A thin-sheet, combined tension and bending specimen

Validating stress intensity factor solutions for combined tension and bending is an arduous task because the necessary experimental data are not readily available. Toward this end, a tension and bending test specimen was designed to produce controllable levels of both tension stress and bending stress at the crack location. The specimen was made from 2024-T3 clad aluminum, which is commonly used in aircraft structures. The need for testing multiple specimens of various geometries and stress levels prompted the development of an analytical tool for specimen design. An extention of the Schijve line model, based on simple beam theory, was developed to calculate the stress distributions of tension and bending through the length of the specimen. A comparison of measured static strain levels with those predicted by the model showed the model to be accurate to within 5 percent, confirming its efficacy for specimen design. As expected, for the same remote stress (100 MPa), cracks in the tension and bending specimens grew faster than those in middle-cracked tension specimens.     

An asymptotic linear thin-walled rod model coupling twist and bending

A linear one-dimensional model for thin-walled rods with open strongly curved cross-section, obtained by asymptotic methods is presented. A dimensional analysis of the linear three-dimensional equilibrium equations yields dimensionless numbers that reflect the geometry of the structure and the level of applied forces. For a given force level, the order of magnitude of the displacements and the corresponding one-dimensional model are deduced by asymptotic expansions. In the case of low force levels, we obtain a one-dimensional model whose kinematics, traction, and twist equations correspond to the Vlassov ones. However, this model couples twist and bending effects in the bending equations, unlike the Vlassov model where the twist angle and the bending displacement are uncoupled     

Intense bending waves in a bar

Summary In this paper, the work presented in [1] is extended to study higher-order approximations of nonlinear effects in a bar. It has been found that long bending waves, being the low-frequency modes involved in resonant triads, are stable against small perturbations. Consequently, a bending wave with group velocity which is less than that of longitudinal waves should behave as a linear quasi-harmonic wavetrain. On the other hand, one may expect self-modulation instability of intense bending wavetrains during the long-time evolution. This paper overcomes such a contradiction. To describe the nonlinear dynamics in detail, one should allow for higher-order approximation effects in the model. Such effects are associated with the diffusion of linear wave packets due to different group velocities, and amplitude dispersion caused by nonlinearity. Within the second-order approximation analysis, an amplitude modulation is indeed experienced for intense bending waves. As a result, envelope solitons can be formed from unstable bending wavetrains. The group matching of long longitudinal and short bending waves, being a particular case of the self-modulation, is of special interest as a limit case of the triple-wave resonant interactions. It demonstrates the relation between the first- and the second-order approximation effects. Accepted for publication 20 July 1996     

Analysis of microbending tests for polycrystalline materials using the modified strain gradient theory

A modified strain gradient theory is proposed based on the nonhomogeneity of polycrystalline metallic materials and free surface effects. Consideration of the geometrically necessary dislocations on the grain boundary and the free surface effect suggests a relationship between the characteristic length, specimen size and grain size. This relationship can explain the size effects and flow stress in micro/nanoscale structures. We will propose a new model for bending tests using the modified strain gradient plasticity theory. Using the proposed model, bending behavior of polycrystalline materials in micron-scale structures is investigated, and compared with experimental results from other researchers.     

Buckling behavior of perfect and defective DWCNTs under axial, bending and torsional loadings via a structural mechanics approach

The buckling behavior of perfect and defective double-walled carbon nanotubes (DWCNTs) under axial compressive, torsional and bending loadings is investigated using a structural mechanics model. The effects of van der Waals (vdW) forces are further modeled using a nonlinear spring element. Critical buckling loads, critical buckling moments and the effects of vacancy defects were studied for armchair nanotubes with various aspect ratios. The results show that vacancy defects greatly reduce the critical buckling load of DWCNTs. The density of defects plays an important role in buckling of DWCNTs. The results of this numerical model are in good agreement with their comparable existing works.     

复合材料结构力学分析CAE软件现状

复合材料结构分析软件是用以分析、设计复合材料结构的重要工具,常用的复合材料结构分析软件包括基于CAD软件发展而来的复合材料分析工具、通用有限元软件自带复合材料分析工具和以Digimat等为代表的专业化复合材料结构分析软件。本文对常用的复合材料分析软件进行了综述,介绍其主要功能,从学术、应用等多方面探讨相关产品的优点及不足;论述了专业化复合材料结构分析软件的特点及功能;分析了复合材料结构分析软件的现状和发展趋势;探讨了复合材料结构力学分析CAE软件在国产化方面所需进一步解决的问题。     

隔水管弯曲对钻柱振动影响的计算与分析

海洋油气资源钻探中隔水管的弯曲对钻柱振动以及钻进特性有特别的影响。为得到隔水管弯曲对钻柱振动的影响规律,对南海已钻深水井使用非线性有限元软件建立全井钻井数值计算模型,研究获得了不同垂深时隔水管弯曲对钻柱振动特性的影响规律。研究表明:隔水管弯曲会加剧钻柱的振动,钻柱振动加剧会导致钻井能耗上升、钻头切削能力下降并且会加快钻柱疲劳;当隔水管的弯曲达到某临界值,钻柱与隔水管间的接触力会陡增;井口的钩载越大,隔水管弯曲带来的井口钩载波动量越大;井越深,隔水管弯曲对全井钻柱最大弯矩和钻头切削能力的影响越小。     

