样条单元族及其在桥梁结构中的应用

本文用三次B样条建立了样条单元族。与通常的有限单元法相比,具有计算精度高,占用存储和机时少等显著特点。与样条能量法相比,本法在使用时更加灵活。文末还给出了一些数例。     

三次及双三次样条函数应用于土的非线性分析

本文论述应用三次样条函数及双三次样条函数求变形模量E及泊松比υ的方法.并应用于大塘埇水坠坝比奥固结课题有限元的非线性分析中,计算与实测相比,颇为近似。+     

样条函数法解圆柱壳问题

本文用三次、五次B样条函数和级数求解圆柱壳的静力问题,与通用有限元及有限条法相比,具有精度高,未知数少,程序易于编制,可在微型机及小型计算机上求解工程实际问题。文中给出数值算题,由电算结果表明,本方法是十分有效的。     

基于双三次B样条插值的空间结构自由曲面

双三次B样条插值曲面方法是工业造型、机械制造领域应用成熟的一种自由曲面设计方法，本在分析空间结构曲面设计现状、需求以及不足的基础上，提出了应用C^2连续的双三次B样条插值曲面方法进行空间结构自由曲面设计算法，并通过实例论证了该算法的可行性和有效性。     

基于胡-鹫津原理的多变量样条有限元法分析扁壳问题

本文提出一种基于胡-鹫津原理的多变量样条有限元法分析扁壳问题.文中应用乘积型双三次B样条插值函数来构造扁壳的多变量场函数,其中包括位移、广义力和广义应变三类场函数,根据胡-鹫津广义变分原理建立扁壳的多变量样条有限元模型,在计算各类场变量时,不用求导,也不用应力应变关系.其次,独立设置各类场函数,由于样条函数具有解析与数值的双重特性,连续性强,以及逼近精度高等优点,因而,对各类场变量均有足够的精度.文中给出若干板壳结构的弯曲、振动与稳定问题的数值算例,应用文中所得的计算数据,验算了应力应变关系式,得到了近似满足.本文方法可推广应用于工程与物理领域中的多变量场问题.     

关于B样条曲线在拱坝设计中的应用研究

基于B样条曲线的几何特性,在拱坝体型设计中,用3次B样条曲线来拟合拱坝中轴线,用"密切圆包络法"法来计算拱坝的上、游拱曲线,进而确定拱坝体型。此方法能充分发挥B样条曲线的特点,能增加拱坝坝型设计的多样性,改善拱坝的受力条件,在拱坝设计中必有良好的应用前景。     

建筑热环境分析干球温度逐时计算方法比较:以上海地区为例

选择上海某台站2012年每日4次定时干球温度,分别采用调和分析和三次样条方法计算其全年逐时温度,比较了2种方法的计算结果与实测值之间的均方根误差与绝对误差,讨论了这2种方法的计算精度与适用性。结果表明:调和分析与三次样条方法均能满足典型气象年生成与室外计算参数统计的要求;三次样条方法的计算精度略高于调和分析。     

厚/薄板稳定分析的样条无单元法

把挠度和剪应变作为独立的场变量,以Mindlin-Reissner中厚板理论为基础,建立了厚/薄板稳定分析的样条无单元法的计算格式。样条无单元法无需单元分划,仅对整个求解区域作少量的样条结点离散,采用双向3次B样条基函数乘积的线性组合构造场函数,可充分发挥无单元法和B样条函数的优点。数值计算结果表明,该方法适用于不同厚度、不同边界的板的稳定分析,且精度高,收敛快,自由度少,无剪切闭锁现象,程序简便。     

圆板大挠度的样条函数解法

本文以三次 B样条函数为试函数 ,用牛顿迭代法分析了圆板大挠度的非线性问题。文中考虑了固定夹紧、可移夹紧、铰支承及简单支承等四种边界条件 ,在计算例题中 ,荷载考虑了均布荷载和均布边弯矩荷载。计算结果表明 ,算法是有效的。     

样条函数法在解板壳问题中的应用

本文采用三次B样条作为插值函数,并根据板、壳势能变分原理对下程常用、规则区域的板壳问题(板的弯曲问题,板的平面应力问题和薄壳结构按有矩理论的内力与位移分析问题)建立了总体刚度矩阵并给出了系数矩阵的显式表达式。与通常有限元相比较,具有精度高、计算量少,程序易于编制等显著特点。板壳问题可以统一处理,应用甚为简便。通过实例计算,这个方法的计算精度能满足工程设计要求。     

Plate bending analysis by unequally spaced splines

A cubic B-spline finite strip method (BFSM) is developed to analyze thin plates in bending. The basic mathematical relationships are derived for a direct stiffness formulation using a series type strip displacement function. Longitudinal behavior is modeled by a spline series in which unequal spline spacing is permitted. This feature allows local refinement of the discretization near patch and concentrated loads. Accuracy and convergence vis-à-vis alternative methods are compared. These include various finite element models, the conventional finite strip method and the BFSM with equally spaced splines. Comparisons show comparable accuracy with improved convergence. Oscillatory convergence due to Gibb's phenomenon, evident in some of the models, is avoided in the BFSM.     

