冲击下混凝土试样应变率效应和惯性效应探讨

结合混凝土试件的真三轴静载冲击实验结果,分别运用考虑应变率效应的Holmquist-Johnson-Cook (HJC)模型和考虑静水压效应的Drucker-Prager (DP)模型进行数值分析,以探讨研究混凝土试样应变率效应和惯性效应的方法。在探究混凝土的应变率效应和横向惯性效应的关系时,使用HJC模型的数值模拟结果来拟合DP准则的各个参数。结果表明:随着应变率的升高,混凝土的强度会提高,并且这种强度的提高,也有一部分原因是第一应力不变量I₁的增大所导致的。因此,混凝土试件的应变率效应和横向惯性约束具有较强的耦合作用。理论和数值分析了冲击下试样内部的横向应力分布特征与应变率、静水压和试样尺寸的关系,结果发现:试样内部横向应力的幅值随着应变率、静水压的升高而增大,但随着试样尺寸的增大而减小。为了探讨横向惯性带来的强度提升效果,提出了一个有关冲击方向最大应力σ_x和等效应力σ_e的参数ξ,且ξ=(σ_x?σ_e)/σ_x。此参数具有尺寸效应、应变率效应和静水压效应,但是此参数与应力三轴度的关系表现出应变率无关特性,可为应变率效应的研究提供新的思路。     

疲劳裂纹塑性闭合特性的数值分析方法

塑性诱导裂纹闭合是导致裂纹闭合发生的主要机理之一.利用弹塑性有限元法模拟含中心裂纹矩形板试件的疲劳裂纹扩展,并确定疲劳裂纹张开、闭合应力水平.通过计算,考察应力比R、裂纹长度、最大应力强度因子Kmax等对疲劳裂纹张开闭合应力的影响规律.论文阐述了所采用的裂纹扩展模拟方法及确定裂纹张开和闭合应力的原理.采用了等K加载方式,即在裂纹扩展中裂尖应力强度因子的最大值Kmax保持不变(给定R比,最大应力σmax随裂纹长度变化).分析了两种Kmax水平下R比分别为0.3,0,-0.5和-1.0共8种载荷工况.结果表明,对各个载荷工况,用瞬时最大应力σmax正则化的裂纹张开、闭合应力水平σop/σmax和σcl/σmax与裂纹长度无关.等K循环加载比等幅循环加载更有利于分析影响裂纹闭合水平的因素和闭合效应对疲劳裂纹扩展的影响规律,为建立基于裂纹闭合效应的疲劳裂纹扩展规律模型提供了一种新的思路.     

基于精化锯齿理论的功能梯度夹心微板静弯曲模型

基于精化锯齿理论和新修正偶应力理论,建立了能够准确预测功能梯度夹心微板挠度、位移和应力的静弯曲模型。为了描述微板不同方向上的尺度效应,将两个正交材料尺度参数引入本文模型。以受双向正弦载荷作用的简支板为例,探究了夹心微板弯曲行为中尺度效应对结构刚度的影响。算例结果表明,当微板几何参数与材料尺度参数接近时,基于本文模型所测微板的最大弯曲挠度、局部位移和应力均小于传统精化锯齿理论给出的结果,捕捉到了尺度效应;尺度效应随着微板几何尺寸的增大而逐渐减弱,当微板几何尺寸远大于材料尺度参数时,尺度效应消失。此外,板的跨厚比和功能梯度变化指数也会对尺度效应产生一定影响。     

