高层建筑结构分析的新方法

样条子域法是高层建筑结构分析的一种新方法。本文利用样条子域法对高层建筑结构进行了分析,建立了高层建筑结构的各种样条子域,导出了静力问题、动力问题、稳定性问题、几何非线性问题、塑性极限问题及结构与地基相互作用问题相应的计算格式。对这种方法,我们已用FORTRAN语言编制了程序。效果很好。实践证明,利用这种方法分析高层建筑结构是一种经济有效的方法,比有限元法及有限条法都优越。     

平板网架结构分析的超级样条子域法

本文探讨了一种求解网架结构的半解析数值方法－超级样条子域法，不计网架杆件为布状况，将网架结构划分为超级子域，并等代为各向同性或正交和向异性中厚板。考虑中厚板的非经典变形效应，用双三次Ｂ样条函数的乘积形式逼近板的位移，推导了超级子域的刚度方程，并吸收子结构法的优点组装和求解总体结构方程。     

折板基础的实用计算方法

本文将作用了折板上的地反力换算成等效的均布荷载。考虑折板纵向支承为固定，仅等虑弯曲变形，采用位移法，设定位移函数，应用伽辽金法和能量变分原理得到折板单元中各板长边与短边之比大于３和小于３两种情况的解答。     

映射样条子域法分析斜弯复合型板桥

本文采用映射样条子域法，对端截面与桥轴线斜交的不规则弯板桥进行力学分析。该方法分析这类桥梁具有计算精度高、自由度少及计算输入输出简便等优点。文中针对斜桥、弯桥及斜弯复合型桥梁，建立了统一的计算模式，对之进行统一处理，为今后分析这类桥梁提供了又一新的理论和方法。     

双样条子域法分析等高度变截面连续直箱梁桥

本文采用三次和一次样条相结合的样条子域法对等高度变截面连续直箱梁桥进行静力分析。该方法精度高计算量少,解决问题面广。对于工程中常见的单箱单室、单箱双室等直箱梁桥可用微机方便地分析。     

冷却塔自振特性敏度分析的广义样条子域法

本文以弹簧约束模拟冷却塔的实际支撑体系,用广义样条子域法建立主体旋转壳动力位移模式.其中,沿壳体两个主曲率线方向的弹簧约束系数通过实际支撑杆件与弹簧系统沿相应方向变形能相等的原则确定,且将弹簧约束模拟为一个广义样条环域与主体结构相连接,从而建立了冷却塔自振特性关于任一参数的敏度分析公式,并通过算例讨论了支撑参数对冷却塔自振特性的影响.     

周边简支组合折板屋盖的自由振动和受迫振动的级数解

本文首先借助两套局部斜坐标系和广义函数－－符号函数和阶跃函数，建立了组合折板屋盖的曲面方程，然后应用弹性薄壳振动理论和变分法求得了四边简支组合折板屋盖受迫振动响应的挠度和内力表达式。本文还可解决组合折板的自由振动和静力问题，以及Ｖ型折板和长方形双向折板的静力、自由振动和受近振动等问题。故本文实际上包含了九个问题的解。     

用样条子域法分析船舶撞击码头非线性动力响应

国内外对高桩码头在船舶撞击下的动力分析,虽作了不少研究,但所有理论都限于线性振动问题。针对广泛采用的防冲设备——橡胶护舷(非线性弹簧),本文提出一种复合体系(船舶-护舷-码头)非线性动力响应分析方法。导出复合体系刚度矩阵,采用Ritz变换先将刚体模态分离,对非线性动力方程,用样条子域法进行直接积分,分段线性化与割线迭代相结合进行数值分析.提供船舶撞击力及结构动内力.算例表明效果良好。     

简支折板的内力与挠度的级数解

本文引入符号函数,以扁壳的弯曲微分方程表示具有小拱度的折板的弯曲微分方程,给出了四边简支折板在任意竖向集中力及均布力作用时内力与挠度的级数解。     

桩承高层建筑与土体间动力相互作用研究

采用样条子域法，半解析无限元法和直梁的弯剪单元模型相耦合的方法，对于带有多层地下室的桩承单，双塔高层建筑与周围土体组成的体系在地震作用下的动力相互作用反应进行了分析研究，算例表明，本文方法具有输入数据简单，计算量较小，精度较高的优点，并且较好瓜了工程上此类建筑物考虑与地基共同工作时的动力性能和内在机理。     

Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method

Based on the first-order shear deformation theory, a mesh-free Galerkin method for free vibration analysis of stiffened and un-stiffened folded plates and plate structures is presented in this paper. The folded plate or plate structure is modelled as a composite structure that consists of flat plates. The stiffness and mass matrices of the flat plates are derived based on the mesh-free formulation. To avoid the failure of direct superposition, a treatment is introduced to modify the stiffness and mass matrices. The global stiffness and mass matrices of the entire folded plate or plate structure are then obtained by superposing the modified stiffness and mass matrices of the flat plates. The analysis of the stiffened folded plates or plate structures proceeds in a similar fashion, as they are regarded as composite structures of stiffened and un-stiffened flat plates. The stiffness and mass matrices of the stiffened flat plates are also given by the mesh-free method. As no meshes are used in deriving the stiffness and mass matrices, the proposed method is more flexible in studying problems for which remeshing is inevitable with the finite element methods. Several numerical examples are computed with the proposed method to demonstrate its accuracy and convergence. The results show good agreement with the solutions that have been given by other researchers and ANSYS.     

