新型空间薄壁梁单元

基于Timoshenko梁理论和Vlasov薄壁杆件约束扭转理论,建立了具有内部结点的新型空间薄壁截面梁单元．通过对弯曲转角和翘曲角采取独立插值的方法,考虑了横向剪切变形,扭转剪切变形及其耦合作用,弯曲变形和扭转变形的耦合以及二次剪应力等因素影响,由Hellinger-Reissner广义变分原理,推得单元刚度矩阵．算例表明所建模型具有良好的精度,可用于空间薄壁杆系结构的有限元分析．     

旋转壳的抗扭刚度

本文列出了旋转壳在包括扭转在内的轴对称变形下的一般平衡方程,并证明了旋转对称壳内的剪应力独立于壳内其它薄膜和弯曲应力.本文求解了只考虑薄膜应力的扭转问题,也求解了考虑弯曲扭应力在内的扭转问题,并指出了在薄壳中,抗扭刚度的主要部份来源于薄膜应力.     

非均匀变截面弹性圆环在任意载荷下的弯曲问题

本文在等刚度弹性圆环的初参数公式的基础上,利用[2]提出的阶梯折算法,进一步研究非均匀变截面弹性圆环的弯曲,得到了这类问题的通解,应当指出,这组通解对非均匀变截面圆柱拱的相应问题也是适用的.为验证所得的公式并说明这种方法的应用,文末给出了示例并进行了求解,圆环、圆拱是工程上经常采用的结构,它们的弯曲,Timoshenko,S.[5],Barber,J.R.[3],Roark,R J[4],津村利光[6]等曾作过很多研究.然而,迄今只求得了均匀材料、等截面圆环的通解。对变截面问题,仅仅求得了抗弯刚度是坐标的线性函数这一特殊情况的解.由于非均匀变截面问题常常导出变系数微分方程,它们的求解遇到很大的数学困难.本文通过阶梯折算法把非均匀变截面弹性圆环弯曲问题的变系数微分方程转化成一等效的等刚度圆环弯曲的常系数微分方程.为保证内力连续,引入虚拟内力,并以[1]导出的初参数公式为影响函数,通过积分构造出了非齐次解,从而求得了非均匀变截面弹性圆环弯曲问题的通解.     

空间弹性变形梁动力学的旋量系统理论方法

所谓空间弹性梁,即同时考虑受弯曲、拉伸和扭转等力作用而发生空间变形的梁.借助于刚体运动的旋量理论,引入了"变形旋量"这一概念,进而提出了空间弹性梁的旋量理论.在基本的运动学假设和材料力学理论基础上,分析并给出了梁的空间柔度.接着研究了空间弹性梁的动力学,用旋量理论分析了其动能和势能,从而得到了Lagrange算子.通过对边界条件和变形函数的讨论,进一步运用Rayleigh-Ritz方法计算了系统的振动频率.将空间弹性梁与纯弯曲、扭转或者拉伸等简单变形情况下的特征频率做了对比研究.最后,运用所提出的空间弹性梁理论研究了一关节轴线互相垂直的两空间柔性杆机械臂的动力学,通过动力学仿真发现了关节的刚性运动和空间柔性杆的弹性变形运动之间的耦合影响.该文的研究工作阐明了运用旋量系统理论解决具有空间弹性变形杆件的机构动力学问题的有效性.     

计及弯曲刚度的印刷运动薄膜横向振动控制研究

研究了不同边界条件下,计及弯曲刚度的轴向运动薄膜横向振动的主动控制问题.建立计及弯曲刚度的印刷运动薄膜的计算模型.利用有限差分法,对轴向运动薄膜的振动微分方程进行离散,推导出轴向运动矩形薄膜横向振动控制系统的状态方程.采用次最优控制法,对不同边界条件下轴向运动矩形薄膜横向振动进行主动控制研究.计算结果表明:采用次最优控制法能够在短时间内迅速、有效地降低运动薄膜的振动强度,并使之衰减趋近于0.作动器作用在固定位置点处时,对运动薄膜施加控制后,四边简支边界条件下的控制效果好.作动器作用在不同位置点处时,两种边界条件下中心点处的控制效果最好.计算证明次最优控制法能够有效地抑制印刷过程中计及弯曲刚度的轴向运动薄膜的横向振动,从而提高印刷套印精度,保证精密印刷质量.     

