边界积分方程中应用的一些数值计算问题。 展开更多
关键词 B-Spline函数 高阶元 水弹性力学
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Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness 认领 引用 被引量：2
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作者 侯朝胜 李婧 龙泉 《Transactions of Tianjin University》 CAS 2003年第4期321-325,共5页
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 supp... 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. 展开更多
关键词 variable thickness buckling large deflection circular plate spline function
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APPLICATION OF WAVELET THEORY IN RESEARCHON WEIGHT FUNCTION OF MESHLESS METHOD 认领 引用 被引量：1
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作者 张红 张选兵 葛修润 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第5期662-666,共5页
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is ort... Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given. 展开更多
关键词 meshless method weight function spline wavelet multiresolution analysis
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