Geometric Nonlinear Formulation for a Rectangular Plate with Large Deformation

Absolute nodal coordinate formulation for a rectangular plate with large deformation was improved. Based on nonlinear elastic theory, a precise strain expression is used to derive the equations of motion. Both shear strain and transverse normal strain are taken into account. Different from the previous absolute nodal coordinate formulation, the absolute nodal coordinates, which describe the displacement and slope of the element nodes, are separated into three parts: the absolute nodal coordinates in X, Y and Z directions, respectively, so that the dimension of the mass, stiffness and force matrices is reduced. Furthermore, by using constant matrices, which can be calculated and saved before simulation, the nonlinear stiffness matrices can be calculated by matrix multiplication for each time step, so that the computational efficiency can be improved. Finally, simulation example of a rectangular plate with large deformation was used to verify the accuracy and efficiency of the present formulation.     

Rigid-liquid-flexible dynamic formulation for a two-dimensional tank undergoing translational and rotational motion

Considering rigid-liquid-flexible coupling effect, dynamic formulation for a two-dimensional rectangular tank with liquid sloshing connected to a flexible beam is proposed. Differing from the traditional formulation which considered either the rotational motion or the translational motion of the tank, this formulation can be applied for rigid-liquid-flexible coupling dynamic analysis of tank undergoing translational and rotational motion based on the theorem of momentum and the theorem of moment of momentum. Furthermore, stiffening terms are included in the dynamics equations of the flexible beam. Firstly, the dynamic equations of the rigid-liquid coupling system and the flexible beam are derived, respectively, and then by introducing the Lagrange-multipliers, the rigid-liquid-flexible coupling equations can be combined with acceleration constraint equations. Finally, the mix differential-algebraic equations are solved to investigate the rigid-liquid-flexible coupling dynamic performance of the system.     

关于厚梁横向振动的研究

本文应用哈密顿变分原理较简捷地建立了厚梁横向振动的微分方程.同时得到梁的边界条件和运动的初始条件,进而导出了简支厚梁的频率方程.由计算数据可知剪切变形和转动惯量对厚梁振动(以及薄梁的高阶振型)的影响至关重要.不容忽略.     

建立Timoshenko深梁单元的新方法

基于Timoshenko两广义位移梁理论，建立考虑剪切效应的Timoshenko深梁单元横向线位移、转角和剪应变的各自插值函数，利用有限元方法导出单元线弹性刚度、一致质量矩阵和几何刚度矩阵。算例结果表明此公式用于静力、动力和稳定性分析是可靠的，并且不出现剪切闭锁现象。     

桥梁横向地震碰撞响应研究进展

在强震作用下,桥梁上、下部结构由于动力特性的不同而发生不同相振动,从而引起梁体与挡块间的非线性碰撞。汶川大地震中,大量公路桥梁遭到严重破坏,横向抗震挡块破坏尤其严重,其中部分是由于横向碰撞而引起。针对这种碰撞现象,对正交简支梁桥、连续梁桥、斜交桥及高速铁路桥梁的横向碰撞反应进行了回顾和总结,并介绍了横桥向防撞措施及震后加固技术的研究现状,同时指出目前我国在这方面亟需解决的问题和进一步研究的方向。     

下承式脊骨梁横向剪力滞效应

下承式脊骨梁作为一种新型的城市轨道交通高架桥,具有小脊梁、大悬臂的特点．作为主梁的一部分,悬臂翼缘板也产生纵向弯曲,其横向剪力滞效应非常显著．本文采用ANSYS软件建立下承式脊骨梁的有限单元模型,计算了集中荷载及均布荷载作用下各横截面底板弯曲正应力,并与按初等梁理论的计算结果对比,得出横向剪力滞系数沿底板的分布规律．     

地震下城市高架桥横向偏心碰撞响应与防撞效果分析

为适应材料因温度等因素的变化而产生的横向伸缩变形及其对结构的影响,通常梁体与挡块之间会留有一定间隙。针对城市高架桥中梁体与挡块在强震作用下的横向碰撞现象,建立了考虑上部结构与挡块间偏心距和支座非线性的横桥向单墩碰撞模型。采用非线性地震反应时程分析方法,研究了初始间隙及其大小对桥梁结构横向地震反应的影响,并评估了设置橡胶缓冲垫后的防撞效果。研究结果表明：城市高架简支梁桥横向间隙处的偏心碰撞放大了桥墩的地震需求,通过在挡块内侧安装橡胶缓冲垫,可以大幅减小间隙处的碰撞力,将有效改善桥梁结构的横向抗震性能。     