考虑非局部剪切效应的碳纳米管弯曲特性研究

基于Hamilton(哈密顿)变分原理和非局部连续介质弹性理论,建立了新型非局部Timoshenko(铁木辛柯)梁模型（ANT）,推导了碳纳米管（CNT）的ANT弯曲平衡方程以及两端简支梁、悬臂梁和简支 固定梁的边界条件表达式,分析了剪切变形效应和非局部微观尺度效应对碳纳米管弯曲特性的影响.数值计算结果显示,碳纳米管的弯曲刚度随着小尺度效应的增强而升高.其次,这种小尺度效应对自由端受集中力的悬臂梁碳纳米管有明显作用,其刚度变化规律和其它约束条件的碳纳米管一样,这一点是ANT模型区别于普通非局部纳米梁模型的主要特点.经分子动力学模拟验证,ANT模型是合理分析碳纳米管力学特性的有效方法.     

变截面二维功能梯度微梁的振动和屈曲特性北大核心CSCD

基于修正的偶应力理论和Timoshenko梁理论,应用变分原理建立了变截面二维功能梯度微梁的自由振动和屈曲力学模型.模型中包含金属组分和陶瓷组分的材料内禀特征尺度参数,可以预测微梁力学行为的尺度效应.采用Ritz法给出了任意边界条件下微梁振动频率和临界屈曲载荷的数值解.数值算例表明:微梁厚度减小时,无量纲一阶频率和无量纲临界屈曲载荷增大,尺度效应增强.锥度比对微梁一阶频率的影响与边界条件密切相关,同时,对应厚度和对应宽度锥度比的影响也有明显差异.变截面微尺度梁无量纲一阶频率随着陶瓷和金属的材料内禀特征尺度参数比的增加而增大,且不同边界条件时增大程度不同.厚度方向和轴向功能梯度指数对微梁的一阶频率和屈曲载荷也有显著的影响.     

双层交叉孔型中纤板的仿真分析与弯曲强度公式

运用ANSYS有限元分析软件,对双层交叉孔型中密度纤维板不同孔径和孔间距条件下的弯曲力学行为进行了仿真计算。分析所得到的数据表明该板的等效弯曲刚度分别与孔径的4次方以及开孔间距的倒数存在线性关系,恰好符合理论推导公式反映的变化规律。运用仿真结果对理论公式进行修正,得到了双层交叉孔型中密度纤维板弯曲等效刚度的计算公式。     

一维纳米准晶层合梁的非局部振动、屈曲与弯曲研究

基于非局部理论,建立了一维纳米准晶层合简支深梁模型,研究了其自由振动、屈曲行为及其弯曲变形问题.采用伪Stroh型公式,导出了纳米梁的控制方程,并通过传递矩阵法获得简支边界条件下纳米准晶层合梁固有频率、临界屈曲载荷及弯曲变形广义位移和广义应力的精确解.通过数值算例,分析了高跨比、层厚比、叠层顺序及非局部效应对一维纳米准晶层合简支梁固有频率、临界屈曲载荷和弯曲变形的影响.结果表明：固有频率和临界屈曲载荷随着非局部参数增大而减小;外层准晶弹性常数更高时,固有频率和临界屈曲载荷更大;叠层顺序对纳米准晶梁的力学行为有较大影响.所得的精确解可为纳米尺度下梁结构的各种数值方法和实验结果提供参考.     

变刚度复杂梁结构损伤检测方法研究

提出了适用于复杂梁结构损伤检测的子段模态应变能法SSEM(subsectionstrainenergymethod),并分析了该方法的适用性条件．通过对变截面梁的有限元计算,以及对纤维增强复合材料风机叶片缩比模型的试验分析,验证了SSEM方法确定的结构损伤指标对损伤准确定位的可靠性．该基于振动的变刚度复杂梁结构的损伤检测方法,可应用于工程实际中梁和类梁整体结构的损伤检测．     

Simplified modelling of joints and beam-like structures for BIW optimization in a concept phase of the vehicle design process

The paper proposes an engineering approach for the replacement of beam-like structures and joints in a vehicle model. The final goal is to provide the designer with an effective methodology for creating a concept model of such automotive components, so that an NVH optimization of the body in white (BIW) can be performed at the earliest phases of the vehicle design process. The proposed replacement methodology is based on the reduced beam and joint modelling approach, which involves a geometric analysis of beam-member cross-sections and a static analysis of joints. The first analysis aims at identifying the beam center nodes and computing the equivalent beam properties. The second analysis produces a simplified model of a joint that connects three or more beam-members through a static reduction of the detailed joint FE model.In order to validate the proposed approach, an industrial case-study is presented, where beams and joints of the upper region of a vehicle's BIW are replaced by simplified models. Two static load-cases are defined to compare the original and the simplified model by evaluating the stiffness of the full vehicle under torsion and bending in accordance with the standards used by automotive original equipment manufacturer (OEM) companies. A dynamic comparison between the two models, based on global frequencies and modal shapes of the full vehicle, is presented as well.     