钢框架非线性分析中的一种新单元模型

为避免稳定函数方法在轴力为拉、压和零时刚度系数表达式各异的不便 ,提出了点平衡三次B样条函数单元。该单元是以满足节点位移及分别在 1 3和 2 3跨度点处的平衡条件来构造的。由此模型 (PES)导出的刚度系数表达式 ,具有比五次多项式单元简单 ,易于应用等优点。通过算例表明 ,PES单元针对 1个单元 构件模型具有较高精度。     

箱梁剪力滞分析的样条有限点法

主要采用样条有限点法分析箱梁剪力滞,并结合试验比较了样条有限点法和有限元法分析箱梁剪切滞的结果,表明采用样条有限点法分析箱型结构简洁有效。     

具有自由边的板弯曲分析的样条加权残值法

本文提出结构工程中具有自由边界条件的板式结构弯曲分析的加权残值法,该法采用五次Ｂ样条函烽为位移试函数,原理简单,计算效果显著优于有限元法。文中还提出了分析此类结构应注意的问题。     

Coupled static and dynamic buckling of thin walled beam by spline finite element

For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames.     

Post-local-buckling of fiber-reinforced plastic composite structural shapes using discrete plate analysis

In this paper, post-buckling of rectangular composite plates rotationally restrained at the longitudinal unloaded edges and subjected to end shortening strain at the simply-supported loaded edges is analyzed using the first-order shear deformation plate theory-based spline finite strip method, and its application to post-local-buckling of fiber-reinforced plastic (FRP) composite structural shapes is illustrated with discrete plate analysis. Two cases of elastically- and rotationally-restrained plates are analyzed using the spline finite strip method: rotationally-restrained along both the unloaded boundary edges (RR) and one rotationally-restrained and the other free along the unloaded edges (RF). The two cases of rotationally-restrained plates (i.e., the RR and RF plates) are further treated as the discrete plates of closed and open section FRP shapes, and by considering the effect of elastic restraints at the joint connections of flanges and webs, post-local-buckling of various FRP shapes under end shortening is studied. The numerical comparisons with the finite element modeling demonstrate that the proposed discrete plate analysis technique and spline finite strip method can be used as an efficient and valid tool for post-local-buckling analysis of FRP shapes.     

高层建筑结构分析的样条单元法

本文针对高层建筑结构的特点，提出一种能广泛适用于高层建筑结构分析的样条单元法。在考虑单元的分片样条插值时，适当地选择纵向与横向样条插值函数的次数，从而有效地减少了计算自由度。与传统的有限条法相比，本文的样条单元能够很方便地处理具有不规则开洞与边界条件的结构形式。剪力墙与筒体结构的计算实例表明，这种单元具有优越的静动力性能。     

Application of vector form intrinsic finite element on integrated simulation of wind turbine

Large wind turbine system is a periodic time‐varying system with many rigid‐flexible coupling bodies. It is difficult to deal with the singular stiffness matrix produced by the rotation of blades via the traditional finite element method. However, the vector form intrinsic finite element (VFIFE) method can effectively solve the geometric deformation of elastic continuum, the nonlinear or discrete constitutive model, the coupling motion continuum, and rigid body. In this study, a solver program of space beam element is developed by VFIFE method, and three typical examples are chosen to verify its accuracy. And then the integrated simulation of wind turbine system is established, and its dynamic response is analyzed. The natural frequencies of the turbine system, which are obtained by modal parameter identification, can agree well with the results obtained by traditional finite element method. The weighted amplitude wave superposition method and the proper orthogonal decomposition method as well as B‐spline surface interpolation are employed to obtain the wind time series of wind turbine under the normal operation condition. The wind‐induced dynamic response of wind turbine system is calculated by VFIFE method. The numerical results can reflect the periodic influence of gravity on the internal forces of blades and the interaction between blades and the tower.     

Static and free vibration analysis of variable-depth bridges of arbitrary alignments using the isoparametric spline finite strip method

The isoparametric spline finite strips for shells are employed to solve static and free vibration problems of variable-depth bridges of arbitrary alignments. Using this approach, a continuous bridge is first split up into substructures. Each substructure is modelled as an assemblage of isoparametric spline finite strips. Compatibility between substructures is ensured by suitable transformation at the interface. The presence of support diaphragms and bearings can also be accounted for. This method retains the computational efficiency of the spline finite strip method while it is much more flexible in geometric modelling. Solutions of this method are compared with other available solutions, and good agreement is observed.