含铰接杆系结构几何非线性分析子结构方法

将细长杆系结构按长度方向划分为多个子结构,由于在子结构坐标系下的节点位移均是小位移,可以将子结构内部自由度凝聚到边界. 考虑到子结构端面在变形过程中保持为刚性截面,将端面节点自由度进一步凝聚到端面形心点,这样每一个子结构就减缩成形式上只有两个节点的广义梁单元,大大减缩了自由度. 大位移大转动是细长杆系结构产生几何非线性效应的一个重要原因,基于共旋坐标法,建立了随单元一起运动的随动坐标系,推导了子结构单元的节点力平衡方程及其切线刚度阵. 同时,考虑到工程机械中细长杆系结构含有相互铰接的刚体加强块,给出了非独立自由度节点力转换到独立参数下的广义节点力及其导数. 最后,通过履带式起重机的副臂工况算例,给出了其在不同载荷下的臂架结构位移,验证了方法的正确性.      

考虑建造过程的多重子结构分析矩阵位移法

根据三维空间结构节点的变位分析,建立了模拟建造过程的多重子结构分析矩阵位移法。工程实例的计算结果表明,该方法是合理且实用的。     

具有不同对称性的子结构耦合分析

本文就一般有限元结构,对具有不同点群对称性的子结构间的耦合问题,提出了一种分解为独立子问题的结构分析新方法。文中在引入节点对称轨道和子轨道概念的基础上,给出了按对应的子轨道分别建立对称基向量的算法;论述了关联子问题的确定方法并推演了具有不同对称性的组合位移、变形能系数间的直接转换公式。这种分析方法不仅利用了每一子结构的对称性,而且还可进一步利用连接为一体后的对称性。作为例子,本文对某些具有典型对称性的子结构耦合问题,给出了具体公式。     

基于界面主从位移控制的频响子结构方法

在复杂工程结构频响子结构分析中,各个子结构的频响函数往往是由不同的部门获得,各个子结构的频响函数可能是在不同的坐标系下得到,亦或有些子结构具有某种对称性,这需要对相应的子结构频响函数进行旋转和镜像变换后才能进行整体拼接。此外,子结构拼接时交界面的连接点有时可能存在不一致,为了满足位移协调和力平衡条件,本文基于界面主从位移控制原理,提出一种改进的频响子结构方法,该方法既能考虑子结构的旋转和镜像变换,也能考虑子结构界面间的柔性连接,并可大幅提高计算效率。当界面位移控制阵为单位阵时,改进的方法退化为传统的频响子结构方法。数值算例验证了所提方法的正确性和有效性。     

动力子结构模态综合解法的并行算法

本文根据动力子结构模态综合法,提出了相应的并行算法。该算法有效地将整个结构分成独立的多个子结构,然后由多个CPU同时独立求各子结构的分支模态和进行各子结构的分支模态变换。再串行组集界面刚度和质量阵,并求解缩减后的整体方程。最后返回各子结构求结点位移对于(`ω~2`)的模态(φ),这一步也在各CPU内独立地同时进行。该方法在西安交通大学的ELXSI-6400并行机上程序实现,表明能有效地节省计算时间,为一种大型结构动力分析方法。     

流固耦合的周期加强板的振动及声辐射研究

研究了流体负载下的无穷大双周期加强板, 在周期谐振力作用下的振动响应和声辐射,并提出了一种基于有限元和空间波数法的半解析半数值方法. 首先利用有限元的方法对周期结构进行单元离散, 并将结构对薄板的作用力等效为节点力的作用. 然后通过周期结构的振动方程, 结合薄板与结构的位移边界条件, 建立了节点力与薄板节点位移的函数方程. 最后应用空间波数法和傅里叶变换, 并采用数值计算的方法求解出薄板的节点位移, 得到了周期加强板关于离散节点位移的振动和辐射声压方程. 在数值算例中, 对该方法的正确性进行了验证, 并且分析了周期结构对薄板的振动和声辐射的影响.     

抗泥石流冲击吊脚楼房屋结构竞赛模型设计

介绍了一种抗泥石流冲击吊脚楼房屋结构竞赛模型的设计方案.该方案采用框架结构,在底层空心楼面梁中内置了能量转换梁,能量转换梁上表面在上部子结构柱支承处设置有斜面,能量转换梁在撞击后产生水平位移的同时能够带动上部子结构的升高,将外部撞击的水平动能转换为上部子结构升高所需的势能.给出了这种结构的细部构造设计方案,并进行了力学的概念分析和简化的结构计算.实验表明模型结构的抗撞击性能良好.     