A reduced beam and joint concept modeling approach to optimize global vehicle body dynamics

Ideally, NVH simulations become available already in the concept phase of vehicle development. The initial computer-aided design (CAD) can then be improved (by already including countermeasures), and the feasibility to balance NVH with other performance attributes is increased. In this early design stage, when exact geometrical information is not or scarcely available, conventional virtual prototyping techniques based on detailed CAD and FE models are not directly applicable. A state-of-the-art overview of concept NVH simulation methods in vehicle industry is given.This paper then presents a “Reduced Beam and Joint Modeling” approach to analyze and optimize the global bending and torsion modes of a vehicle body. Concept modifications in the body beam-like sections and in the joints are analyzed using the body reduced modal model. This small-sized model can be used to quickly and accurately optimize the low-frequency vehicle performance. The modifications are considered with respect to the existing (predecessor) model. Equivalent beam properties are estimated from the body FE model; modifications in the beam-like sections are then implemented with beam elements from a standard FE library. The joint modifications are considered through static superelements: stiffness formulations between the end points of the joint connected to the beam layout. The validity of the approach is first demonstrated on simple example models. An industrial vehicle BIW application case is subsequently presented. A beam and joint layout is created, and used for a fast sensitivity analysis to identify suitable modifications to improve the global modes. Next, two application cases are presented. First, a fast optimization analysis is performed to optimize the global body modes. Subsequently, suitable physical modifications are identified and applied to the full FE model; it is shown that the effect of these physical modifications is accurately predicted with the fast sensitivity analysis.     

Free vibration analysis of cracked composite beams subjected to coupled bending–torsion loads based on a first order shear deformation theory

In this paper, free vibration analysis of cracked composite beam subjected to coupled bending–torsion loading is presented. The composite beam is assumed to have an open edge crack of length a. A first order shear deformation theory is applied to count for the effect of shear deformations on natural frequencies as well as the effect of coupling in torsion and bending modes of vibration. Governing equations and boundary conditions are derived using Hamilton principle. Local flexibility matrix is used to obtain the additional boundary conditions of the beam in cracked area. After obtaining the governing equations and boundary conditions, generalized differential quadrature (GDQ) method is applied to solve the obtained eigenvalue problem. Finally, some numerical results of beams with various boundary conditions and different fiber orientations are given to show the efficiency of the method. In addition, to study the effect of shear deformations, numerical results of the current model are compared with previously given results in which shear deformations were neglected.     

Influence of Different Factors on the Stiffness and Strength of Multilayer Composite Elements

In the paper, the bending stiffness and strength of multilayer structural elements in relation to the mechanical properties of layers and their number layout and sizes are investigated and the corresponding correlations are established. It is found that the most rational structure of a multilayer element in bending is a symmetric three-layer structure formed from two materials with the thickness of the core less than the half-thickness of the element. The values of normal stresses in the layers of a multilayer beam in bending depends on its bending stiffness and the position of layers relative to the neutral axis. The influence of the number of layers on the stiffness of the structural element and on the magnitude of normal stresses is insignificant.     

Multi-scale modeling of beam-like structures: A new boundary condition concept for the RVE

In this work a coupled two-scale beam model using Timoshenko beam elements [1] with finite displacements on the macro scale and fully non-linear 3D brick elements on the micro scale is proposed. The calculation is carried out with the so-called FE² concept. To achieve the coupling between the beam and the brick elements, the algorithm from [2] is adapted. Within the degenerated concept of the Timoshenko beam, the introduction of a pure shear deformation leads to significant problems concerning the equilibrium condition on the micro scale. Applying this deformation mode on the RVE with periodic boundary conditions results in a rigid body rotation. Using linear displacement boundary conditions instead, the wrapping deformation is suppressed on the boundary, leading to a length dependency in the torsional deformation mode. In addition, the shear forces introduce a bending moment, which depends on the length of the RVE and adds spurious normal stresses and a length dependency of the shear stiffness. To overcome these problems, periodic boundary conditions are applied and the displacement assumptions are modified such that the shear deformation is achieved with force pairs on both ends of the RVE. The resulting model leads to length independent results in tension, bending and torsion and a domain which is able to produce a pure shear stress state. Consequently, only this domain of the model should be homogenized which can be accomplished by modifying the variations in the algorithm [2]. The concept is validated by simple linear and non-linear test problems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类柔性臂机器人的稳定性

