Failure analysis of RC beams subjected to shear through different numerical approaches

This work discusses and compares different numerical approaches that can be adopted for the analysis up to failure of reinforced concrete beams, also when they experience a brittle shear collapse. Since the development of inclined shear cracks causes a variation of the strain field normal to the element axis, as well as of the shear strains in the beam depth, this type of problem is often dealt with refined bi-dimensional nonlinear finite element analyses. The effectiveness of this type of simulations is in turn mainly related to the adoption of a sound constitutive law for the material. This work highlights that, given the same material model, also more “traditional” approaches, based on sectional analysis or on 1D finite element simulations, can be satisfactorily applied to study the problem, if their kinematic assumptions are improved and extended. In these cases, a subdivision of beam depth into several layers is also recommended. In fact, this allows to both simulate the actual position of steel reinforcement, and to widen the applicability of the method to elements characterized by a generic cross-section shape.     

Effect of shear deformations and rotary inertia on optimum beam frequencies

Accounting for shear deformations and rotary inertia effects, necessary condition for optimum fundamental frequency of a vibrating beam of constant volume and with a given distribution of non-structural mass, is obtained through the calculus of variations. Minimum cross-section of the beam is controlled by the introduction of an inequality constraint. A finite element displacement formulation is then used in an iterativve manner to arrive at the optimum fundamental frequency and the corresponding material distribution for the discretized beam models with various boundary conditions. A comparison is then made with the corresponding results of an Euler beam.     

不同截面梁构件的刚度和稳定性优化设计

本文运用有限元分析与优化设计软件JIFEX，对五种常用截面梁结构的尺寸和形状进行了抗剪、抗弯、抗扭的刚度优化设计和在轴力、剪力作用下的结构稳定性优化设计。通过对优化设计的计算结果分析，得到了对工程设计有意义的若干结论。然后通过飞机结构中一种波形梁构件的优化，进一步讨论了波形梁的波数对结构稳定性和刚度的影响。     

复合材料空间薄壁梁的有限元分析模型

在剪切梁理论的基础上, 采用9 节点平面单元模拟梁任意截面形状; 采用27 节点体单元, 模拟截面出平面外的二次翘曲位移, 从而建立了空间复合材料任意截面薄壁梁考虑二次翘曲的有限元分析模型。根据本文中导出的复合材料有限元模型编制了相应的分析计算程序。算例表明: 本文中建立的复合材料薄壁梁模型正确, 可以用于考虑多种耦合影响因素作用下复杂结构空间薄壁复合材料梁的有限元分析计算。      

六边形孔蜂窝梁和蜂窝组合梁抗剪性能分析

该文对不同参数下的正六边形孔蜂窝梁和蜂窝组合梁抗剪性能进行了试验与有限元分析研究。以试验研究为基础,基于有限元软件ABAQUS 建立非线性有限元模型,对不同开孔率、不同翼缘宽度和厚度的蜂窝梁和蜂窝组合梁进行分析比较,发现蜂窝梁和蜂窝组合梁抗剪承载力大小与翼缘厚度、开孔率和连接程度均有关。结果表明:蜂窝梁翼缘厚度变化对其抗剪承载力影响较大,而蜂窝组合梁中翼缘厚度的变化对其抗剪性能影响相对较小;混凝土板提高了蜂窝梁的抗剪极限承载能力;最后,给出蜂窝梁和蜂窝组合梁抗剪计算公式。     

Hamilton体系下的功能梯度电磁弹性固体内的导波研究

根据Hamilton原理建立了三维压电压磁动力学耦合系统的Hamilton对偶体系，将经典的弹性力学一类变量问题转化为二类变量，建立了Hamilton正则方程组，研究了功能梯度电磁材料（FGMM）板／管内的弹性导波的频散特性及波结构特征。结果表明：（1）压电效应提高了Lamb波的频率和波速，而磁效应则相反，压电效应对波动的影响远大于磁效应；它们而对SH波没有影响（厚度方向极化）。（2）短路及断路电学边界条件对SH波不发生任何影响（厚度方向极化），而短路对Lamb波的频率和波速有不同程度的降低（相同波数下）。（3）在波结构上，对平板而言，所谓的“对称”和“反对称”Lamb波由于材料的梯度特性而变得不再严格的关于中心线对称或反对称。对管而言，由于材料的非均匀分布导致存轴对称栩转波模态中出现了横截面翘曲现象．轴对称纵向波也出现厚度剪切应力。     