三维机织复合材料细观几何建模研究

论文提出一种简化的纱线变形方法建立三维机织复合材料细观几何模型，考虑了纱线截面形状、纱线截面扭转、纱线弯曲系数等模型参数，建立了模型参数可灵活调整的建模方法.采用该方法分析了纱线的层数、模型尺寸、纱线的弯曲系数对材料性能的影响.结果表明，当纱线层数较小时，表层的边界效应对材料性能影响较大，厚度方向不建议采用周期性边界条件；在自由边界条件下，模型长度约为2倍单胞、宽度约为1.5倍单胞尺寸时，可以实现刚度测试误差范围控制在2%以内.此外，纱线弯曲系数对复合材料单胞刚度计算结果有较大影响，适当的纱线弯曲系数能够使刚度计算误差控制在7%以内.     

三角形格构式塔身体型系数及屏蔽特性研究Study on shape coefficient and shielding effects of triangular latticed tower body

为满足高压／特高压输电铁塔风致倒塌问题对铁塔体型系数的精准度需求,研究了完全结构化多块网格对格构式三角形输电塔塔身流场的模拟能力,探讨了不同规范体型系数对某铁塔的适用性,并分析了塔身杆件复杂流动干扰作用下的屏蔽特性。结果表明,数值模拟与风洞试验的体型系数吻合很好;完全结构化网格能高保真、高度正交地对铁塔塔身这类复杂空间桁架流场进行离散;《英国杆塔荷载规范》的规定结果虽偏于保守,但其趋势最为接近真实值;在塔身桁架结构各个杆件之间流动干扰作用下,角钢弯折角朝向来流比背向来流的屏蔽作用更强;斜材弯折角背向气流和竖向辅助材弯折角朝向气流的组合之间的流动干扰,使得其对气流的屏蔽作用最强。     

Analysis,modelling, and optimization of laminated glasses as plane beam

A simply supported glass/polyvinyl butyral (PVB)/glass beam is modelled by plane finite elements. The distribution of strain and stress through the beam thickness and along its axis is obtained as a result of linear finite element analysis. It shows that the bending stress in the glass layers is determinant for the load-bearing capability of laminated glasses, but the shear in the PVB-interlayer plays an important role for glass-layer interaction. A mathematical model of triplex glass beam is derived, consisting of a bending curvature differential equation and a differential equation of PVB-interlayer shear interaction. The derived equations are solved analytically with boundary conditions of simply supported beam under uniform transverse load. A parametric study of the derived mathematical model is carried out. The model is utilized for lightweight structure optimization of layer thicknesses. The results of the optimization show that laminated glasses could be superior to monolithic glasses.     

A non-classical Kirchhoff plate model incorporating microstructure,surface energy and foundation effects

A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale parameter to account for the microstructure effect, three surface elastic constants to describe the surface energy effect, and two foundation moduli to represent the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the newly developed plate model includes the models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases and recovers the Bernoulli–Euler beam model incorporating the microstructure, surface energy and foundation effects. To illustrate the new model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate with or without the elastic foundation predicted by the current model is smaller than that predicted by the classical model. Also, it is observed that the difference in the deflection predicted by the new and classical plate models is very large when the plate thickness is sufficiently small, but it is diminishing with the increase of the plate thickness. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the elastic foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. These predicted trends of the size effect at the micron scale agree with those observed experimentally. In addition, it is shown both analytically and numerically that the presence of the elastic foundation reduces the plate deflection and increases the plate natural frequency, as expected.     

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Based on the nonlocal theory and Mindlin plate theory, the governing equations (i.e., a system of partial differential equations (PDEs) for bending problem) of magnetoelectroelastic (MEE) nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle. The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions (MPS) to solve the governing equations numerically. It is confirmed that for the present bending model, the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points. The effects of different boundary conditions, applied loads, and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method. Some important conclusions are drawn, which should be helpful for the design and applications of electromagnetic nanoplate structures.     

Linear viscoelastic model for bending and torsional modes in fluid membranes

This paper develops and applies a linear viscoelastic model for bending and torsional modes of fluid membranes, based on the nonlinear Cosserat surface fluid model. The linearized fluid membrane model in spherical and cylindrical geometries is shown to decouple bending and torsional viscoelastic modes. It is found that solutions of the membrane viscoelastic model to small-amplitude oscillatory bending and torsion allows for the measurement of the bending and the torsion viscosity. The model and its potential in characterizing the bending and torsion viscoelasticity of membranes complements the on-going efforts to establish the role of curvature in dissipative process of biological membranes.     

Koiter’s Shell Theory from the Perspective of Three-dimensional Nonlinear Elasticity

Koiter’s shell model is derived systematically from nonlinear elasticity theory, and shown to furnish the leading-order model for small thickness when the bending and stretching energies are of the same order of magnitude. An extension of Koiter’s model to finite midsurface strain emerges when stretching effects are dominant.     

