平板裂纹前缘三维效应区的弹性力学分析

本文利用Kane和Mindlin关于弹性乎板面内问题位移的基本假设及Fourier变换求解了无限大板的I型裂纹问题,得到了裂纹尖端应力位移场的渐近形式、应力强度因子随板厚的变化规律以及板厚对裂纹前缘三维效应区的影响.研究表明,对线性硬化材料,在塑性切线胰量不太小的情况下,线弹性分析的结果可近似适用于弹塑性材料.     

V型缺口裂端的三维应力状态及约束分析

利用三维有限元方法，研究了有限厚度板中V型缺口根部穿透裂纹前沿的三维弹性应力场。对不同厚度、不同缺口张开角和裂纹长度对应力强度因子及裂尖附近的三维约束程度的影响进行了分析，同时还讨论了三维约束区的大小。研究结果显示：当缺口张开角小于60度时，不同缺口的应力强度因子和离面约束因子的分布基本一致，角度的影响不明显。应力强度因子是厚度的函数，板中面的应力强度因子随厚度的增加逐渐减小趋近干平面值，最大为1．08倍的平面值。当板厚超过15倍的缺口深度时，应力强度因子最大值将从中面转移至接近自由表面位置，距中面约0．4倍板厚。三维约束非常明显的区域在裂尖前沿约0.45倍厚度的范围内．二维到三维的过渡区在裂尖前沿1.5倍厚度的区域内；在中面上三维效应影响区最大，随着离中面距离的增加逐渐减小，在自由表面上降为0。     

钢方管截面柱考虑损伤的滞回性能分析

结构钢本构关系的精度直接影响分析结果的可靠度.根据能量等效性假设、热力学第二定律,推出损伤材料的弹性本构方程;采用混合强化准则,考虑Bauschinger效应、屈服平台、硬化(软化)效应及损伤和损伤演化影响,建立了的结构钢弹塑性各向异性损伤本构关系.结合构建的本构关系,采用八节点超参数壳体单元,推导了用U.L.格式及Cauchy应力描述的板壳双重非线性有限元方程,并编制了计算程序.利用U.L.格式的壳体大挠度双重非线性有限元分析方法,对钢方管截面短柱进行面内拉压循环荷载作用下的滞回性能分析.     

偏心裂纹板在裂纹面受一对集中拉应力作用时弹塑性解析解

利用裂纹线场方法对理想弹塑性材料偏心裂纹板在裂纹面受一对集中拉力问题进行了弹塑性分析,并且获得了理论解．这个解包括：裂纹线附近弹塑性边界上的单位法向矢量,裂纹线附近的弹塑性解析解、最大塑性区长度、裂纹线上的塑性区长度随荷载的变化规律及其承载力．该分析不受小范围屈服假设的限制,并且不附加假使条件．结果在裂纹线附近足够精确．     

功能梯度平板的二维热弹性分析

本文研究正交各向异性功能梯度平板的二维热弹性问题.该平板在y方向无限长,x方向对边简支且温度恒定.从热弹性力学的基本方程出发,假设材料参数沿板厚方向(z方向)按同一函数规律变化,基于状态空间法,在板的上下表面作用机械荷载和热荷 载的情况下,获得了功能梯度平板二维热弹性问题的Peano-Baker级数解.通过算例,验证了Peano-Baker级数解的正确性;同时也分析了材料参数沿板厚方向不同的幂函数分布对平板响应的影响.     

有限厚双边U型切口板的三维弹塑性有限元分析

针对单向拉伸载荷作用下的有限厚双边 U型切口板 ,本文对其切口根部的三维效应进行了详细的三维弹塑性大变形有限元分析 ,得到了不同于平面切口问题的新结果 :( 1 )在线弹性阶段 ,三维切口根部的应力集中因子 Kt高于二维情形 ,且 Kt在板厚 ( B)约为 8倍切口根部半径 (ρ)时达到峰值 ;进入塑性后 ,切口根部的 Kt随载荷水平的增加逐渐下降 ,并介于平面应力和平面应变情形之间 ;( 2 )切口前缘等效应变εe的最大值出现在约束最高的中面 ,且可比约束最低的自由表面处的应变值高一倍 ;( 3)薄板中 ,塑性区尺寸 xp 的最大值不是出现在约束较低的自由表面 ,而是出现在约束较高的中面 ,但随 B/ρ的增大逐渐向自由表面外推 ;( 4 )面内应力比 Tx在切口根部塑性区内的分布对板厚和载荷水平不敏感 ,可以用 Hill的滑移线解很好地近似。另外 ,对三维影响区内一些重要的三维约束参量进行了详细分析 ,总结了它们的三维分布规律。     