Finite element analysis of linear and non-linear planar deformations of elastic initially curved beams

We discuss both linear and geometrically non-linear finite element analysis of elastic beams, taking into account the shear deformation. In linear analysis, a novel shallow beam element formulaton is consistently derived, and the end result is more suitable for the finite element implementation than earlier attempts. The element is very resourceful for an explanation of membrane and shear locking phenomena and exploration of their possible remedies. In addition, it sheds some light on locking phenomena in non-linear analysis. In non-linear analysis, we discuss the finite element implementation of the finite strain beam theory of Reissner.     

Thermally-induced bending-torsion coupling vibration of large scale space structures

In this paper, a finite element scheme is developed to solve the problem of thermally-induced bending-torsion coupling vibration of large scale space structures, which are usually composed of thin-walled beams with open and closed cross-section. A two-noded finite element is proposed to analyze the transient temperature field over the longitudinal and circumferential direction of a beam. Since this temperature element can share the same mesh with the two-noded beam element of Euler–Bernoulli type, a unified finite element scheme is easily formulated to solve the thermal-structural coupling problem. This scheme is characterized with very strong nonlinear formulation, due to the consideration of the thermal radiation and the coupling effect between structural deformations and the incident normal heat flux. Moreover, because the warping is taken into account, not only the thermal axial force and thermal bending moments but also the thermal bi-moment are presented in the formulation. Consequently, the thermally-induced bending-torsion coupling vibration can be simulated. The performance of the proposed computational scheme is illustrated by the analysis of the well-known failure of Hubble space telescope solar arrays. The results reveal that the thermally-induced bending-torsion coupling vibration is obviously presented in that case and could be regarded as a cause of failure.     

Analyses of magneto-electro-elastic plates using a higher order finite element model

In this paper is presented a higher-order model for static and free vibration analyses of magneto-electro-elastic plates, which allows the study of thin and thick plates. The finite element model is a single layer triangular plate/shell element with 24 degrees of freedom for the generalized mechanical displacements. Two degrees of freedom are introduced per each element layer, one corresponding to the electrical potential and the other for magnetic potential. Solutions are obtained for different laminations of the magneto-electro-elastic plate, as well as for the purely elastic plate as a special case. Results are compared with alternative models for static and free vibrations situations.     

An improved theory and finite-element model for laminated composite and sandwich beams using first-order zig-zag sublaminate approximations

A new beam finite element based on a new discrete-layer laminated beam theory with sublaminate first-order zig-zag kinematic assumptions is presented and assessed for thick and thin laminated beams. The model allows a laminate to be represented as an assemblage of sublaminates in order to increase the model refinement through the thickness, when needed. Within each sublaminate, discrete-layer effects are accounted for via a modified form of DiSciuva's linear zig-zag laminate kinematics, in which continuity of interfacial transverse shear stresses is satisfied identically. In the computational model, each finite element represents one sublaminate. The finite element is developed with the topology of a fournoded rectangle, allowing the thickness of the beam to be discretized into several elements, or sublaminates, if necessary, to improve accuracy. Each node has three engineering degrees of freedom, two translations and one rotation. Thus, this element can be conveniently implemented into general purpose finite-element codes. The element stiffness coefficients are integrated exactly, yet the element exhibits no shear locking due to the use of a consistent interdependent interpolation scheme. Numerical performance of the current element is investigated for an arbitrarily layered beam, a symmetrically layered beam and a sandwich beam with low and high aspect ratios. The comparisons of numerical results with elasticity solutions show that the element is very accurate and robust.     