考虑地基水平摩阻的Winkler地基上板模型解析

在Winkler地基模型基础上，采用板与地基之间的水平摩阻应力正比于板与地基接触点间水平位移假设，推演了包含板弯曲和轴向拉压效应的非线性地基板微分方程；应用摄动法分析竖向集中力作用下，板与地基水平摩阻应力对板内力（弯曲力、轴向力和剪应力）、位移（挠度、水平位移）的影响规律，实证了板与地基水平摩阻应力对板剪应力的非线性影响可以忽略不计，从而得到了轴对称条件下计入地基水平摩阻的Winkler地基上薄板的线性微分方程．随后通过汉克尔变换得到了轴对称无限大板的解析解，以及包含四项复宗量贝塞尔函数的轴对称圆形板的解析解，给出了板内力、位移的计算式；最后，通过算例分析了板与地基间水平摩阻状况对板挠度、截面弯矩的影响规律．结果表明：地基板挠度与弯矩随着板与地基间水平摩阻的增大而减少；当地基板水平摩阻参数大于0.01时，地基水平摩阻力对板挠度和弯矩影响有可能超过2%，应予考虑；无限大板作用圆形均布荷载时，水平摩阻的存在最大可使板最大挠度（即荷载圆中心点处挠度）下降约50%，板最大截面弯矩（即荷载圆中心点处弯矩）下降约70%.     

复合材料非均匀圆柱正交异性圆板弯曲

本文研究了圆柱正交异性复合材料圆板的弯曲,求得了折算刚度按半径线性变化的非均匀圆柱正交异性圆板在均布载荷作用下的通解;同时给出了周边固定和简支、以及具有线性过渡区(核)的圆板的精确解和算例,结果表明,当核径比λ=δ/R小于10％时,非均匀性对最大挠度的影响不超过0.289％。     

考虑Reissner效应的表面裂纹的非线性线弹簧模型

本文在非经典板的弯曲理论基础上,对应力-应变关系满足ε/ε_o=σ/σ_o α(σ/σ_o)~n的幂硬化材料的表面裂纹的弹塑性断裂分析,建立了非线性线弹簧模型,计算了表面裂纹的应力强度因子及其最大深度点的J积分值,研究了幂硬化指数n和系数α以及波桑比ν对J积分值的影响。     

双参数地基圆(环)形板的边界剪力及其力学响应

针对目前考量双参数地基上圆形或环形板边界剪力中存在的一些不足,应用Hankel变换法求得双参数地基的解析解,研究了任意环状线荷载作用下双参数地基的挠度、转角及地基反力间的关系。指出双参数地基在线荷载处的转角差与表示横向联系的地基参数之乘积等于线荷载集度;环内的分布荷载仅影响环内侧转角,而环外分布荷载也仅影响环外侧转角;进而又给出了适用于双参数地基圆形或环形板的内/外边界剪力的简明表达式。最后分别给出了双参数地基上自由边界圆形薄板中点承受集中力、圆形均布荷载作用时边界剪力对板中点挠度、弯矩的影响规律;双参数地基边界剪力对板挠度、弯矩有较明显影响,尤其是板的相对半径ρ_04或是荷载距板边界较近时这种影响更为明显。     

基于统一理论的改进的组合式L形钢管混凝土短柱轴压承载力计算

为了研究改进的组合式L形钢管混凝土短柱轴压承载力计算方法,结合改进的组合式L形钢管混凝土短柱轴压试验和有限元计算结果,分析了改进的组合式L形钢管混凝土短柱受力机理和轴压组合强度f_(sc)影响参数,在对比了已有的L形钢管混凝土短柱轴压承载力计算方法的基础上,采用钢管混凝土统一理论,提出了改进的组合式L形钢管混凝土短柱轴压承载力的计算公式。研究结果表明:约束效应系数ξ对试件名义压应力σ_(sc~-)平均压应变ε关系曲线影响较大,当ξ4.8时,曲线具有下降阶段,且ξ越小,下降趋势越明显;当ξ≥4.8时,曲线没有下降阶段,且ξ越大,强化段增长趋势越明显;钢管厚度对轴压组合强度f_(sc)影响最大,提高幅度约为84.82%(t由5mm→16mm),矩形钢管长宽比对轴压组合强度f_(sc)影响相对较小;所提轴压承载力计算公式具有更高的准确性和可靠性,总均值和总均方差分别为0.989和0.0432。     

拟弹性SMA对复合材料板抗低速冲击响应性能的影响

以形状记忆合金(SMA)纤维增强复合材料板为研究对象,根据SMA拟弹性曲线的特性,建立了一种SMA拟弹性应力-应变关系的分段线性化模型;在此基础上,采用分步能量平衡法,求解了SMA增强复合材料板受低速冲击时的横向位移和应力,分析了SMA的拟弹性特性对复合材料板低速冲击性能的影响.研究结果表明,SMA的能量吸收特性能有效地增强复合材料板抗低速冲击能力,板的最大位移和最大应力都明显减少.冲击速度为10m/s的情况下,板的最大挠度和应力降低了18%左右;冲击速度为25 m/s的情况下,板的最大挠度和应力降低了42%左右.     

