加捻纤维复合材料三维残余应力分析

本文提供一种对于含有加捻纤维束的复合材料由于固化而产生的热残余应力的分析研究.纤维束中的纤维经过加捻产生了一种螺旋形状,这种形状所产生的三维热弹性力学问题可以利用能量法获得解答.这个问题的热残余应力场可以表示为纤维、基体材料的性质以及纤维束几何参数的函数.纤维/基体界面上的残余应力(包括环向和径向的应力)都可以从这些分析中得到.本文分析的结果表明:加捻纤维束构成的复合材料,由于纤维的适当加捻,可以减弱由于纤维与基体各具不同的热膨胀系数而产生的热固化残余应力.     

不用Kirchhoff－Love假定的三维弹性板近似理论及其边界条件

经典弹性板理论采用了着名的克希霍夫(Kirchhoff)[1]-拉甫(Love)[2]的经典基本假定,在卡氏张量坐标x_i(ι=0,1,2)中,这些基本假定是:(1)略去横向即x₀轴向正应变,即假定e₍₀₀₎=0;(2)略去横向剪应变,即假定e_0α=0,其中α=1,2;(3)略去横向正应力,即假定σ₀₀=0.人们利用这些假定,建立了应变位移关系和应力位移关系,再利用应力平衡的三维方程,通过跨厚度的积分,找到弹性板中面上的各待定量所应满足的经典理论方程。前文[3,4,5],曾在不用克希霍夫-拉甫经典假定的弹性板三维理论中建立了一种近似理论,但并未证明这种近似理论的唯一性,也没有研究相应的近似边界条件。本文将用三维弹性体的广义变分原理[6]研究相同的问题。本文通过变分驻值条件,求得唯一的近似方程和相应的近似边界条件。本文详细研究了一级近似的平衡方程和近似边界条件。     

具周期洞的无限弹性平面第二基本问题

献[1]中讨论了一个周期单元只具一个洞的情况,本则类似[2]处理非周期的无限多连通域的方法,对一个周期带中有多个孔洞的第二基本问题进了讨论,建立了Fredhom方程。     

带弹性范围物质理论和背应力定义

在推广Lucchesi和Podio-Guidugli(1988)的带弹性范围物质理论的基础上,表明了背应力作为Cauchy应力空间中屈服面“中心”的定义存在问题.背应力是Lagrange型变量,只能定义在Lagrange型应力空间上.     

对称迭层矩形板的平面应力分析

常用的对称迭层板为各向异性板．根据平面应力问题的基本方程精确地用应力函数解法求得了各向异性板的一般解析解．推导出平面内应力和位移的一般公式,其中积分常数由边界条件来决定．一般解包括三角函数和双曲函数组成的解,它能满足4个边为任意边界条件的问题．还有代数多项式解,它能满足4个角的边界条件．因此一般解可用以求解任意边界条件下的平面应力问题．以4边承受均匀法向和切向载荷以及非均匀法向载荷的对称迭层方板为例,进行了计算和分析．     

基于曲梁弹性理论的弯曲覆岩变形及应力分析

引入适用于极坐标下曲梁的位移函数,通过理论分析得出用位移函数表示的曲梁控制方程和位移分量、应力分量.在此基础上,采用差分原理给出曲梁控制方程、位移分量和应力分量的差分代数方程.最后,采用数值计算方法,分析了煤层开采后弯曲覆岩的位移和应力分布特征,结果表明:1)煤层开采后弯曲覆岩产生下沉变形;弯曲岩层环向位移既有拉伸也有压缩.2)离开切眼不远处径向应力将达到峰值,径向应力由内边界向外逐渐增大;工作面后方不远处环向应力将达到峰值,环向应力较容易引起压缩破断;离开切眼不远处剪应力将达到峰值,对于小角度截面上的剪应力由内边界向外逐渐增大.研究结果为煤矿工程提供了科学依据与参考.     