考虑剪滞变形时箱形梁广义力矩的数值分析

为了简化变截面箱梁等复杂结构的剪滞效应分析,在明确定义相应于剪滞位移的广义力矩和有关几何特性的基础上,提出一种梁段有限元数值分析方法。选取控制微分方程的齐次解作为单元位移函数,以各积分常数为中间转换变量,推导梁段单元刚度矩阵和等效节点力向量的具体表达式,并给出用单元节点力直接计算应力的一般公式。编制了箱梁梁段有限元程序,对简支、悬臂、连续箱梁3个有机玻璃模型进行计算并与实测结果对比,验证了该文方法及公式的正确性。用所编程序对箱梁的剪滞广义力矩进行数值分析,并揭示了其变化规律。研究表明,在竖向荷载作用下,剪滞力矩与弯矩具有相似的分布规律,而且数值大小也接近。     

The hybrid Laplace transform/finite element method applied to the quasi-static and dynamic analysis of viscoelastic Timoshenko beams

The quasi-static and dynamic responses of a linear viscoelastic beam are solved numerically by using the hybrid Laplace transform/finite element method. In the analysis, the Timoshenko beam theory, which includes the transverse shear and rotatory inertia effect and conventional beam theory, are used to solve this problem. The temperature field is assumed to be constant and homogeneous and that the relaxation modulus has the form of the Prony series. In the hybrid method, the Laplace transform with respect to time is applied to the coupled equations and the finite element model is developed by applying Hamilton's variational principle without any integral transformation. The numerical results of quasi-static and dynamic responses for the models of Maxwell fluid and three parameter solid types are presented and discussed.     

Shear correction factors in Timoshenko's beam theory for arbitrary shaped cross-sections

 In this paper shear correction factors for arbitrary shaped beam cross-sections are calculated. Based on the equations of linear elasticity and further assumptions for the stress field the boundary value problem and a variational formulation are developed. The shear stresses are obtained from derivatives of the warping function. The developed element formulation can easily be implemented in a standard finite element program. Continuity conditions which occur for multiple connected domains are automatically fulfilled.     

Locking-free finite elements for shear deformable orthotropic thin-walled beams

Numerical models for finite element analyses of assemblages of thin-walled open-section profiles are presented. The assumed kinematical model is based on Timoshenko–Reissner theory so as to take shear strain effects of non-uniform bending and torsion into account. Hence, strain elastic-energy coupling terms arise between bending in the two principal planes and between bending and torsion. The adopted model holds for both isotropic and orthotropic beams. Several displacement interpolation fields are compared with the available numerical examples. In particular, some shape functions are obtained from ‘modified’ Hermitian polynomials that produce a locking-free Timoshenko beam element. Analogously, numerical interpolation for torsional rotation and cross-section warping are proposed resorting to one Hermitian and six Lagrangian formulation. Analyses of beams with mono-symmetric and non-symmetric cross-sections are performed to verify convergence rate and accuracy of the proposed formulations, especially in the presence of coupling terms due to shear deformations, pointing out the decay length of end effects. Profiles made of both isotropic and fibre-reinforced plastic materials are considered. The presented beam models are compared with results given by plate-shell models. Copyright © 2007 John Wiley & Sons, Ltd.     

基于小波有限元的悬臂梁裂纹识别

研究了悬臂梁裂纹识别中的正反问题．即通过裂纹位置和尺寸求解梁的固有频率以及利用梁的固有频率．识别裂纹位置和尺寸。以矩形截面裂纹悬臂梁为例，利用小波有限元方法建立了梁自由振动的有限元模型．其中裂纹被看作为一刚度已知的扭转线弹簧，求解出了系统的固有频率；通过行列式变换，将反问题求解简化为只含线弹簧刚度一个未知数的一元二次方程求根问题，分别做出了以不同固有频率作为输入值时裂纹位置与弹簧刚度之间的解曲线，曲线交点预测出裂纹的位置与尺寸。数值算例证实了算法的有效性，为工程结构裂纹故障预示与诊断提供了新的方法。     

