Axisymmetric loading on nanoscale multilayered media

Multilayered nanoscale structures are used in several applications. Because the effect of surface energy becomes nontrivial at such a small scale, a modified continuum theory is required to accurately predict their mechanical behaviors. A Gurtin–Murdoch continuum model of surface elasticity is implemented to establish a computational scheme for investigating an elastic multilayered system under axisymmetric loads with the incorporation of surface/interface energy. Each layer stiffness matrix is derived based on the general solutions of stresses and displacements obtained in the form of the Hankel integral transform. Numerical solutions to the global equation, which are formulated based on the continuity conditions of tractions and displacements across interfaces between layers, yield the displacements at each layer interface and on the top surface of the multilayered medium. The numerical solutions indicate that the elastic responses of multilayered structures are affected significantly by the surface material properties of both the top surface and interfaces, and that they become size dependent. In addition, the indentation problem of a multilayered nanoscale elastic medium under a rigid frictionless cylindrical punch is investigated to demonstrate the application of the proposed solution scheme.     

Soil–structure interaction effects on base-isolated buildings founded on soil stratum

The present study investigates the effects of soil–structure interaction (SSI) on the response of base-isolated multistory buildings founded on an elastic soil layer overlying rigid bedrock and subjected to a harmonic ground motion. Initially a four-degree-of-freedom system (4-DOF) is developed and the equations of motion are formulated in the frequency domain. Frequency independent expressions are used to determine the stiffness and damping coefficients for the rigid surface foundation on the soil-stratum underlined by bedrock at shallow depth. Assuming the foundation mass to be negligible, an equivalent two-degree-of-freedom (2-DOF) system is derived. The first mode of motion of the equivalent 2-DOF system appears to be sufficient to describe the response of the overall system for all ranges of stiffness and inertia properties of the structure and its isolation. An extensive parametric study demonstrates that SSI effects are significant, primarily for squat, light structures, founded on soil-stratum of low stiffness. The methodology could serve as a means to perform a preliminary seismic design of base-isolated building structures founded on homogenous soil-stratum over bedrock.     

偶应力对含充填层状岩体边界层效应的影响

 传统的连续介质理论本构关系没有考虑材料微结构的影响。岩石材料的微结构尺度一般在毫米量级以上,并且在高应变梯度情况下,层状岩体的弯曲变形非常显著。采用偶应力理论和有限单元法,对含充填层状岩体结构面边界层效应进行研究,并对经典理论和偶应力理论的结果进行对比。结果表明：考虑偶应力后,尺度效应明显。层状岩体结构面边界层内应力、应变的绝对值均有所减小;层状岩体结构面边界层内剪应变出现一个过渡区域,剪应变突变有所改善,但剪应力却不再连续。特征长度影响过渡区域大小,第二剪切模量、泊松比、弹性模量不改变过渡区域大小。     

Numerical simulation of crack propagation with equivalent cohesive zone method based on virtual internal bond theory

The virtual multi-dimensional internal bond (VMIB) model is developed within the framework of the virtual internal bond (VIB) theory. The VIB theory considers a solid as a three-dimensional network consisting of randomized material particles at the microscopic scale, which are bonded with VIBs possessing “normal stiffness”. In VMIB, however, the material particles are bonded with virtual normal bonds possessing both normal stiffness and shear stiffness. The macroscopic constitutive relationship is derived in terms of the normal and shear stiffness of the bonds. In this paper, we use the VMIB to simulate propagation of the pre-existing cracks with the equivalent cohesive zone (ECZ) method. To make the cracked body a seamless continuum, an ECZ is embedded into the pre-existing crack. The ECZ has the same microstructure as the surrounding material, but an initial internal deformation is assigned to it to ensure that the interaction between the two crack faces is negligible. Thereafter, the ECZ can behave as a pre-existing crack. For the ECZ possesses the same microstructure with the surrounding material, the ‘mended’ cracked body can be described with a uniform constitutive relation. The properties of the pre-existing cracks are implicitly incorporated into the constitutive relationship of VMIB. The advantages of this method are that: (i) the meshing process can be carried out regardless of the geometrical integrity of cracked material; (ii) remeshing is not necessary when crack propagates and (iii) the fracture criterion is embedded into the constitutive relationship. The example simulation shows that the method is efficient and feasible.     