由横向稀肋加固的斜锥壳的渐近解法

在文献[1]中作者得到了具有刚性加强端的斜锥壳的渐近解法.本文在此基础上进一步讨论横向稀肋加固的斜锥壳的渐近解法.所谓“稀肋”是指相邻两肋的简单边界效应相互影响在工程精度范围内可忽略不计的肋条,例如肋间距l≥3(rh)~(1/2)时(2h——薄壳厚度,r——两肋处壳体的最大平均半径).对于本文所讨论的常用的肋条横截面尺寸,分析结果表明,作为应力状态的第一次渐近解[误差为(h/λ)~(1/2)量级,λ——壳体中心面的特征曲率半径],肋对壳体薄膜应力状态没有影响.而在求解简单边界效应时,可将肋与壳的连接处看成弹性固支边界来处理,即认为此处的壳体转角γ_1为零,而周向应变ε_2等于肋的应变值。在分析过程中,讨论了肋截面形心偏心及形心主轴偏斜等因素对壳体应力状态的影响,证明了在第一次近似时它们可忽略不计. 为了验证所得结果的精确程度,在文献[1]的试件上,进一步作了具有稀肋加强的斜锥壳的电测试验.试验结果证实,本文所得的渐近解的误差基本上在(h/λ)~(1/2)及斜锥偏度m~2的量级范围内. 为了节省篇幅,本文不再给出斜锥壳各基本应力状态的内力及位移表达式,以及它们的待定函数的确定方法,需要时可参阅文献[1].     

Effect of indenter tip radius on the load deflection behavior of thin plates

The effect of indenter radius on the load-deflection behavior of a clamped, thin isotropic and homogeneous plate is discussed. A depth-sensing nanoindenter was used to apply a transverse load to the plate center and measure the corresponding plate center deflections. The applied stress is assumed to be uniformly distributed over the contact area. This study shows that the central deflection of the plate is insensitive to small changes of indenter tip radius when the normalized indenter tip radius is smaller than about 0.10 (here, normalized indenter tip radius is defined as the ratio of the indenter tip radius to the plate radius). For these small normalized indenter tip radii, the indenter radius effect is the same in both the small (linear) deflection range and in the large (nonlinear) deflection range. Blunt indenter tips help to minimize material nonlinearity in the region of contact due to localized plastic deformation and/or microcracks, allowing geometrically nonlinear deflection data to be obtained in a less ambiguous manner.     

Large deflections of prestressed simply supported rectangular plates under uniform pressure

The von Kármán large deflection equations for laterally loaded rectangular plates are extended to include uniform prestresses parallel to the edges and are solved for uniform load and for edges which are simply supported against movement normal to the plane of the plate and which are either held or free to move as a rigid body in the plane of the plate. Calculated values of center deflection and maximum stress parameters are given as functions of the load parameter for plates of various aspect ratios.     

非均匀圆柱型正交各向异性圆板的弯曲

研究了非均匀圆柱型正交各向异性圆板在均布横向载荷作用下的弯曲问题，求得了折算刚度随半径按指数规律变化的非均匀圆柱型正交各向异性圆板弯曲问题的渐近解，给出了周边固支和简支条件下的渐近解．通过算例可以看出，这种非均匀性对圆板中心挠度的影响是显著的     

含基体横向损伤的黏弹性板的蠕变后屈曲分析

基于Schapery三维黏弹性损伤本构关系，引入沈为和Kachanov损伤演化方程，建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型；应用von Karman板理论，导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散，时间上采用增量算法和Newton-Cotes积分法离散，控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响，且与已有文献的结果进行了比较. 数值结果表明：随着外载荷或者初始挠度的增大，板后屈曲趋于稳定时的挠度就愈大，损伤的影响愈明显；而随着长宽比的增大，板后屈曲趋于稳定时的挠度愈小，损伤的影响却随之增大.     