GEOMETRICALLY NONLINEAR FE FORMULATIONS FOR THE MACRO-ELEMENT UNIPLET OF FOLDABLE STRUCTURES

Introduction　　 Pantographic foldable structure works on theprinciple of a pantograph[1,2 ] . A structure of thistype may be referred to as“pantograph structure”,or simply“p- structure”. The basic unit for the p-structure is a componentso- called duplet[3 ] ,orpan-tograph unit[4] ,Scissor- Like Element ( SLE) [5] ,asshown in Fig.1 .A pantograph unitconsists of twocoplanar straightbars called uniplet,which are ca-pable of rotating about the intermediate pivot,re-ferred to as a scissor h…     

典型藏式古建木构梁柱连接传力机理分析

为研究典型藏式古建木构梁柱连接的力学性能,采用非线性有限元方法,建立梁柱连接的实体模型,分析了在楼面竖向荷载作用下,组成梁柱节点的各组件的受力状态,从而获得竖向荷载下节点的传力机理及破坏模式.研究结果表明：在楼面竖向荷载作用下,梁、弓木为受弯构件,垫木为横纹承压构件,斗、柱为顺纹承压构件,暗销主要承受顺纹压力、横向剪切力,组件之间通过接触面的摩擦力、挤压力及暗销剪切力传递荷载,以协同工作.节点的破坏极限采用应力准则确定,当梁受拉侧屈服时认为节点发生破坏.     

Dynamic investigation on composite flexible multi-body system considering thermal effect

The dynamic performance of composite flexible multi-body system under the simultaneous action of thermal fields and driving constraint is analyzed. Based on strain-displacement relation of the Mindlin plate theory which includes transverse shear deformation, and considering thermal effect, variation equations of laminated plate are derived by the principle of virtual work. The finite element method is used for discretization. According to kinematics constraint relation, dynamic equations for spatial slider-crank system are established. Simulation results show that spatial deformation (torsion deformation) appears in the multi-layered composite slider-crank mechanism which is simulated with planar motions. Furthermore, the influence of coupling between thermal expansion and flexible deformations of non-symmetrical composite plates on the large overall motion under the uniform temperature field is investigated. Finally, significant change in constraint force due to the spatial deformation is shown.     

考虑弹性应变阈值的频率相关等效线性化方法

传统等效线性化方法由于原理简单、参数获取方便而广泛应用于工程场地非线性地震反应分析中．实际工程应用中发现,这种方法由于对各个频率分量采用了等效剪应变水平,使得地面最大峰值加速度和高频段计算结果明显偏低．若干实验表明,应变幅值对土的力学行为起着关键性作用,当应变低于弹性应变阈值时,土体处于线弹性状态,弹性应变阈值主要与土的塑性指数有关．本文在对各种频率相关等效线性化理论方法分析的基础上,结合弹性应变阈值理论,建立了考虑弹性应变阈值的频率相关等效线性化方法,运用本文方法对海口某实际场地进行了土层地震反应分析,对比了与传统等效线性化方法的差异;同时对不同覆盖层厚度遭遇不同地震动强度的地震动进行了计算分析．总结了不同覆盖层犀度下本文方法和传统等效线性化方法计算结果的差异及规律．     

In-plane Auto-Parametric Vibration of Inclined Cables under Random Transverse Excitation

In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton＇s laws of motion and Galerkin＇s modal truncation principle, the influences of geometry nonlinearity induced by sag and large displacement of cables and the initial equilibrium state are taken into account. Meanwhile, the three-dimensional non-linear differential equations of inclined cables for coupling vibration are deduced, equivalent stochastic linearization method is applied to derive the 14-dimensional first-order nonlinear differential equations of state vectors, and the Runge-Kutta integration method is utilized to obtain the root mean square （RMS） response. Results show that when the transverse random excitation imposed on the stayed cable exceeds a critical value, the in-plane transverse vibration of the cable are excited due to tim auto-parametric nonlinear coupling, and the critical value of random excitation increases with the damping ratio. In this motion, the cable response possesses non-stationary characteristics, even though the loading keeps stationary.     

有黏结预应力梁中预应力筋的几何非线性分析

以常规的非线性平面梁元平衡方程为基础,将预应力束视为两端通过刚臂与混凝土梁元节点连接的平面杆元,在局部坐标系(随转坐标系)中计入预应力,根据刚臂在受力后只有刚体运动而本身不变形的特点,采用微分方法导出其在结构坐标系中的切线刚度矩阵,从而获得混凝土梁元与预应力束杆元在结构坐标系中的组合单元切线刚度矩阵;编制了程序,对预应力钢筋混凝土悬臂梁进行几何非线性分析;与ANSYS计算结果比较表明,提出的方法在非线性程度很高时仍能获得高精度数值解,具有对单元数量不敏感,预应力作为非保守荷载的特点容易被计入的优点。     

