Statics of thin-walled pretwisted beams

The displacement and strain fields of thin-walled pretwisted beams are prescribed in terms of generalized displacements for extension, bending, torsion and warping. Differential equations and boundary conditions are obtained from the elastic potential energy functional without assuming coincidence of the beam axis with any of the structural axes. This procedure gives a unique consistent definition of sectional moments and generalized forces. Some simple explicit formulae are derived for homogeneous tension–torsion. For the general case a computer code is developed on the basis of discretized generalized displacements and a modified energy functional, devised to obtain consistent lengthwise variation of the stresses and a unique decomposition of the torsional moment. Examples show agreement with analytical results for cylindrical beams and illustrate the various coupling effects for beams with pretwist. They also demonstrate the usefulness of the explicit formulae for homogeneous tension–torsion.     

Effect of stochastically anisotropic morphology on the mechanical behavior of microbeams

In many Micro-Electro-Mechanical-Systems (MEMS) applications such as polysilicon microstructures, the size of the basic element (grain), compared with the structure’s scale, is not negligible. In these cases, the random microstructure causes statistical dispersion of its response to load, experimentally observed by many researchers. The accompanying calculations, which generally treat the material as homogeneous and isotropic, do not model the structures properly. In this work, we analytically study the relations between morphological properties and the generalized displacements of statically determinate beams, frequently used in MEMS. The analysis includes shear deformation effects, material and structural couplings such as shear and bending deformations due to normal forces, and nonisotropic effects. The governing equations are presented in a special tensorial form, which enables finding analytical expressions for the mean and covariance matrix of the generalized deflections in terms of well defined morphological parameters and their statistics.     

基于正交异性材料的预应力梁频率的试验研究

进行了一根无粘结预应力简支梁的动力试验,结果表明:预应力梁的固有频率随着预应力的增加而增加,这与Clough提出的轴力作用下各向同性材料梁的理论分析结果相反。其原因是传统的结构分析方法将混凝土视为各向同性、均质的线弹性材料。但是对预应力混凝土结构进行动力分析和检测,要求计算结果必须具有相对高的计算精度。为此该文从混凝土的微观结构入手,将预应力混凝土梁看作各向异性复合材料梁,采用正交异性的线弹性本构模型进行分析,将复合材料梁的刚度视为钢筋混凝土梁的刚度与预应力筋等效刚度之和,然后对预应力混凝土梁的频率与预应力的关系进行分析计算,计算结果与试验结果吻合较好。同时,利用该文提出的分析方法对Saiidi等人的试验梁进行了分析对比,其计算结果与其试验值也符合较好。     

A beam finite element for magneto-electro-elastic multilayered composite structures

A new finite element based upon an elastic equivalent single-layer model for shear deformable and straight magneto-electro-elastic generally laminated beam is presented. The element has six degrees of freedom represented by the displacement components and the cross-section rotation of its two nodes. The magneto-electric boundary conditions enter the discrete problem as work-equivalent forces and moments while the electro-magnetic state characterization constitutes a post-processing step. The element possesses the superconvergence property for the static problem of beams with uniform cross-section and homogenous material properties along the beam axis direction. Moreover, it is free from the shear locking phenomenon. The developed finite element is validated through comparison with plane-stress results for piezoelectric and magneto-electro-elastic structures. Last, applications for more complex magneto-electro-elastic systems are described.     

基于均匀化方法的节理岩体等效弹性性能预测

假定节理岩体具有均质的宏观结构和非均质的周期性分布的细观结构,利用均匀化方法,根据材料周期性特点,通过摄动理论建立依赖于两尺度坐标变量而变化的渐进位移场,推导出反映节理岩体细观结构的控制方程,并结合有限元法,数值模拟得到其宏观等效弹性模量。将算例得到的等效弹性模量与Taylor方法、自洽方法及Hashin-Shtrikman结果进行对比分析,证实了均匀化算法的合理性。同时探讨了节理岩体的弹性性能与组份性能及细观结构的关系,并考察了节理岩体的岩质材料泊松比对宏观力学性能的影响。     

Radiation pressure cross sections and optical forces over negative refractive index spherical particles by ordinary Bessel beams

When impinged by an arbitrary laser beam, lossless and homogeneous negative refractive index (NRI) spherical particles refract and reflect light in an unusual way, giving rise to different scattered and internal fields when compared to their equivalent positive refractive index particles. In the generalized Lorenz-Mie theory, the scattered fields are dependent upon the Mie scattering coefficients, whose values must reflect the metamaterial behavior of an NRI scatterer, thus leading to new optical properties such as force and torque. In this way, this work is devoted to the analysis of both radial and longitudinal optical forces exerted on lossless and simple NRI particles by zero-order Bessel beams, revealing how the force profiles are changed whenever the refractive index becomes negative.     

