横向撞击下弹性支承轴向受力梁的动力响应

研究了具有弹性支承轴向受力梁在横向撞击下的动力响应.基于Timoshenko梁理论,综合考虑了梁端支承的抗推刚度、抗转刚度和撞击点处的平衡条件,导出了撞击体系的动力学微分方程,采用积分变换方法求解,得到时域内的各种动力响应.通过对不同支承条件下撞击力、横向位移、弯矩的对比分析,说明了弹性支承对结构动力响应的影响.最后分析了弹性支承下轴压力对结构的影响情况,得出了一些有益的结论.     

组合框架结构柱和梁板间耗能分配规律分析

将能量原理运用到钢-混凝土组合框架结构地震反应分析中,利用有限元软件模拟组合框架在地震荷载作用下的动力响应,分析结构阻尼比、地震动峰值和持时等因素对滞回耗能分配规律的影响,探讨组合结构总输入能量及层间和柱、梁板间能量分配规律.研究表明总输入能受阻尼比和地震动频谱特性影响较大,地震动峰值影响较小;滞回耗能在结构层间分布为底层大顶层小的梯形分布;柱耗散的滞回能随阻尼比、地震动峰值或卓越周期增加而增加,阻尼耗能随之减少,梁耗散与柱相反;地震动持时对柱和梁的耗能分配影响很小.     

基于移动有限元法的裂纹梁振动分析

采用移动有限元法和局部柔度法对移动质量作用下含裂纹简支梁进行了振动计算分析.计算考虑了裂纹和移动质量的相对位置对梁固有频率的影响,以及移动质量在不同位置、速度情况下对裂纹梁的动力响应的影响.结果分析表明,裂纹与移动质量的存在会使得梁的动态位移有不同程度的增大,且随着移动质量位置和裂纹位置的改变会使得梁的固有频率变小.     

悬索桥主缆初应力对桥梁动力特性的影响

为掌握主缆初应力对桥梁动力特性的影响,以悬索桥为例,采用静力非线性分析方法计算应力变化过程中悬索桥的跨中挠度、缆索轴力及加劲梁的轴力变化;将得到的内力作为结构的预加应力进行有预应力的模态分析. 应用ANSYS软件进行分析,其中有限元建模时采用4种单元类型:空间梁单元BEAM4用于模拟加劲梁和塔;空间杆单元LINK10用于模拟主缆及吊杆;通过设定BEAM4和LINK10单元初应变进行有预应力的模态分析;采用MASS21单元模拟横隔板、吊杆锚固装置和桥面上的栏杆,并分别考虑质量和质量惯性矩的作用. 分析表明,悬索桥主梁竖弯振动频率受主缆初应力的影响较大,而侧弯振动频率和扭转振动频率受此影响较小. 该结果为同类桥梁的动力特性分析提供参考.     

水平单调载荷作用下的桩基桥墩滞回特性

为研究桩基桥墩-地基系统的非线性性能,根据模型与原型的物理相似关系制作1∶5比例的桩基桥墩模型. 采用力-位移混合控制加载的拟静力试验方法,通过在墩顶施加水平单调增加载荷,得到墩顶水平载荷下桩基桥墩的载荷-位移滞回曲线、骨架曲线和滞回特性. 用非线性弹簧单元模拟土体、用梁单元模拟桩和桥墩,建立模型桥墩的计算模型. 计算模型的骨架曲线与试验模型的骨架曲线吻合较好,表明采用非线性弹簧单元和梁单元分别模拟土体和桩是可行的,可以为考虑土-结构相互作用时的桥梁抗震分析提供参考依据.     

自传感介电弹性体执行器的动力学设计及应用

本文提出了一种传感与作动一体化的介电弹性体(DE)软执行器,可用于薄膜结构形面变形的同步测量和控制.首先,建立DE软执行器电致驱动过程的动力学模型,描述其力电耦合行为.其次,通过开展动态作动实验,辨识该动力学模型的参数.第三,分析不同参数对作动器动态响应的影响,以理解其基本动力学特性.第四,建立DE软执行器自传感过程的简化电路模型,并对其电学参数与位移之间的关系进行实验标定.最后,开展平面薄膜结构的形面位移自适应调整实验,并设计相应的控制策略.实验结果表明,该DE软执行器在作动和传感方面均具有较高精度.因此,其在构建高精度空间薄膜天线方面具有较好的应用前景.     

斜拉桥中拉索对桥面动力特性的影响

将斜拉桥的拉索和桥面抽象为带弹性支承的压弯弹性梁模型,并根据轴向受力梁的弯曲振动方程和哈密尔顿原理,建立了考虑拉索索力影响的单梁多索索梁结构-梁的动力学控制方程,应用传递矩阵法进行求解,并编制了求解程序.通过算例对影响桥面动力学特性的索的刚度、张拉力和桥面裂纹等因素进行了数值分析.分析结果表明,在斜拉桥的施工阶段,随着梁的长度的改变,梁的刚度讯速下降,由于索对梁的支承作用使结构的刚度有一定的提高,而索的拉力对桥面作用的压力越来越大,轴向压力使结构的刚度降低越来越明显,另一方面轴向压力对桥面裂纹引起的刚度降低有一定的抑制作用.由此,在桥梁的建设中应重视索力对桥面动力特性的影响.     