Large deflection of a non-linear,elastic, asymmetric Ludwick cantilever beam subjected to horizontal force,vertical force and bending torque at the free end

The investigated cantilever beam is characterized by a constant rectangular cross-section and is subjected to a concentrated constant vertical load, to a concentrated constant horizontal load and to a concentrated constant bending torque at the free end. The same beam is made by an elastic non-linear asymmetric Ludwick type material with different behavior in tension and compression. Namely the constitutive law of the proposed material is characterized by two different elastic moduli and two different strain exponential coefficients. The aim of this study is to describe the deformation of the beam neutral surface and particularly the horizontal and vertical displacements of the free end cross-section. The analysis of large deflection is based on the Euler–Bernoulli bending beam theory, for which cross-sections, after the deformation, remain plain and perpendicular to the neutral surface; furthermore their shape and area do not change. On the stress viewpoint, the shear stress effect and the axial force effect are considered negligible in comparison with the bending effect. The mechanical model deduced from the identified hypotheses includes two kind of non-linearity: the first due to the material and the latter due to large deformations. The mathematical problem associated with the mechanical model, i.e. to compute the bending deformations, consists in solving a non-linear algebraic system and a non-liner second order ordinary differential equation. Thus a numerical algorithm is developed and some examples of specific results are shown in this paper.     

SIZE EFFECTS OF ELASTIC MODULUS OF FCC METALS BASED ON THE CAUCHY-BORN RULE AND NANOPLATE MODELS

In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the strain energy for the nano-sized plate under tension and bending, the relationship between the elastic modulus and the plate thickness is found. Size effects of the elastic modulus are displayed by the relative differences of the elastic modulus between the nano-sized plate sample and the bulk sample. By comparing the present results with those of others, the effectiveness of the Cauchy-Born rule model in studying the size effects of material properties are shown.     

考虑Steigmann-Ogden表面的微纳米圆柱解析模型

基于Steigmann-Ogden（S-O）表面理论,研究了圆柱形微纳米材料在轴向对压荷载作用下的力学性能。利用级数展开求解材料内部的弹性控制方程,获得了考虑表面效应时的域内解析表达式。当所得结果忽略表面弯曲参数时可退化为Gurtin-Murdoch（G-M）表面模型。用文献中有限元数值结果对本理论进行退化验证,结果得到良好一致性。在此基础上,讨论了表面弯曲参数和圆柱尺寸大小对材料特性的影响。结果显示：考虑了表面弯曲效应的S-O模型和G-M模型在应力分布中有很大的不同。另外,随着圆柱尺寸的减小,其表面效应对材料的力学特性的影响逐渐增大。     

Analysis of microbuckling for monomolecular layers adhering to a substrate

A two-dimensional linear spring model is established to study the microbuckling of a plane monomolecular layer adhering to a substrate. The model is for the layer subjected to a compressive load having an arbitrary angle with the chemical bond of the layer. The effects of the load angle, the strength of adhesion and the bending stiffness and shearing stiffness (the capability of resisting transverse bending and in-plane shearing) of the layer on the minimal buckling force and the critical buckling mode are discussed. It is found that the minimal buckling force increases with increasing load angle and, for a given bending stiffness, increases with increasing strength of adhesion and decreasing shearing stiffness. Furthermore, a critical condition under which the buckling of the layer can just occur is obtained, which is helpful to avoid buckling in an engineering application. The project supported by the National Distinguished Young Scientist Fund, Cheung Kong Scholars Programme, the National Natural Science Foundation of China (10272082, 10172068) and Shanghai Postdoctoral Science Foundation     

Liquid crystal model of vesicle deformation in alternating electric fields

Considering the effects of osmotic pressure, elastic bending, Maxwell pressure, surface tension, as well as flexo-electric and dielectric properties of phospholipid membrane, the shape equation for sphere vesicle in alternation (AC) electric field is derived based on the liquid crystal model by minimizing the free energy due to coupled mechanical and AC electrical fields. Besides the effect of elastic bending, the influence of osmotic pressure and surface tension on the frequency dependent behavior of vesicle membrane in AC electric field is also discussed. Our theoretical results for membrane deformation are consistent with corresponding experiments. The present model provides the possibility to further disclose the frequency-depended behavior of biological cells in the coupled AC electric and different mechanical fields.     

Peridynamic beams: A non-ordinary,state-based model

This paper develops a new peridynamic state based model to represent the bending of an Euler–Bernoulli beam. This model is non-ordinary and derived from the concept of a rotational spring between bonds. While multiple peridynamic material models capture the behavior of solid materials, this is the first 1D state based peridynamic model to resist bending. For sufficiently homogeneous and differentiable displacements, the model is shown to be equivalent to Eringen’s nonlocal elasticity. As the peridynamic horizon approaches 0, it reduces to the classical Euler–Bernoulli beam equations. Simple test cases demonstrate the model’s performance.