湿-热-机-弹耦合FGM梁的稳定性及振动特性

研究了初始轴向机械载荷作用下Winkler-Pasternak弹性地基上功能梯度材料（FGM）梁在湿-热环境中的稳定性及振动特性。假设温度和湿度沿梁厚度方向稳态分布,材料的物性依赖于温度且按Voigt混合幂律模型连续分布。首先,基于一种扩展的n阶广义梁理论,应用Hamilton原理,统一建立了以轴向位移、弯曲变形项挠度及剪切变形项挠度为基本未知函数FGM梁的屈曲及自由振动方程,采用Navier解法获得了FGM简支梁静动态响应的精确解。其次,通过算例验证并给出了该广义梁理论阶次n的理想取值,丰富梁理论的同时,可供验证或改进其他各种剪切变形梁理论。最后,着重探讨了3种湿-热分布下湿度与温度增加、初始轴向机械载荷、跨厚比、地基刚度、梯度指标等诸多参数对FGM梁稳定性和振动特性的影响。     

Stochastic surface effects in nanobeam sensors

This work analyzes the statistical properties of nanobeam deflections due to stochastic surface stresses, induced by the surface adsorption/desorption of surrounding particles. A mechanical model for a heterogeneous nanobeam is first introduced. The model considers combined axial forces and bending moments due to non-uniform surface effects. Then, local surface interactions are statistically derived from the Langmuir interaction model and their corresponding stochastic surface stresses are introduced. Two types of nanobeam sensor are studied: a cantilever beam with pure surface bending effect and a clamped beam with mixed surface force and bending moment effects. The advantages of each type are discussed. The deflection statistics are found analytically and validated by Monte Carlo simulations. An analytical relation between the adsorption/desorption rates and the maximum deflection variance is found.     

Thermoelastic Characterization of Changing Phase Distribution in Hardened Steel by Laser Ultrasonics

The increase of hardness of steel during a heat treatment intended to give components more performance is a result of a drastic change in grain size and microstructure, which in turn can be analyzed via changes in acoustic wave scattering. The degree of scattering is related to the grain size, alloy phases, elastic anisotropy, and phonon spectra, which are connected with the structural heterogeneity. In this study, an axially oriented hardening profile in a steel rod was induced by a Jominy test. All-optical photoacoustic excitation and detection schemes were used to establish the relation between the hardness, the elastic modulus, the elastic scattering, and the thermal diffusivity on a series of eight samples cut out from the gradient part of the rod. For each sample, the scattering of the photoacoustically excited traveling surface acoustic waves detected in a heterodyne diffraction and beam deflection setup was extracted from their damping behavior at different wavelengths and frequencies. Also, the thermal diffusivity was determined by fitting the slow time evolution of the laser-induced photo-thermoelastic displacement signal, and was found to be decreasing with decreasing grain size and increasing hardness.     

On the size-dependent behavior of functionally graded micro-beams

In this paper, the size-dependent static and vibration behavior of micro-beams made of functionally graded materials (FGMs) are analytically investigated on the basis of the modified couple stress theory in the elastic range. Functionally graded beams can be considered as inhomogeneous composite structures, with continuously compositional variation from usually a ceramic at the bottom to a metal at the top. The governing equations of motion and boundary conditions are derived on the basis of Hamilton principle. Closed-form solutions for the normalized static deflection and natural frequencies are obtained as a function of the ratio of the beam characteristic size to the internal material length scale parameter and FGM distribution functions of properties. The results show that the static deflection and natural frequencies developed by the modified couple stress theory have a significant difference with those obtained by the classical beam theory when the ratio of the beam characteristic size to the internal material length scale parameter is small.     