热弹性理论准静态问题解的一般公式及其应用

本文利用分解定理［１］求得热弹性理论的准静态问题在无限空间中的Ｇｒｅｅｎ函数组．从而，借助于文［２］中的互易定理建立了该问题解的一般公式．     

不用Kirchhoff—Love假定的三维弹性板近似理论及其边界条件

红典弹性板理论采用了著名的克希霍夫（Ｋｉｒｃｈｈｏｆｆ）－拉甫（Ｌｏｖｅ）的经典基本假定，在卡氏张量坐标ｘｉ（ｉ＝０，１，２）中，这些基本假定是：（１）略去横向即Ｘ０轴向正应变，即假定ｅ００＝０；（２）略去横向剪应变，即假定ｅ０ａ＝０，其中ａ＝１，２；（３）略去横向正应力，即假定σ００＝０。人们利用这些假定，建立了应变位移关系和应力位移关系，再利用应力平衡的三维方程，通过跨厚度的积分，找到弹性板中     

汇率传递弹性动态变化特征的实证研究——基于状态空间模型的分析

将状态空间时变参数模型应用于汇率传递效应的研究,实证分析了2005M07~2012M06人民币名义有效汇率对通货膨胀传递弹性的动态时变特征.实证分析的结果表明:第一,汇率制度改革后人民币汇率传递弹性总体为正,这与通常认为的升值抑制通货膨胀的观点并不一致;第二,在样本时间段内,汇率传递弹性在0.72至0.73之间变动,汇率传递弹性随时间呈现出先下降后缓慢上升的"U"型趋势,说明外部经济通过汇率机制在一定程度上推高了国内物价水平.最后针对结论给出了相应的政策含义.     

有限长圆柱体轴对称问题的弹性理论解

本文利用H变换和Stockes变换.导出双变量函数及其编导数在闭区间上完整的双级数表达式,从而求得弹性力学中有限长圆柱体的轴对称问题的一般解析解.文中以轴向拉伸圆柱体为例,考虑不同的外力作用区域,分析了圆柱体上位移和应力的分布.本文所提的方法具有一般性.可以用来求解其它学科领域中有关柱坐标的轴对称边值问题.     

钢筋混凝土旧工业厂房结构加固方案优选

当前人们选择旧工业厂房结构加固方案效率低下,且所考虑的因素较为片面,为了全面、高效地解决这一问题,通过综合考虑安全性、经济性、时间性、可行性和适用性等因素,以加固效果显著的工程案例为标准,以全面的18个参数为评价指标,构建了一种基于蛛网面积相似和形状相似的结构加固方案优选模型。该模型中首先运用熵权法确定18个指标权重,并将参数值归一化处理,随后运用Python计算蛛网结构相似度,检索出与目标范例最为相似的源范例。最后以结构加固效果显著的工程为例,验证了该模型能有效减少主观误差,具有较强的实用性,并以此模型优选出了某轧钢厂房结构加固方案。     

基于尺寸效应的无腹筋钢筋混凝土梁的剪切强度公式

取无腹筋钢筋混凝土梁的临界斜裂缝及其顶端横截面所截隔离体为研究对象,根据极限平衡法,建立平衡方程组.分析临界剪压区主应力与梁斜截面破坏形式的关系,并对临界剪压区进行应力分析,再应用Ba(z)ant提出的尺度律,得到同时适用于斜拉破坏和剪压破坏的无腹筋钢筋混凝土梁的剪切强度公式,其中,临界剪压区高度是该公式的未知参数.通过对Ba(z)ant试验数据库进行Levenberg-Marguardt非线性最小二乘曲线拟合,得到临界剪压区高度与各参数的幂指数关系.最后经与Collins试验数据库比较可知,相对于ACI 318-08和GB 50010-2010对应的剪切强度公式,所得的剪切强度公式能更好地与试验数据吻合,且和Ba(z)ant的剪切强度公式计算结果接近.     

基于裂纹尖端二阶弹性解的断裂过程区尺度

基于Westergaard应力函数裂纹尖端二阶弹性解,推导了裂纹尖端微裂区的轮廓线和特征尺寸的解析表达式;采用幂函数模型描述的拉应变软化模型,确定了在最大拉应力强度理论和最大拉应变强度理论下断裂过程区（FPZ）临界值的解析表达式;将基于Westergaard应力函数一阶弹性解及二阶弹性解、Muskhelishvili应力函数和Duan-Nakagawa模型确定的FPZ临界值进行了比较．结果表明裂纹尖端微裂区和FPZ临界值随着Poisson比的减小而增加并逐渐趋近于应用最大拉应力强度理论确定的结果;二阶弹性解确定的裂纹尖端微裂区和FPZ临界值大于一阶弹性解的值;FPZ临界值随着拉应变软化指数的增加而增加;二阶弹性解确定的FPZ临界值的精度远高于一阶弹性解确定的值.     

