Nonlinear stability of timber column strengthened with fiber reinforced polymer

By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer (FRP) sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.     

Nonlinear stability of timber column strengthened with fiber reinforced polymer

By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer (FRP) sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.     

纤维增强聚合物布加固裂纹木梁的稳定性

梁中横向裂纹等效为无质量内部转动弹簧，假定纤维增强聚合物(FRP)布与梁表面紧密粘贴，建立了考虑轴向压力二阶效应FRP 布加固裂纹梁线性弯曲的控制方程，并得到其显式解析通解．在此基础上，研究了FRP加固简支裂纹木梁的稳定性，通过数值求解方程，分析了纤维增强聚合物(CFRP)布含量、裂纹深度和位置以及数量等因素对CFRP 布加固简支裂纹杉木梁临界载荷的影响，结果表明：CFRP 加固可明显减小裂纹深度和数量等对裂纹杉木梁临界载荷的影响，且裂纹处弯矩较大或裂纹较深时加固效应愈加显著；CFRP 加固裂纹木梁临界载荷随CFRP 布加固层含量的增加而增加，但当CFRP 布含量达到一定值后，进一步增加CFRP 含量对CFRP加固裂纹梁临界载荷提高并不明显．     

考虑轴力二阶效应的损伤梁弯曲摄动解

将损伤梁等效为阶梯型变刚度Euler-Bernoulli梁,利用Heaviside广义函数,给出了阶梯型变刚度梁抗弯刚度的统一表达式．在此基础上,考虑轴向压力二阶效应,并以损伤为摄动参数,得到了均布横向载荷作用下,简支损伤梁弯曲挠度的一阶和二阶摄动解析解,并数值分析了摄动解析解的精度和损伤梁的弯曲变形特性,结果表明：随着轴向压力和刚度损伤参数的增加,挠度一阶和二阶摄动解析解误差增加,挠度二阶摄动解析解误差通常小于其一阶摄动解析解误差,且二阶摄动解的误差很小,满足工程应用的精度．同时,损伤梁的挠度和转角分布与完整梁的挠度和转角分布差异较大,在刚度变化位置处损伤梁转角斜率存在突变．这些结果可为轴力作用下Euler-Bernoulli梁损伤识别提供理论支撑．     

用“膜力因子法”分析简支刚塑性圆板的大挠度动力响应

在板的变形过程中,当其挠度与厚度同量级时,膜力的作用与弯矩的作用同样重要;当其挠度超过厚度甚至接近板的面内尺寸的量级时,相对于弯矩的作用,膜力的作用是更主要的。本文发展了一种基于能量平衡的简便的“膜力因子法”,有效地解决了当板的挠度达到厚度量级时弯矩和膜力联合作用问题;用这种方法并结合塑性膜阶段的分析成功地求解了简支刚塑性圆板在冲击载荷作用下的大挠度塑性响应问题。所得结果与Florence实验结果符合良好,比已有理论近似结果有所改进。     

Analysis of the large deflection dynamic plastic response of simply-supported circular plates by the “membrane factor method

Based on energy equilibrium, a new procedure called the Membrane Factor Method is developed to analyze the dynamic plastic response of plates with deflections in the range where both bending moments and membrane forces are important. The final deflection of a simply-supported circular rigid-plastic plate loaded by a uniformly distributed impulse is obtained. In comparison with other approximate solutions, the present results are found to be simpler and in better agreement with the corresponding experimental values reoorded by Florence. The project supported by a fund from the National Educational Committee.     

基于裂纹诱导弦挠度的简支外伸梁裂纹损伤识别

基于梁横向开裂纹的线性扭转弹簧模型,给出了具有任意裂纹数目的简支外伸梁弯曲挠度的显式解析解,研究了集中载荷作用下简支外伸梁裂纹诱导弦挠度函数的性质,给出了裂纹位置和裂纹等效扭转弹簧柔度的近似表达式,从而实现了梁横向裂纹位置及裂纹损伤程度的识别．在此基础上,为利用裂纹梁的测量挠度识别裂纹损伤,提出了分段线性函数的最佳拟合法,实现了简支外伸梁裂纹的损伤参数识别．通过数值试验验证了该识别方法的适用性和可靠性,考察了识别结果对梁挠度测量误差和裂纹深度的敏感性,结果表明随着挠度测量误差的增大,裂纹损伤参数识别误差增大,但裂纹损伤识别方法具有较强的鲁棒性,在工程实际中具有一定的应用性．     

不可压饱和多孔Timoshenko梁动力响应的数学模型

基于饱和多孔介质理论,假定孔隙流体仅沿梁的轴向运动,本文建立了横观各向同性饱和多孔弹性Timoshenko梁动力响应的一维数学模型,通过不同的简化,该模型可分别退化为饱和多孔梁的Euler-Bernoulli模型、Rayleigh模型和Shear模型等。研究了两端可渗透Timoshenko简支梁自由振动的固有频率、衰减率和阶梯载荷作用下的动力响应特征,给出了梁弯曲时挠度、弯矩以及孔隙流体压力等效力偶等随时间的响应曲线,并与饱和多孔Euler-Bernoulli简支梁响应进行了比较,考察了固相与流相相互作用系数、梁长细比等的影响。可见,固相骨架与孔隙流体的相互作用具有粘性效应,随着作用系数的增加,梁挠度振动幅值衰减加快,并最终趋于静态响应,Euler-Bernoulli梁的挠度幅值和振动周期小于Timoshenko梁的挠度幅值和周期,而Euler-Bernoulli梁的弯矩极限值等于Timoshenko梁的弯矩极限值。     

Nonlinear behavior of composite sandwich beams in three-point bending

The load-deflection behavior of a composite sandwich beam in three-point bending was investigated. The beam was made of unidirectional carbon/epoxy facings and a polyvinyl chloride closed-cell foam core. The load-deflection curves were plotted up to the point of failure initiation. They consist of an initial linear part followed by a nonlinear portion. A nonlinear mechanics of materials analysis that accounts for the combined effect of the nonlinear behavior of the facings and core materials (material nonlinearity) and the large deflections of the beam (geometric nonlinearity) was developed. The theoretical predictions were in good agreement with the experimental results. It was found that the effect of material nonlinearity on the deflection of the beam is more pronounced for shear-dominated core failures in the case of short span lengths. It is due to the nonlinear shear stress-strain behavior of the core. For long span lengths, the observed nonlinearity is small and is attributed to the combined effect of the facings nonlinear stress-strain behavior and the large deflections of the beam.     

基于等效弹簧模型的裂纹Euler-Bernoulli梁弯曲变形分析

考虑裂纹的缝隙效应,研究了开闭裂纹Euler-Bernoulli梁的弯曲变形．首先,将裂纹等效为内部旋转弹簧,利用广义函数,给出了考虑裂纹缝隙影响的Euler-Bernoulli梁的等效抗弯刚度,推导了具有任意数目开闭裂纹梁弯曲变形的显式通解．在此基础上,研究了均布载荷作用下上侧单裂纹简支梁以及裂纹处承受集中力和集中力偶共同作用的固支梁的弯曲变形,分析了梁长细比、裂纹深度和位置以及载荷等对裂纹开闭状态和梁弯曲变形的影响。结果表明：梁挠度分布在裂纹处存在尖点,而转角分布存在跳跃;梁挠度与载荷的响应关系一般为双折线形式,分别对应于裂纹的张开和闭合状态;且裂纹张开时,裂纹梁的柔度随着梁长细比的增加和裂纹深度的减小而减小。这些结果对梁裂纹无损检测具有指导意义．