考虑拉压模量不同的沥青路面力学计算方法与分析

现行沥青路面设计理论为传统的线弹性理论,设计时采用抗压回弹模量作为材料刚度参数,并未充分考虑道路材料拉压模量具有显著差异的特点。为此,文章将双模量理论(即拉压模量不同弹性理论)引入到路面力学分析中,基于迭代思想建立考虑材料拉压模量不同的沥青路面结构数值计算方法,且利用ABAQUS二次开发平台UMAT编制计算子程序,对典型沥青路面结构进行力学分析。结果表明：路面关键点位的力学响应,基于双模量理论与传统线弹性理论的计算结果之间的偏差高达30%～50%,应引起高度重视;沥青路面表面存在着较大的拉应力和拉应变,应为沥青路面破坏源之一,建议将沥青面层的设计点位从层底移至路表轮隙区;应用双模量理论对路面结构进行力学分析可有效地解决道路材料弹性模量的不唯一性问题。     

Elastic mimicry of elasto-plastic responses

A range of successively more elaborate elastic models is developed, with responses that in many ways mimic those of plastic specimens under load. The bilinear stiffness of a simple one degree-of-freedom elastic prop, which experiences a symmetric point of bifurcation, is first used to model the fundamental elasto-plastic response: the introduction of an imperfection corresponds to the Ramberg-Osgood approximation, rounding off the bilinearity. Upper and lower yield points are reproduced by a model termed the elastic hook, in which an elastic spring of the first model is itself replaced by an elastic prop with a bilinear stiffness. Finally, the normality relation of incremental plasticity theory is reproduced by two props at right-angles: responses are also traced for two hooking models in this configuration, for which no real comparison in plasticity theory seems to exist at present.     

隧道纵向剪切效应的简化弹性地基柱壳理论解析

基于弹性板理论，考虑板壳剪切变形的影响，将隧道作为弹性地基上的柱壳，采用弹性柱壳理论及简化三角函数表达的地基位移函数，经理论推导，提出将盾构管片隧道刚度离散为显式的环向剪切刚度及径向剪切刚度，并从理论上计算分析和探讨板壳弯曲刚度和剪切刚度对隧道横断面结构内力的影响，得出提高隧道切向剪切刚度能够改善纵向结构传力性能，减少横向弯曲变形等重要结论；提出在软弱地层中，隧道横向采用一定刚度的柔性设计，而隧道纵向则采用一定柔度的刚性设计的设计思想，这对于优化现行隧道纵、环向刚度设计具有指导意义，是隧道纵向剪切传递理论的一个重要补充。     

基于波场等效的节理面刚度参数取值研究

节理岩体中的节理面往往有一定厚度,如果采用无厚度的线性节理模型分析,其刚度参数的确定非常困难。通过分析弹性波穿过节理面时的波场效应,建立了基于节理后振动强度相等的波场等效法,用于确定带厚度节理的刚度参数,并分析了各因素对弹性波在节理上传播的影响。结果表明:线性节理面的刚度参数是节理岩体的固有属性,与外界荷载无关,采用波场等效法计算刚度参数可行;在弹性波范围内,这种等效参数与入射波频率、入射角等因素关系不大。该方法可用于有厚度节理面动强度参数的确定与分析,完善现有的节理面刚度取值方法。     

桩的刚度计算

现行桩的刚度计算大都假设桩为刚性。当桩较短时，由此带来误差不大，但当桩较长时则与实际情况相差较大。本文提出用分层荷载传递法计算单桩刚度，能方便地考虑桩的可压缩性、分层土的性质和桩截面的变化。本文讨论了桩的刚度随桩长、直径、桩身材料弹性模量的变化影响，并把计算值与实测值进行了比较。结果比较一致。     

Application of vector form intrinsic finite element on integrated simulation of wind turbine

Large wind turbine system is a periodic time‐varying system with many rigid‐flexible coupling bodies. It is difficult to deal with the singular stiffness matrix produced by the rotation of blades via the traditional finite element method. However, the vector form intrinsic finite element (VFIFE) method can effectively solve the geometric deformation of elastic continuum, the nonlinear or discrete constitutive model, the coupling motion continuum, and rigid body. In this study, a solver program of space beam element is developed by VFIFE method, and three typical examples are chosen to verify its accuracy. And then the integrated simulation of wind turbine system is established, and its dynamic response is analyzed. The natural frequencies of the turbine system, which are obtained by modal parameter identification, can agree well with the results obtained by traditional finite element method. The weighted amplitude wave superposition method and the proper orthogonal decomposition method as well as B‐spline surface interpolation are employed to obtain the wind time series of wind turbine under the normal operation condition. The wind‐induced dynamic response of wind turbine system is calculated by VFIFE method. The numerical results can reflect the periodic influence of gravity on the internal forces of blades and the interaction between blades and the tower.     