倒三角形荷载下双重弯剪型结构的位移计算方法

为了研究双重弯剪型结构承受倒三角形荷载的位移计算方法,在前期研究工作基础上,首次推导出倒三角形荷载下双重弯剪型结构中两个子结构的弯曲变形、剪切变形、总水平位移的通用表达式,进一步完善了广义双重结构的位移计算理论.针对框架-密肋复合墙结构、框架-剪力墙结构的变形特点,由双重弯剪型结构的位移计算公式出发,推导出前两种结构承受倒三角形荷载时的特解与位移解析解,证明了:框架-密肋复合墙结构是双重弯剪型结构的一个子结构抗弯刚度趋于无穷大的具体表现形式;框架-剪力墙结构是双重弯剪型结构的一个子结构抗弯刚度趋于无穷大且另一个子结构抗剪刚度趋于无穷大的具体表现形式.本文对具有不同变形特征的双重结构位移计算方法的分析有助于从更高层面理解水平荷载下任意双重结构的变形规律及相互之间的关系.     

基于数值子结构方法的结构弹塑性分析

结合震害调研及数值分析可知,结构最终失效可能仅由部分关键构件破坏引起,大部分构件仍处于弹性或小变形状态。因此为提高计算效率,在结构全过程分析中一致采用非线性单元建模并非必要,同时为准确考虑关键构件的非线性响应,本文提出一种新的数值子结构建模策略。进入弹塑性状态后,针对一般钢构件或钢筋混凝土构件采用动态替换子结构方法在单元或截面层次将其替换成非线性单元或非线性截面,并基于OpenSees平台开发了两类新单元予以实现;针对可能发生严重损伤的关键构件,采用隔离子结构方法将其隔离并建立精细化分析模型,考虑主、子结构间不同尺度边界耦合,并推导了切线刚度的传递关系,采用Client/Server技术在OpenSees平台开发了一类新的接口单元予以实现主、子结构之间的信息传递。为验证新开发单元的合理性,分别以钢及钢筋混凝土平面框架结构为例,采用纤维单元、动态替换子结构方法以及隔离子结构方法建模进行静、动力分析。计算结果表明,采用本文提出的动态替换子结构方法与常规建模方法的计算结果完全吻合并且可大幅缩短计算耗时,随着荷载水平的增大,结构中受到动态替换的构件比例急剧增大,计算效率提高程度略有降低,但仍远高于常规模型;采用本文提出的接口单元可准确传递主、子结构间的界面信息,为隔离数值子结构方法在结构弹塑性分析中的应用提供了基础。     

用样条子结构法分析高层建筑结构

本文提出分析高层建筑结构的样条子结构法,根据抗侧力体系的布置,把高层结构划分成几个子结构,采用样条级数与三角级数来描述子结构的位移场,在变分原理的基础上形成子结构刚度矩阵,考虑各子结构间的位移协调与边界条件,建立结构的总体刚度矩阵。与有限元及有限条法相比,具有精度高,计算量小,程序易编制等特点,且对各种类型的高层建筑结构均可适用。实例计算表明,本文方法精度能满足工程设计的要求。     

An asymptotically correct classical model for smart beams

An asymptotically correct classical beam model has been developed for smart slender structures using the variational asymptotic method. Taking advantage of the slenderness of the structure, we asymptotically split the original three-dimensional electromechanical problem into a two-dimensional electromechanical cross-sectional analysis and a one-dimensional beam analysis. The one-dimensional beam analysis could be geometrically nonlinear or linear depending whether the original three-dimensional analysis is geometrically nonlinear or linear. The cross-sectional analysis, implemented using the finite element method, provides an asymptotically correct, one-dimensional constitutive model for smart slender structures without a priori assumptions regarding the geometry of the cross section, the distribution of the electric field, and the location of smart materials, such as embedded or surface mounted. Several examples are used to validate the accuracy of the present theory with available results in the literature and three-dimensional commercial finite element packages.     

刚接与铰接混合连接杆系结构的几何非线性分析

本文提出用子结构原理解决具有刚接与铰接混合连接空间杆系结构的几何非线性分析,实现其非线性稳定性分析的载荷-位移全过程跟踪。该法无须单独推导刚接、铰接以及一端刚接一端铰接单元的弹性刚度矩阵和几何刚度矩阵,而可以直接由空间梁单元退化得到,而且可以将平面问题与空间问题、刚接与铰接混合连接体系进行统一处理,算例表明,本文方法对于杆系结构的统一和整体分析是有效的。     

弹性薄板分析的条形传递函数方法

提出一种用于矩形弹性薄板变形分析的条形传递函数方法．一个矩形区域首先沿某一个方向被剖分成若干个条形子域,分割这些子域的直线称为结线,在结线上定义位移函数,它是结线坐标的一维函数,结线的两个端点称为结点．为适应复杂边界条件,在边界结线上定义若干结点,该结线的位移函数用结点位移参数插值表示．每个条形子域的变形用结线位移函数和适当的插值函数（形函数）表示．结线位移函数和结点位移参数满足的平衡微分方程及代数方程由变分原理给出     

Strain-based geometrically nonlinear beam formulation for modeling very flexible aircraft

This paper introduces a strain-based geometrically nonlinear beam formulation for structural and aeroelastic modeling and analysis of slender wings of very flexible aircraft. With beam extensional strain, twist, and bending curvatures defined as the independent degrees of freedom, the equations of motion are derived through energy methods. Some special treatments are applied to the formulation to effectively model split-beam systems and beam configurations with multiple nodal displacement constraints. Using the strain-based formulation, solutions of different beam configurations under static loads and forced dynamic excitations are compared against ones from other geometrically nonlinear beam formulations.     