Experimental Study on the Flexural Ductility of BFRP Bar Concrete Beams With Bamboo Fiber and Steel Wire Mesh北大核心CSCD

To study the effects of bamboo fiber and steel wire mesh on the flexural ductility of basalt fiber reinforced polymer（BFRP）bar concrete beams, 7 BFRP bar concrete beams with bamboo fiber and steel wire mesh were tested with different bamboo fiber lengths (0 mm, 30 mm and 45 mm) and different steel wire mesh layout ranges (0, 1/2 maximum bending moment point layout and full beam length layout). The flexural failure tests of the 7 beams were carried out, and the initial crack loads, the crack developments, the ultimate loads and the deformations were detected. The effects of the fiber length and the wire mesh layout range on the crack resistance and the deformation resistance of the specimens were analyzed based on the test data. With the function model, the equivalent yield points of the 7 test beams were obtained, and their ductility coefficients were calculated. The results show that, the addition of bamboo fiber and steel wire mesh increases the cracking loads of BFRP bar concrete beams by 12%~68%, decreases the crack spacings and the crack length development speed, reduces the test beam deformation under the same load, and increases the ductility coefficient by 1.58%~31.75%. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

钢筋混凝土筏基的挠度分析

本假设筏基为一搁量在三参数地基上的钢筋混凝土薄板，利用伽辽金法求解了受均布荷裁的四边固定的钢筋混凝土板，所得结果颇具广泛性，且清度较高。     

Tensile Characterization of FRP Rods for Reinforced Concrete Structures

The application of FRP rods as an internal or external reinforcement in new or damaged concrete structures is based on the development of design equations that take into account the mechanical properties of FRP material systems.The measurement of mechanical characteristics of FRP requires a special anchoring and protocol, since it is well known that these characteristics depend on the direction and content of fibers. In this study, an effective tensile test method is described for the mechanical characterization of FRP rods. Twelve types of glass and carbon FRP specimens with different sizes and surface characteristics were tested to validate the procedure proposed. In all, 79 tensile tests were performed, and the results obtained are discussed in this paper. Recommendations are given for specimen preparation and test setup in order to facilitate the further investigation and standardization of the FRP rods used in civil engineering.     

Elastic Deformation of Dispersely Failing Unidirectionally Reinforced Composites

A phenomenological model is proposed for describing the elastic deformation of a unidirectionally reinforced composite capable of accumulating scattered microdamages during its loading. The composite is considered as a homogeneous transversely isotropic solid. Its damaged state at every point is characterized by a centrally symmetric scalar function on the unit sphere (the damage function), which is used to account for variations in the elastic properties of the material during its deformation. The damage itself depends on the history of some equivalent strain, for which four simplified variants are suggested. The relation between strains and stresses is defined in a differential form. Dependences are presented for determining all unknown constants from simple mechanical experiments. As an example, an actual unidirectionally reinforced GFRP is considered, for which the main two-dimensional sections of corresponding failure surfaces are also constructed.     

Cracking Analysis of FRP-Reinforced Concrete Flexural Members

The paper is dedicated to the cracking analysis of FRP (Fiber-Reinforced Polymer)-reinforced concrete elements. A general nonlinear calculation procedure, based on the slip and bond stresses, is described and adopted for the prediction of the crack width and crack spacing in FRP-reinforced concrete beams. An analytical expression of the bond-slip law is estimated using the corresponding experimental results available in the literature. A numerical investigation is carried out and the influence of the mechanical and geometrical parameters of the material (bond-slip law, reinforcement ratio, concrete strength, diameter of rebars, etc.) on the crack formation is investigated. Referring to glass-FRP-reinforced concrete beams, a comparison between the theoretical predictions and experimental results is made. The results obtained are presented and discussed.     

Modeling of the Behavior of Concrete Tension Members Reinforced with FRP Rods

The paper is devoted to the analysis of cracking and deformability of concrete tension members reinforced with fiber-reinforced polymer (FRP) rods. A theoretical nonlinear model, derived from a cracking analysis founded on slip and bond stresses, is adopted for evaluating the crack width, crack spacing, and elongation of tension members. The procedure takes into account the local bond-slip law, experimentally determined by means of pullout tests, and allows us to evaluate the influence of tensile stiffening. The analysis is performed with considering all parameters influencing the behavior of tension members, such as the concrete strength, the kind of FRP rebars, the surface treatment of FRP rebars, and the concrete cover thickness. The theoretical predictions are compared with available experimental results, obtained on cylindrical concrete specimens reinforced with carbon FRP (CFRP) rods, and with predictions of the traditional models usually adopted for design purposes.