沿轴向飞行粘弹性夹层梁热弹耦合振动响应分析

研究了沿轴向飞行粘弹性夹层梁的热弹耦合振动响应.考虑材料变形与传热的相互影响,建立了轴向运动粘弹性夹层梁的热弹耦合振动控制方程;将方程中激励项(温度函数与外激力)拟合为时间的函数,采用伽辽金法得到方程的位移解,并在每一个微小的时间段内采用迭代收敛的数值方法对热传导方程进行求解得到温度场.使用数值方法讨论了轴向飞行运动速度和热载荷持续时间对其振动响应的影响.研究表明:稳定振动时飞行速度对位移影响较大,对温度影响较小;热冲击对振动位移响应有较大影响,并改变振动特性.     

旋转运动柔性梁的压电质量和刚度效应

对旋转运动柔性梁的压电质量效应和刚度效应进行了研究,给出了基于经典层板理论的压电层合结构的等效抗弯刚度.研究中考虑了大范围运动已知和未知两种情况.仿真结果显示,当压电长度很短时,压电材料对系统动力特性的影响不大,可以忽略不计;当压电长度较长且小于梁长度的一半时,压电刚度对系统特性有着较大影响,而压电质量的影响较小;当压电长度大于梁长度的一半时,压电质量对系统特性有着较大影响,而压电刚度的影响较小.     

不同脱层位置下脱层屈曲梁振动实验研究

通过实验对一端固定一端夹支脱层屈曲梁在轴向周期激励作用下的非线性动力响应进行了实验研究.利用位移时间历程图,相图和频谱图,对多组不同脱层位置下脱层屈曲梁的非线性动力响应进行了分析.实验表明脱层梁结构存在倍周期以及混沌运动等非线性动力学行为.同时实验还表明,在相同的脱层长度下,脱层位置对脱层梁的动力学特性有明显影响,即脱层区域中心越靠近梁结构的中心位置,脱层梁的一阶自然频率越低,且越容易在较低的激励频率和激励荷载下发生周期分叉和混沌等行为.     

Exact dynamic stiffness matrix of non-symmetric thin-walled beams on elastic foundation using power series method

Exact dynamic element stiffness matrix for the flexural–torsional free vibration analysis of the shear deformable thin-walled beam with non-symmetric cross-section on two-types of elastic foundation is newly presented using power series method based on the technical computing program Mathematica. For this, the shear deformable beam on elastic foundation theory is developed by introducing Vlasov's assumption and applying Hellinger–Reissner principle. This beam includes the shear deformation effects due to the shear forces and the restrained warping torsion and due to the coupled effects between them, and rotary inertia effects and the flexural–torsional coupling effects due to the non-symmetric cross-sections. And then equations of motion and force–deformation relations are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components and the exact dynamic element stiffness matrix is determined using force–deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the analytical solutions and the finite element solutions using the isoparametric beam elements. Particularly the influences of the coupled shear deformation on the vibrational behavior of non-symmetric beam on elastic foundation are investigated.     

Dynamic stiffness matrix of non-symmetric thin-walled curved beam on Winkler and Pasternak type foundations

Using the technical computing program Mathematica, the dynamic stiffness matrix for the spatially coupled free vibration analysis of thin-walled curved beam with non-symmetric cross-section on two-types of elastic foundation is newly presented based on the power series method. For this, the elastic strain energy considering the axial/flexural/torsional coupled terms, the kinetic energy including the rotary inertia effect, and the energy due to the elastic foundation are introduced. Then, equations of motion are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Finally, the exact dynamic stiffness matrix is determined using force–displacement relations. In order to demonstrate the validity and the accuracy of this study, the natural frequencies of thin-walled curved beams with mono-symmetric and non-symmetric cross-sections are evaluated and compared with the analytical solutions and finite element solutions using Hermitian curved beam elements and ABAQUS’s shell elements. In addition, some results by a parametric study are reported.     

Vibrations of grids by the finite element method

The finite element method is applied to the free vibration analysis of grids with arbitrary configuration. Grid bars are of solid or thin-walled doubly symmetric cross-section. Stiffness and consistent mass matrices for flexural behavior include the effects of shear deformation and rotary inertia in bending. The torsional behavior of solid sections is approximated by a linear displacement field, and of thin-walled sections, by a cubic. Rotary inertia in torsion is included in both cases and warping inertia, in the latter.

The computer program performs the free vibration analysis starting from the element stiffness and consistent mass matrices. A numerical solution of a thin-walled beam and a parametric solution of an orthogonal and a skew grid with solid and thin-walled bars are presented.     

A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner–Mindlin plates

This paper proposes a quadrilateral finite element method of the lowest order for Reissner–Mindlin (R–M) plates on the basis of Hellinger–Reissner variational principle, which includes variables of displacements, shear stresses and bending moments. This method uses continuous piecewise isoparametric bilinear interpolation for the approximation of transverse displacement and rotation. The piecewise-independent shear stress/bending moment approximation is constructed by following a self-equilibrium criterion and a shear-stress-enhanced condition. A priori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t. Numerical experiments confirm the theoretical results.     