Studies of nonlinear deformation and stability of oval and elliptic cylindrical shells under axial compression

The stability of noncircular shells, in contrast to that of circular ones, has not been studied sufficiently well yet. The publications about circular shells are counted by thousands, but there are only several dozens of papers dealing with noncircular shells. This can be explained on the one hand by the fact that such shells are less used in practice and on the other hand by the difficulties encountered when solving problems involving a nonconstant curvature radius, which results in the appearance of variable coefficients in the stability equations. The well-known solutions of stability problems were obtained by analytic methods and, as a rule, in the linear approximation without taking into account the moments and nonlinearity of the shell precritical state, i.e., in the classical approximation. Here we use the finite element method in displacements to solve the problem of geometrically nonlinear deformation and stability of cylindrical shells with noncircular contour of the transverse cross-section. We use quadrilateral finite elements of shells of natural curvature. In the approximations to the element displacements, we explicitly distinguish the displacements of elements as rigid bodies. We use the Lagrange variational principle to obtain a nonlinear system of algebraic equations for determining the unknown nodal finite elements. We solve the system by a step method with respect to the load using the Newton-Kantorovich linearization at each step. The linear systems are solved by the Kraut method. The critical loads are determined with the use of the Silvester stability criterion when solving the nonlinear problem. We develop an algorithm for solving the problem numerically on personal computers. We also study the nonlinear deformation and stability of shells with oval and elliptic transverse cross-section in a wide range of variations in the ovalization and ellipticity parameters. We find the critical loads and the shell buckling modes. We also examine how the critical loads are affected by the strain nonlinearity and the ovalization and ellipticity of shells.     

Studies of nonlinear deformation and stability of noncircular cylindrical shells in transverse bending

The variational finite element method in displacements is used to solve the problem of geometrically nonlinear deformation and stability of cylindrical shells with a noncircular contour of the cross-section. Quadrangle finite elements of shells of natural curvature are used. In the approximations of element displacements, the displacements of elements as solids are explicitly separated. The variational Lagrange principle is used to obtain a nonlinear system of algebraic equations for the unknown nodal finite elements. The system is solved by the method of successive loadings and by the Newton-Kantorovich linearization method. The linear system is solved by the Crout method. The critical loads are determined in the process of solving the nonlinear problem by using the Sylvester stability criterion. An algorithm and a computer program are developed to study the problem numerically. The nonlinear deformation and stability of shells with oval and elliptic cross-sections are investigated in a broad range of variation of the elongation and ellipticity parameters. The shell critical loads and buckling modes are determined. The influence of the deformation nonlinearity, elongation, and ellipticity of the shell on the critical loads is examined.     

基于共旋列式的空间梁的稳定性分析

基于独立于单元的共旋列式(EICR),将一种几何线性的无剪切锁死的Timoshenko梁单元扩展用于空间梁结构的几何非线性分析。考虑到三维分析中发生大转动时转动顺序的不可交换性,也即转动自由度不能作为向量采用加法规则更新,采用了四元变量来存储和更新转动自由度,使得共旋列式适用于位移任意大和转动任意大但应变很小的几何非线性分析。同时改进了Riks弧长法使之适用于带有大转动的三维几何非线性分析。给出了几个数值算例,结果表明本文方法具有较高的计算精度和效率。     

Linear and geometrically nonlinear analysis of non-uniform shallow arches under a central concentrated force

In this paper an integral equation solution to the linear and geometrically nonlinear problem of non-uniform in-plane shallow arches under a central concentrated force is presented. Arches exhibit advantageous behavior over straight beams due to their curvature which increases the overall stiffness of the structure. They can span large areas by resolving forces into mainly compressive stresses and, in turn confining tensile stresses to acceptable limits. Most arches are designed to operate linearly under service loads. However, their slenderness nature makes them susceptible to large deformations especially when the external loads increase beyond the service point. Loss of stability may occur, known also as snap-through buckling, with catastrophic consequences for the structure. Linear analysis cannot predict this type of instability and a geometrically nonlinear analysis is needed to describe efficiently the response of the arch. The aim of this work is to cope with the linear and geometrically nonlinear problem of non-uniform shallow arches under a central concentrated force. The governing equations of the problem are comprised of two nonlinear coupled partial differential equations in terms of the axial (tangential) and transverse (normal) displacements. Moreover, as the cross-sectional properties of the arch vary along its axis, the resulting coupled differential equations have variable coefficients and are solved using a robust integral equation numerical method in conjunction with the arc-length method. The latter method allows following the nonlinear equilibrium path and overcoming bifurcation and limit (turning) points, which usually appear in the nonlinear response of curved structures like shallow arches and shells. Several arches are analyzed not only to validate our proposed model, but also to investigate the nonlinear response of in-plane thin shallow arches.