A mixed finite element method for beam and frame problems

 In this work we consider solutions for the Euler-Bernoulli and Timoshenko theories of beams in which material behavior may be elastic or inelastic. The formulation relies on the integration of the local constitutive equation over the beam cross section to develop the relations for beam resultants. For this case we include axial, bending and shear effects. This permits consideration in a direct manner of elastic and inelastic behavior with or without shear deformation. A finite element solution method is presented from a three-field variational form based on an extension of the Hu–Washizu principle to permit inelastic material behavior. The approximation for beams uses equilibrium satisfying axial force and bending moments in each element combined with discontinuous strain approximations. Shear forces are computed as derivative of bending moment and, thus, also satisfy equilibrium. For quasi-static applications no interpolation is needed for the displacement fields, these are merely expressed in terms of nodal values. The development results in a straight forward, variationally consistent formulation which shares all the properties of so-called flexibility methods. Moreover, the approach leads to a shear deformable formulation which is free of locking effects – identical to the behavior of flexibility based elements. The advantages of the approach are illustrated with a few numerical examples. Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years.     

Evaluation of three-dimensional effects in short deep beams using a rigid-body-spring-model

Three-dimensional (3-D) effects in short deep beams without stirrups that failed in shear were investigated experimentally and analytically. Two deep beams with a shear span to depth ratio (a/d) of 0.5 and with different beam widths were tested. The effect of beam width on load-carrying capacity, failure mode, crack pattern and 3-D behavior was investigated, and shape effect due to beam width was clarified. In addition, the beams were analyzed by the 3-D rigid-body-spring model (RBSM). RBSM is a discrete form of modeling that presents realistic behavior from cracking to failure, and 3-D RBSM is applicable to simulate 3-D behavior as well as the confinement effect of concrete. Analytical results in terms of load–displacement curves and crack pattern are compared with the experimental results. Three-dimensional deformations, strut widths and cross-sectional stress distribution are investigated analytically and compared with the experimental results to determine 3-D behavior in detail. The 3-D effects in short deep beams are clarified.     

冲击荷载作用下装配式钢筋混凝土梁力学性能研究

为了研究装配式钢筋混凝土梁（简称PC梁）的抗冲击力学性能,通过对5根PC梁和1根作为对比的现浇钢筋混凝土梁（简称RC梁）进行落锤冲击试验,研究了不同拼装位置和套筒灌浆料饱满度对PC梁的抗冲击性能影响。详细地分析了各个试件的破坏形态、冲击力、支座反力、跨中位移、整体变形耗能能力等性能。结果表明:1）冲击作用位置,拼装位置以及冲击荷载强度共同影响构件的破坏形态。随着冲击位置远离于构件拼装位置,PC梁破坏形态、接触刚度、整体抗冲击刚度等力学性能均接近于RC梁的力学性能,其抗冲击性能的设计可以参考RC梁进行设计;2）相同强度的冲击荷载作用下,预制试件拼装位置与冲击位置相同时,PC梁破坏形态表现为拼装处严重的局部破坏,刚度退化较大,整体变形耗能不如其他拼装位置的梁以及RC梁,考虑此工况的构件需采取合理的措施,提高其抗冲击能力;3）套筒灌浆饱满度对梁的抗冲击性能有影响较大,其决定PC梁的破坏形态以及刚度;4）拼装位置处交接面的边界条件是影响PC梁抗冲击性能数值分析是否准确的关键因素。     

Efficient laminated composite beam element subjected to variable axial force for coupled stability analysis

A numerically efficient laminated composite beam element subjected to a variable axial force is presented for a coupled stability analysis. The analytical technique is used to present the thin-walled laminated composite beam theory considering the transverse shear and the restrained warping-induced shear deformation based on an orthogonal Cartesian coordinate system. The elastic strain energy and the potential energy due to the variable axial force are introduced. The equilibrium equations are derived from the energy principle, and explicit expressions for the displacement parameters are presented using the power series expansions of displacement components. Finally, the member stiffness matrix is determined using the force–displacement relations. In order to verify accuracy and efficiency of the beam element developed in this study, numerical results are presented and compared with results from other researchers and the finite beam element results, and the detailed finite shell element analysis results using ABAQUS; especially, the influence of variable axial forces, the fiber orientation, and boundary conditions on the buckling behavior of the laminated composite beams is parametrically investigated.     