基于能量法的变截面层合管整体稳定承载力计算方法

为计算变截面层合管杆件整体稳定承载力,提出一种基于能量法的理论计算模型。采用基于三维梁理论的层合管等效抗弯刚度计算方法,计算了等截面段、变截面段的等效工程弹性系数。在考虑剪切变形的影响以及杆件变截面对轴压挠曲线函数影响的基础上,基于能量法推导了变截面杆整体稳定承载力解析公式。以NASA复合材料变截面杆为算例,进行了理论计算和有限元数值模拟,结果显示:同时考虑上述两因素的理论计算结果与有限元结果最为接近,剪切变形对临界承载力的修正可达10%以上,轴压挠曲线函数的变化对承载力的修正约为1%,可忽略。以锥长和锥角为参数,对变截面杆的承载力、体积和承载效率进行双参数分析,发现变截面对弯曲变形能的影响远大于对剪切变形性能的影响,采用变截面形式能够提高层合管承载效率,且一定锥长下存在承载效率最高对应的最优锥角。     

Simple Efficient Smart Finite Elements for the Analysis of Smart Composite Beams

This paper is concerned with the development of new simple 4-noded locking-alleviated smart finite elements for modeling the smart composite beams. The exact solutions for the static responses of the overall smart composite beams are also derived for authenticating the new smart finite elements. The overall smart composite beam is composed of a laminated substrate conventional composite beam, and a piezoelectric layer attached at the top surface of the substrate beam. The piezoelectric layer acts as the actuator layer of the smart beam. Alternate finite element models of the beams, based on an “equivalent single layer high order shear deformation theory”, and a “layer-wise high order shear deformation theory”, are also derived for the purpose of investigating the required number of elements across the thickness of the overall smart composite beams. Several cross-ply substrate beams are considered for presenting the results. The responses computed by the present new “smart finite element model” excellently match with those obtained by the exact solutions. The new smart finite elements developed here reveal that the development of finite element models of smart composite beams does not require the use of conventional first order or high order or layer-wise shear deformation theories of beams. Instead, the use of the presently developed locking-free 4-node elements based on conventional linear piezo-elasticity is sufficient.     

Static behavior of composite beams using various refined shear deformation theories

Static behavior of composite beams with arbitrary lay-ups using various refined shear deformation theories is presented. The developed theories, which do not require shear correction factor, account for parabolical variation of shear strains and consequently shear stresses through the depth of the beam. In addition, they have strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. A two-noded C¹ finite element with six degree-of-freedom per node which accounts for shear deformation effects and all coupling coming from the material anisotropy is developed to solve the problem. Numerical results are performed for symmetric and anti-symmetric cross-ply composite beams under the uniformly distributed load and concentrated load. The effects of fiber angle and lay-ups on the shear deformation parameter and extension-bending-shear-torsion response are investigated.     

Vibrations of non-uniform functionally graded MWCNTs-polystyrene nanocomposite beams under action of moving load

Free and forced vibrations of non-uniform functionally graded multi-walled carbon nanotubes (MWCNTs)-polystyrene nanocomposite beams are investigated via Timoshenko beam theory. Different MWCNTs distributions in the thickness direction are introduced to improve fundamental natural frequency and dynamic behavior of non-uniform polymer composite beam under action of moving load. So, linear distribution patterns of carbon nanotubes (CNTs) in the thickness direction which can readily be achieved in practice are studied. The effects of shear deformation, rotary inertia, non-uniformity of the cross-section are also considered in the formulation. The finite element method is employed to obtain a numerical approximation of the motion equation. The non-uniform beam is approximated by another beam consisting of n elements with piecewise constant thickness so that the volume remains constant for each element. The effects of non-uniformity parameters, material distributions, velocity of the moving load and boundary conditions on the dynamic behavior are investigated. It is found that the symmetrical linear distribution of MWCNTs results in an increase in the fundamental natural frequency of nanocomposite beams which are higher than those of beams with uniform and unsymmetrical MWCNTs distributions.