Free vibration analysis and shape optimization of prismatic folded plates and shells with circular curved planform

This paper deals with the elastic free vibration analysis and structural shape optimization of prismatic folded plate and shell structures with circular curved planform. The structures are supported on diaphragms at two opposite edges. The basic formulation of a family of curved variable thickness C(0) Mindlin–Reissner finite strips is presented. The accuracy and performance of these newly developed strips are explored through a series of examples including annular plate sectors, a box girder bridge and a cylinder with an interior longitudinal plate. Numerical results obtained are compared with results from other sources. The whole shape optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, sensitivity analysis and mathematical programming. The objective is either the maximization of the fundamental frequency or the minimization of volume by changing the shape or thickness variation of the cross-section of the structure with constraints on the volume or natural frequencies. Several examples are included to illustrate and highlight various features of the optimization, including annular sector plates, a curved box girder bridge and a cylinder shell segment with curved pianform.     

样条有限点法分析板的大挠度问题

样条有限点法已成功地应用于板的线性分析。本文用样条有限点法求解几何非线性平板,以位移u、u和W作为基本未知量,采用三次B样条插值函数与梁函数级数的乘积作为位移试函数,从最小势能原理出发建立基本方程,推导了非线性切线刚度矩阵,用改进的Newton-Raphson方法求解非线性方程组,最后给出了算例,其结果与一些已有的成果进行了比较,表明该方法分析板壳结构的非线性问题是十分有效的。     

Isoparametric spline finite strip method for the bending of perforated plates

The isoparametric spline finite strip method was recently applied by the authors to the linear elastic in‐plane stress analysis of perforated thin‐walled structures. In this paper, the application of the method is extended to the bending of perforated plates. The paper describes the theory of the isoparametric spline finite strip method in the context of Mindlin plate bending theory. It sets out the strain–displacement and stress–strain relationships and derives expressions for the local and global stiffness matrices. The reliability of the method is demonstrated by comparisons with finely meshed finite element analysis results. Square plates in bending containing openings of different shapes are analysed. Copyright © 2007 John Wiley & Sons, Ltd.     

拱结构双重非线性稳定分析的样条有限点法

本文提出利用样条有限点法来分析拱结构非线性稳定问题。用3次B样条函数来构造结构的位移模式,基于最小势能原理导出了拱式结构的单元刚度矩阵。分析中考虑了材料及几何非线性特征,计算公式简便,易于编程。依本文方法编制了程序,对一典型算例进行了分析。     

网架结构动力分析的三次样条辛算法

根据对偶互补的思想,建立了网架结构动力学的相空间非传统Hamilton型变分原理。这种变分原理不仅能反映这种动力学初值-边值问题的全部特征,而且它的欧拉方程具有辛结构。基于该变分原理,空间域采用有限元法与时间子域采用三次样条函数插值的时间子域法相结合,构造了求解网架结构动力响应的一种辛算法,给出了逐步递推计算格式。数值算例结果表明,这种新方法的稳定性、计算精度和效率都明显高于Wilson-θ法和Newmark-β法。     

On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method

This paper augments bubble functions to the ordinary spline finite strip method in order to calculate the elastic local buckling coefficients of plates and plate structures. The results show that the use of bubble functions improves significantly the convergence of the spline finite strip method in terms of the strip subdivision, and therefore leads to smaller storage requirements for the global stiffness and stability matrices, and faster eigenvalue extraction. Benchmark numerical investigations are presented, including the study of plates with different boundary conditions under uniaxial and biaxial stresses, plates with different aspect ratios under shear, and a stiffened panel under combined shear and compression that has been studied elsewhere. These studies demonstrate that by implementation of the bubble functions, rapid convergence of the solution is obtained. The formulation is ideal for analysing local buckling under a variety of boundary and loading conditions. Copyright © 2000 John Wiley & Sons, Ltd.     

粘弹性层状地基上板的动力响应及其参数识别方法

本文系统地研究了粘弹性层状地基上板的动力响应及其结构材料参数识别方法。在一次样条半解析法求解粘弹性地基动力柔度系数[1]的基础上,应用子结构法求解了粘弹性层状地基上板的动力响应。应用快速富利叶变换将落锤式弯沉仪(FWD)所记录的荷载和时程反应曲线转化为频域内的一系列稳态振动[2],[3]。进而利用系统识别技术在频率域内反演结构材料参数。数值分析结果表明,该方法能有效地识别结构参数,从而为进一步研究FWD在混凝土道面的无损检测和承载力评价提供了基础。