Evaluation of the in-plane effective elastic moduli of single-layered graphene sheet

In this paper, an equivalent continuum-structural mechanics approach is used to characterize the mechanical behaviour of nanostructured graphene. The in-plane elastic deformation of armchair graphene sheets is simulated by using finite element modelling. The model is based on the assumption that force interaction among carbon atoms can be modelled by load-carrying beams in a representative two-dimensional honeycomb lattice structure. The elastic properties of beam elements are determined by equating the energies of the molecular structure and the continuum beam model subjected to small strain deformation. Then an equivalent continuum technique is adopted to estimate effective elastic moduli from which elastic constants are extracted. A comparison of elastic constants obtained from current modelling concur with results reported in literature. With the multifunctional properties of graphene sheets as manifested in a broad range of industrial applications, determination of their elastic moduli will facilitate a better design of the corresponding materials at macroscopic level.     

Microstress estimate of stochastically heterogeneous structures by the functional perturbation method: A one dimensional example

A new functional perturbation method (FPM) for calculating the probabilistic response of stochastically heterogeneous, linear elastic structures is developed. The method is based on treating the governing differential operator as well as the unknown displacement function as a functional of material modulus field. By executing a functional perturbation around the homogeneous case, a set of successive differential equations is obtained and solved, from which the average and variance of any local parameter (displacements, stresses, strains) can be found. For a linear problem, the equations to be solved in each approximation order differ from the one for the homogeneous case by a pseudo external loading (right hand side) part only. Thus, only the Green function for the homogeneous case is needed for an analytical solution of the corresponding heterogeneous problem. A one dimensional stochastically heterogeneous rod embedded in a uniform shear resistant elastic medium is solved as an example. The statistical variance of displacements and stresses are found analytically, including the edge regions. Morphological (grain size) and material (modulus) effects on the stochastic response are demonstrated. The above results are essential for estimating the stochastic features of local stress concentrations, which are the source for many strength-related macro properties of materials. Extensive usage of generalized functions (Dirac operator and its derivatives) is needed for the analysis.     

双曲冷却塔结构特性新认识

通过动力特性分析和等效静风荷载作用下响应分析,并借鉴简单圆环结构和悬臂结构的结构特性,对双曲冷却塔结构特性进行了阐述。研究发现,作为圆截面高耸空间薄壁结构,双曲冷却塔的静动力结构特性同时体现了简单水平圆环结构和子午向悬臂结构的特点:对于低阶模态,其振型是上下弹性支撑水平圆环结构(条带)和左右弹性支撑子午向悬臂结构(条带)振型的耦合,且频率主要受环向刚度控制;风荷载作用下塔筒位移和内力的环向分布与外表面风压分布模式一致,各荷载效应的最值主要受迎风区和侧风区风压影响并受环向风压分布的不均匀性所控制;子午向轴力的环向分布提供了整体抗倾覆弯矩,因此表现出明显的向下积聚现象,这也是悬臂结构顺风向整体倾覆弯矩的体现,并且这种积聚效应与子午线型有关。     

变截面门式刚架结构的非线性性能

本文论述了变截面有限梁元几何非线性分析方法;研究了变截面刚架的几何非线性影响;通过非线性屈曲分析考察了屋面均布荷载对刚架柱稳定的影响;计算结果表明,刚架在屋面均布荷载作用下所产生的横梁轴力和弯曲变形对其侧向屈曲荷载的影响不能忽视。     

Determination of concrete fracture parameters based on two-parameter and size effect models using split-tension cubes

The notched beam specimens have been commonly used in concrete fracture. In this study, the splitting-cube specimens, which have some advantages - compactness and lightness - compared to the beams, were analyzed for the effective crack models: two-parameter model and size effect model. The linear elastic fracture mechanics formulas of the cube specimens namely the stress intensity factor, the crack mouth opening displacement, and the crack opening displacement profile were first determined for different load-distributed widths using the finite element method. Subsequently, four series of experimental studies on cubic, cylindrical, and beam specimens were performed. The statistical investigations indicated that the results of the split-cube tests look viable and very promising.