弹性支撑拱结构的动力特性研究

以三次B样条函数的线性组合作为拱结构位移振型函数,根据哈密顿原理推导出了弹性支撑拱结构的频率方程,考虑了拱脚处集中质量的附加惯性力等因素的影响,计算分析了竖向弹性支撑和旋转弹性支撑对拱结构动力特性的影响,提出了竖向临界刚度系数的概念。研究结果表明:竖向弹性支撑会使拱结构的基本频率减小,当矢跨比为0.1左右时影响最为显著,同时还会改变拱结构振型序列特点;竖向临界刚度系数是拱结构动力特性的分界点,此时拱结构的基本频率和第二频率几乎相等,若竖向支撑刚度系数小于临界刚度系数,结构的第1阶振型是对称的,而第2阶振型是反对称的,与刚性支撑拱结构的振型序列不同;若竖向支撑刚度系数大于临界刚度系数,结构的第1阶振型是反对称的,而第2阶振型是对称的,与刚性支撑拱结构的振型序列相同;旋转弹性支撑会使拱结构的基本频率减小,但并不改变其振型序列特点。     

曲杆单元铰接单层网壳弹塑性后屈曲分析

基于曲杆单元应力 弦长关系和矩阵微分理论,推导出曲杆单元在弹性与弹塑性状态下的切线刚度矩阵精确公式。研究构件取理想弹塑性材料,结构支座取固定铰支座和可动铰支座2种约束情况,考虑构件具有初弯曲,采用曲杆单元切线刚度矩阵和广义位移控制法,取结构自重为参考荷载,对节点铰接的K8大跨单层网壳结构进行弹塑性后屈曲分析。结果表明:曲杆单元切线刚度矩阵公式精确性很高,可有效用于大型铰接单层网壳弹塑性后屈曲分析。     

考虑土体真三维波动效应时桩的振动理论及对近似理论的校核

从三维轴对称土体模型出发,同时考虑土体径向和竖向位移,对完整端承桩在垂直谐和激振力作用下与土的耦合振动特性进行了分析。假定桩为竖直弹性等截面体,土为线性粘弹性体,其材料阻尼为滞回阻尼。首先通过引入势函数对土体位移进行分解,将土体动力平衡方程解耦并求解,得到土层的振动模态形式和阻抗因子;然后利用该解以小应变条件下桩土接触面上力平衡和位移连续条件来考虑桩土耦合作用,求解桩的动力平衡方程,得到桩的频域响应解析解,进而得到土层局部复刚度和桩顶复刚度。从土层阻抗因子、土层局部复刚度和桩顶复刚度3方面,将所得解与平面应变解和其他忽略土体径向位移的简化解在主要影响参数变化情况下进行比较,研究表明,不同解在硬土、细长桩并处于低频时有较大差别,随激振频率的提高,它们将趋于一致。     

单层网壳结构动力稳定性分析方法

本文系统分析了单层网壳结构动力稳定性的研究方法。论证了对于在复杂荷载作用下非线性、多自由度复杂结构的动力稳定性问题,基于严格数学定义的Lyapunov运动稳定性理论目前尚不能提供有效的判别准则。通过理论分析和计算指出“刚度矩阵的正定与负定”不足以判定结构是否动力失稳。提出了动力响应全过程曲线的概念,并以此曲线为基础结合结构的时程响应曲线来判定网壳结构的动力稳定性。通过对不同类型荷载、不同计算条件下的网壳结构的弹性和弹塑性动力稳定性的分析,验证了本文所提判别方法的合理性。     