Imperfection sensitivity of ultimate buckling strength of elastic-plastic square plates under compression

The mechanism of imperfection sensitivity of elastic-plastic plates under compression is complex as they undergo elastic and/or plastic buckling, dependent on their width-thickness ratio. For elastic buckling, the Koiter power law is an established means to describe the imperfection sensitivity. Yet, for plastic buckling, there is no such an established way to describe it. In this paper, the quadratic power law is advanced to describe imperfection-insensitive plastic buckling behavior. The Koiter power law is extended by implementing the quadratic law so as to describe the elastic and plastic buckling in a synthetic manner. The finite-displacement, elastic-plastic analysis was conducted on simply-supported square plates under compression by varying the plate thickness and the initial deflection of a sinusoidal form. In association with an increase of the plate slenderness parameter (decrease of plate thickness), the predominant buckling is shown to change from (1) plastic buckling to (2) unstable elastic-plastic buckling and to (3) elastic stable bifurcation followed by a maximum point of load. In accordance with the change of the mechanism of buckling, the power law is changed pertinently to describe the complex imperfection sensitivity of the compression plates in a synthetic manner. The extended imperfection sensitivity law is thus advanced as a simple and strong tool to describe the ultimate buckling strength of elastic-plastic plates.     

Birefringent-coating analysis of laterally loaded perforated plates

The purpose of this investigation was to obtain experimental stress and deflection data for thick, circular, simply supported plates, containing circular transverse perforations in square motif, under uniform lateral loading. The stress-concentration factor and the deflection-multiplier factor, the ratio of the maximum principal stress and the maximum deflection of the perforated plate to that of the solid-plate specimen, respectively, were obtained for each perforated specimen. These factors can be conveniently used for the design of tube sheets, perforated heads, or other similar structural components.     

冷弯薄壁槽形截面钢柱的优化设计

求解冷弯开口薄壁截面短柱的极限承载力是一个板组结构的大挠度弹塑性分析问题，板件之间相互作用和纵向面内加载方式对其局部屈曲后性能和稳定极限承载力有很大的影响。本文应用大挠度弹塑性有限条分析方法系统地研究了冷弯薄壁槽形截面柱的极限承载能力和它们的优化性能，并对荷载偏心距为常数和位移梯度为常数的两种加载条件下的薄壁开口短柱局部屈曲后性能和极限承载力进行了对比分析和探讨。     

A new Kirchhoff plate model based on a modified couple stress theory

In this paper a new Kirchhoff plate model is developed for the static analysis of isotropic micro-plates with arbitrary shape based on a modified couple stress theory containing only one material length scale parameter which can capture the size effect. The proposed model is capable of handling plates with complex geometries and boundary conditions. From a detailed variational procedure the governing equilibrium equation of the micro-plate and the most general boundary conditions are derived, in terms of the deflection, using the principle of minimum potential energy. The resulting boundary value problem is of the fourth order (instead of existing gradient theories which is of the sixth order) and it is solved using the Method of Fundamental Solutions (MFS) which is a boundary-type meshless method. Several plates of various shapes, aspect and Poisson’s ratios are analyzed to illustrate the applicability of the developed micro-plate model and to reveal the differences between the current model and the classical plate model. Moreover, useful conclusions are drawn from the micron-scale response of this new Kirchhoff plate model.     

Unbonded contact between a circular plate and an elastic half-space

The paper concerns the unbonded contact between a thin circular plate of finite radius, governed by Kirchhof or Reissner theory, pressed by means of rotationally symmetric distributed load and its own weight against the surface of an elastic half-space. The contact is assumed frictionless and unbonded. A Hankel transform solution is used for the half-space and the plate deflection is found by inverting the plate equation. The coefficients in a power expansion are obtained by equating plate and half-space deflections at a number of points in the contact region. The variation of contact radius with plate radius, the radius of the uniformly applied load, and the relative stiffness of plate and foundation, is displayed in a series of figures.