本文研究了一类柔性臂机器人的控制问题,且柔性臂的弯曲振动与扭转振动的耦合作用表现在边界方程中。本文运用算子谱理论、算子半群理论等,得到系统的主算子生成的C0-半群的具体表示式,并证明了半群的解析性、非紧性及非一致指数稳定性。     

Green's functions for forced vibration analysis of bending-torsion coupled Timoshenko beam

A method based on Green's functions is proposed for the analysis of the steady-state dynamic response of bending-torsion coupled Timoshenko beam subjected to distributed and/or concentrated loadings. Damping effects on the bending and torsional directions are taken into account in the vibration equations. The elastic boundary conditions with bending-torsion coupling and damping effects are derived and the classical boundary conditions can be obtained by setting the values of specific stiffness parameters of the artificial springs. The Laplace transform technology is employed to work out the Green's functions for the beam with arbitrary boundary conditions. The Green's functions are obtained for the beam subject to external lateral force and external torque, respectively. Coupling effects between bending and torsional vibrations of the beam can be studied conveniently through these analytical Green's functions. The direct expressions of the steady-state responses with various loadings are obtained by using the superposition principle. The present Green's functions for the Timoshenko beam can be reduced to those for Euler–Bernoulli beam by setting the values of shear rigidity and rotational inertia. In order to demonstrate the validity of the Green's functions proposed, results obtained for special cases are given for a comparison with those given in the literature and they agree with each other exactly. The influences of external loading frequency and eccentricity on Green's functions of bending-torsion coupled Timoshenko beam are investigated in terms of the numerical results for both simply supported and cantilever beams. Moreover, the symmetric property of the Green's functions and the damping effects on the amplitude of Green's functions of the beam are discussed particularly.     

Minimum-weight design of elastic sandwich beams with deflection constraints

In this paper, minimum-weight design of an elastic sandwich beam with a prescribed deflection constraint at a given point is investigated. The analysis is based on geometrical considerations using then-dimensional space of discretized specific bending stiffness. Since the present method of analysis is different from the method based on the calculus of variations, the conditions of piecewise continuity and differentiability on specific bending stiffness can be relaxed. Necessary and sufficient conditions for optimality are derived for both statically determinate and statically indeterminate beams. Beams subject to a single loading and beams subject to multiple loadings are analyzed. The degree to which the optimality condition renders the solution unique is discussed. To illustrate the method of solution, two examples are presented for minimum-weight designs under dual loading of a simply supported beam and a beam built in at both ends. The present analysis is also extended to the following problems: (a) optimal design of a beam built in at both ends with piecewise specific stiffness and a prescribed deflection constraint and (b) minimum-cost design of a sandwich beam with prescribed deflection constraints.The results presented in this paper were obtained in the course of research supported partly by the US Army Research Office, Durham, North Carolina, Research Grant No. DA-ARO-31-G1008, and partly by the Office of Naval Research, Contract No. N00014-67-A-0109-0003, Task No. NR 064-496. The authors wish to express their thanks to Professor H. Halkin for pointing out the applicability of optimal control theory to the present problem and to Professor W. Prager for his valuable suggestions.     

A mathematical model for beams on geosynthetic reinforced earth beds under strip loading

In this study, an attempt has been made to analyze a beam on geosynthetic reinforced earth beds subjected to strip loading. Geosynthetic layer has been assumed to have finite bending stiffness and therefore idealized as a beam. The foundation beam has been placed on compacted granular soil layer overlying the geosynthetic layer below which lies on the original weak/loose soil deposit. The upper dense and lower loose soil layers have been idealized as Winkler springs of different stiffnesses. Governing differential equations for the flexural response of the system have been derived and presented in non-dimensional form. These equations have been solved using appropriate boundary and continuity conditions. It was possible to obtain a closed form analytical solution for such a foundation system.