经历有限变形和有限转动薄壳结构的非线性理论

本文基于计及横向剪切变形的修正Ｋｉｒｃｈｈｏｆｆ－Ｌｏｖｅ假定，采用与反映壳体中面法向偏转的正交张量对应转角矢量来描述薄壳结构的有限转动，建立了经历有限变形和有限转动薄壳结构的非线性理论。其间，导出了其壳体黎曼空间中的Ｇｒｅｅｎ－Ｌａｇｒａｎｇｅ应变张量和第二类Ｐｉｏｌａ－Ｋｉｒｃｈｈｏｆｆ应力张量的表达形式，并通过虚功原理，建立了薄壳结构的非线性平衡关系。     

隔震曲线梁桥的地震响应

根据隔震曲线梁桥的特点,利用两个正交的非线性水平弹簧单元来模拟铅芯橡胶支座的双向非线性特性,基于大型有限元分析软件SAP2000,选取强震记录作为地震输入,考虑了曲线梁桥自身特性的影响,建立了隔震与无隔震曲线梁桥的空间有限元模型,并进行了双向地震动作用下的地震响应分析.结果表明：铅芯橡胶支座不仅可以有效地降低曲线梁桥的地震响应,还有助于减少曲率半径对曲线梁桥地震响应的影响.为曲线梁桥减隔震设计的深入和桥梁结构抗震安全性的提高提供了依据和参考.     

变温环境下粘弹性梁的混沌运动

根据Kelvin粘弹性材料本构关系、梁的运动方程及变形几何方程建立了同时具有温度扰动和横向分布力扰动的粘弹性梁非线性动力学模型.用Galerkin方法将系统简化为参数激励和强迫激励耦合的单模态Duffing振子,得到了系统的不动点和同宿轨道.用Melnikov函数法推导出系统混沌运动的临界条件,分析了系统通向混沌的途径.研究表明,非线性粘弹性梁在周期性横向激励及周期性温度联合作用下可能进入混沌运动,并且在发生Smale马蹄意义下的混沌前,将经历多次的次谐分岔.     

钢-混凝土组合简支箱梁剪力滞效应分析

对于钢－混凝土组合箱梁，根据组合冀板微元的变形协调和平衡条件，建立横截面翼板法向应力微分方程。在两端简支的边界条件下采用分离变量法求解偏微分方程，得到用级数表示的应力解，然后根据剪力滞系的定义即可得到组合箱梁冀板的剪力滞系数。通过算例验证了该方法具有收敛较快、计算精度高等特点，且只需简单的计算不可得到较满意的结果。     

京津城际高速铁路弓网动态系统有限元仿真

基于非线性有限元理论,建立了京津城际高速铁路弓网动态系统的有限元模型,采用欧拉-伯努利直梁模拟接触网各部件,采用铰链和非线性弹簧相互耦合模拟受电弓,借助MARC软件,对京津城际高速铁路弓网受流情况进行了动态仿真,并利用MARC的后处理功能显示弓网运动过程中的三维动态情况.计算得到了京津城际弓网动态系统的平均接触压力为160.68 N,接触点动态抬升量变化范围为28.5～87.0 mm.与西门子公司提供的仿真结果及京津城际现场的测试结果比较表明:有限元模型是正确和有效的,京津城际弓网动态系统具有良好的动态受流质量.     

An improved dynamic hysteretic model for soils

A dynamic hysteretic constitutive model for soil dynamics, Ramberg-Osgood model, is introduced and improved in the paper. Since the model is inherently 1D and is assumed to apply to shear components only, other components of the deviatorie stress and strain and their relations in 3D case could not be fully described. Two parameters, the equivalent shear stress and the equivalent shear strain, are defined to reasonably establish relations between each of stress and strain components respectively. The constitutive equations of the initial Ramberg-Osgood model are extended to generalize the theory into multidimensional cases. Difficulties of the definition of load reversal in 3D are also addressed and solved. The improved constitutive model for soil dynamics is verified by comparisons with different soil dynamic testing data covering both sands and clays. Results show that the dynamic nonlinear hysteretie behaviors of soils can be well predicted with the improved constitutive model.     

钢-混凝土组合梁界面纵向剪力重分布

以受均布荷载作用的简支组合梁为对象，研究了栓钉等柔性连接件塑性变形引起的纵向剪力重分布．根据连接件的受力状态，将界面受力全过程划分为弹性阶段、弹塑性阶段和破坏阶段，建立了相应的剪力重分布简化模型，并导出了界面纵向剪力和轴向力的计算公式．研究表明：考虑纵向剪力重分布时，在荷载较小的情况下，轴向力随荷载增大呈线性关系增大；当荷载较大时，轴向力随荷载增大呈非线性关系增大，最后趋于稳定．