小应变下土体刚度非线性分析的试验研究

精确的试验测试显示,土体在小应变下呈非线性作用,用常规的室内试验和传统的线弹性分析方法不能真实描述土的刚度变化,只能采用原位试验和非线性分析方法来确定。基于Bolton等人提出的平面应变下不排水膨胀试验的非线性分析理论,研究了剑桥自钻式旁压试验过程中土体刚度随应变的变化规律,并与线性分析结果进行了对比。试验和分析结果表明:小应变下土体刚度具有高度的非线性,随应变的增加发生衰减,但在不同应变区间衰减程度不同;土体割线模量值大于切线模量值,其差值随应变的增加逐渐减小;传统的线性分析低估了土体弹性作用范围和强度,而采用非线性分析能确定不同应变下土的刚度参数,真实反映土的非线性作用特点。     

Mixed methods and flexibility approaches for nonlinear frame analysis

The principle of virtual forces has long been an attractive tool for linear matrix structural analysis because it provides a means to compute the exact flexibility matrix for a linear, elastic, non-prismatic Bernoulli–Euler beam element while the classical stiffness method, based on the principle of virtual displacements, does not. Nonlinear flexibility methods have recently appeared in the literature as a means of improving the accuracy of frame analysis when the curvature fields are more complex than the moment fields (e.g., when inelastic response is important). This paper surveys the basic methods of formulating nonlinear Bernoulli–Euler beam elements based on classical and mixed variational principles. We show that the variational structure provided by the Hellinger–Reissner and Hu–Washizu functionals gives a framework that reaps the benefits of the so-called nonlinear flexibility methods while allowing a standard treatment of non-linear problems by Newton's method.     

非线性基础隔震结构复振型反应谱设计方法

采用铅芯橡胶支座、弹性滑板支座或摩擦摆支座的基础隔震结构,在利用反应谱方法进行设计时,需要考虑支座的非线性特征.在传统非线性振动分析平均方法或慢变振幅法中引入激励随机性,以等效线性系统和原非线性系统势能和阻尼耗能相等为原则,提出了基于能量平衡的随机等效线性化方法.在该方法中,等效刚度和等效阻尼系数表达为振动幅值的期望,...     

Analytical modeling of nonlinear behavior of composite stub-girders

This paper presents an inelastic analytical model for modeling the nonlinear behavior of partially composite stub-girder under midspan concentrated load with partially end joint stiffness. The method treats the stub-girder as a beam with three distinct layers, the top and bottom layers behave according to the normal beam bending theory, while the middle layer is a shear layer without any bending stiffness. At the interface between the steel and concrete elements, the headed stud shear connectors are modeled as linear elastic built-in cantilevers. The present method smears the effects of all the contributing shear elements, stubs and studs, along the span. The differential equation for the stub-girder is solved to obtain the general expression of elastic deflection for the case when one concentrated load is applied at the mid-span. Based on the present approach a computer program called “PZA” is developed. The program accounts for nonlinear behavior of concrete and steel materials. The accuracy and reliability of the program are demonstrated by the analysis of three stub girders and one composite beam over the entire loading range up to ultimate load and the results are compared with published experiments. A relatively good agreements with the experimental findings are found. Then a parametric study is carried out to discuss the effect of the initial stiffness of shear connector and the stub height on the behavior of stub-girder.     

可压缩桩刚度特征的分析

现行的桩刚度计算方法大多假设桩为刚性，而实际上桩都是可压缩的，尤其是长桩和柔性桩．压缩性非常明显。本文讨论了可压缩桩的刚度随桩长Ｌ、直径Ｄ，桩身材料弹性模量Ｅ和桩端阻力Ｒｕ的变化规律。文中给出了实测结果，证明了本文提出的桩的刚度变化规律的正确性。     

利用刚度矩阵法求解多层弹性半空间体的温度应力

从热弹性力学的基本方程出发,采用Hankel 积分变换和Laplace 积分变换等数学手段,首先推导出了单层弹性半空间轴对称体的温度应力问题的刚度矩阵,然后按传统有限元的方法组成总体刚度矩阵。通过求解由总体刚度矩阵所构成的代数方程组,再对其进行Hankel 和Laplace 积分逆变换就可解出在外荷载和温度联合作用下多层弹性半空间轴对称问题的解析解。由于刚度矩阵的元素中不含有正指数项,计算时不会出现溢出的现象,从而克服了传递矩阵法的缺点。在推导过程中,因不用事先人为的选择应力函数,使得问题的求解更加合理,同时也为进一步研究这类问题如湿度场、动力学等奠定了理论基础。最后,文中还给出了计算实例来证明推导结果的正确性。