A beam element for coupled torsional-flexural vibration of doubly unsymmetrical thin walled beams axially loaded

A coupled torsional-bending finite element with shear deformations and rotatory inertia for vibration of nonsymmetric thin walled beams axially loaded is developed. The equations of motion are based on Vlasov’s theory of thin-walled beams, which are modified to include an axial load. The formulation is also applicable to solid beams. The Hermite cubic polynomials are adopted as shape functions. Mass, elastic stiffness and geometrical stiffness matrices of unsymmetrical cross-section beams are presented. In order to verify the accuracy of this theory and the corresponding beam element developed, a numerical study is presented and compared with the literature and experimental tests.     

空间薄壁梁单元面向对象程序的实现

针对传统有限元分析软件主要面向过程设计,其可维护性和可扩展性等较差的问题,基于面向对象程序设计方法,建立具有内部节点的空间薄壁截面梁单元模型,给出线弹性空间薄壁梁单元的UML类图,介绍矩阵类、截面类、材料类、节点类、单元类和结构类等6种类成员的主要属性和方法.用C#编制相应的有限元程序,通过T形框架算例比较和验证其位移和弯曲转角计算值、理论解和ANSYS的BEAM 189梁单元的数值解,结果表明该程序精度良好,可用于空间薄壁结构的有限元分析.     

Exact dynamic and static element stiffness matrices of nonsymmetric thin-walled beam-columns

An improved numerical method to exactly evaluate 14 × 14 dynamic and static element stiffness matrices is proposed for the spatial free vibration and stability analysis of nonsymmetric thin-walled straight beams subjected to eccentrically axial loads. Firstly equations of motion and force-deformation relations are rigorously derived from the total potential energy for a uniform beam element with nonsymmetric thin-walled cross-section. Next a system of linear algebraic equations with nonsymmetric matrices is constructed by introducing 14 displacement parameters and transforming the higher order simultaneous differential equation into the first order simultaneous equation. And then explicit expressions for displacement parameters are exactly evaluated by solving a generalized eigenproblem with complex eigenvalues. Finally exact element stiffness matrices are determined using force-deformation relations. Particularly straightforward application of the present method may not give the exact static stiffness because of existence of multiple zero eigenvalues in case of static buckling problems. Accordingly, a modified numerical method to resolve this difficulty is developed for two cases depending on the initial state of stress resultants. In order to demonstrate the validity and the accuracy of this method, the natural frequencies and buckling loads of nonsymmetric thin-walled beam-columns having bending-torsional deformation modes are evaluated and compared with analytical and F.E. solutions or results analyzed by ABAQUS’s shell element.     

Identification and elimination of parasitic shear in a laminated composite beam finite element

A displacement-based finite element for the analysis of laminated composite beams is formulated using strain gradient notation. The definition of the beam’s longitudinal displacement possesses only the independent term (axial displacement) and a term which is linear in the thickness coordinate z. Thus, the finite element is first-order shear deformable. As strain gradient notation is physically interpretable, the contents of the coefficients of the polynomial expansions are identified a priori. Thus, the modeling capabilities as well as modeling deficiencies of the element are identified during the formulation procedure. A single parasitic shear term (spurious) is found to be present in the transverse shear strain expression of the element, which is responsible for locking. This parasitic shear term is also found to be the cause of a qualitative error existing in the representation of transverse shear strain along the length of a typical beam model. As the spurious term has been clearly identified, it can easily be removed to correct the element. The effectiveness of the procedure is shown through numerical analyses performed using the element containing the spurious term and then corrected for it. The beam model is validated by comparing numerical solutions with analytical solutions provided by the minimization of the total potential energy for a given laminated composite beam.     

功能梯度双层悬臂梁的有限元建模分析

为考察不同建模形式和界面处理方式对由功能梯度材料构成的双层悬臂梁计算结果的影响,通过有限元计算结果与理论解的对比发现,对于功能梯度悬臂梁,选取八节点二次单元能更好地消除剪力自锁现象,比四节点线性单元的求解结果更加精确;对于双材料理想界面,采取强制位移约束条件比消除重合节点的约束条件更符合真实情况;梁端部附近应力场的有限元解比理论解更加合理.     

Stability of composite thin-walled beams with shear deformability

In this paper, a theoretical model is developed for the stability analysis of composite thin-walled beams with open or closed cross-sections. The present model incorporates, in a full form, the shear flexibility (bending and non-uniform warping), featured in a consistent way by means of a linearized formulation based on the Reissner’s Variational Principle. The model is developed using a non-linear displacement field, whose rotations are based on the rule of semi-tangential transformation. This model allows to study the buckling and lateral stability of composite thin-walled beam with general cross-section. A finite element with two-nodes and fourteen-degrees-of-freedom is developed to solve the governing equations. Numerical examples are given to show the importance of the shear flexibility on the stability behavior of this type of structures.