三维疲劳弹塑性弯曲裂纹塑性区研究

主要研究疲劳载荷作用下的三维弹塑性弯曲裂纹尖端的塑性区问题.用数值解法计算出三维弹塑性弯曲裂纹尖端交变塑性区于裂纹直线部分延长线上的投影长度的最大值和变化幅值,作图分析了三维弹塑性弯曲裂纹尖端交变塑性区尺寸的最大值和变化幅值与三维裂纹体几何尺寸之间的关系.三维弹塑性弯曲裂纹尖端交变塑性区的最大值和变化幅值随着三维裂纹体厚度的增大而减小,随着三维裂纹体厚度的均匀增大,三维弹塑性弯曲裂纹尖端塑性区的最大值和变化幅值不断减小,减小的幅度越来越小,最终趋于平面应变状态下的弹塑性弯曲裂纹尖端塑性区尺寸最大值和变化幅值.当三维裂纹体几何尺寸相同时,三维弯曲裂纹尖端塑性区的最大值和变化幅值随外载荷的不断增大而逐渐增大.建立了一个计算三维弹塑性弯曲裂纹交变塑性区的最大值和变化幅值的崭新理论模型.     

面内功能梯度矩形板的近似理论与解答

提出了面内功能梯度矩形板在竖向载荷作用下的近似 理论与解析解. 假设材料常数在面内x轴方向按指数规 律变化.引入了板理论的Reissner-Mindlin假设, 并考虑了板中面上的剪切变形的影响.推导了板在平行于y轴的两边简支, 平行于x轴方向的两边简支或固支情况下中性层法线转角和挠度用Fourier级数表示的解.讨论了退化为Kirchhoff假设下经典薄板理论的解的情况.提供了经典薄板理论在和Reissner-Mindlin假设下的算例并与三维有限元的计算结果进行了比较, 说明了该方法在厚板情况下也是相当精确的.     

复合材料断裂力学参量的实验测定

本文采用三维云纹干涉仪同步测量含裂纹复合材料弯曲板的面内位移场及离面位移场，并对离面位移场云纹图进行计算机自动采集和处理，编制了云纹数字图像处理软件。文中推导了正交异性复合材料弯曲问题的离面位移场表达式，得到了弯曲板裂纹尖端位移w与应力场强度因子K1的关系式。通过实测位移，结合裂尖位移场推导出应力强度因子K1值。     

功能梯度矩形板的近似理论与解析解

提出了压电功能梯度矩形板在竖向载荷作用下的近似理论与解析解. 引入了板理论的Kirchhoff假设、Reissner-Mindlin假设和提出的补充假设, 并假设材料常数在板厚方向按指数规律变化. 推导了板在周边简支同时又接地情况下中性层法线转角的解和用Fourier级数表示的电势解. 该解在形式上比精确解简单得多, 进行数值计算时也相当方便与快捷. 计算结果与ANSYS软件用三维实体单元的有限元计算结果进行了比较, 证实了该方法即使在厚板情况下仍然具有很高的精度.      

A novel singular finite element of mixed-mode crack problems with arbitrary crack tractions

A novel singular finite element is presented to study cracked plates with arbitrary traction acting on crack surfaces. Firstly, the analytical solution around crack tips is determined using the symplectic dual approach. Subsequently, the solution is used to develop a novel singular finite element, which depicts accurately the characteristic of singular stresses field near crack tips. And the novel element can be applied to solve cracked plates, and both Mode I and Mode II stress intensity factors can be determined directly and accurately. Lastly, two numerical examples are given to illustrate the present method.     

FRP加固金属裂纹板的断裂力学分析

传统的金属结构加固方法会形成新的疲劳源,而粘贴FRP加固则具有明显的优势．提出了“三维实体-弹簧-壳元”有限元模型,金属板采用三维实体单元, FRP采用壳单元,用弹簧单元来模拟FRP与金属板之间的胶层,对金属裂纹板粘贴FRP加固后的性能进行了线弹性断裂力学分析,并对影响金属板裂纹前缘应力强度因子的参数进行了讨论．分析结果表明,采用高弹性模量的FRP和增加FRP的厚度对改善加固效果非常明显．     

The effect of load biaxiality on crack growth in non-linear materials

The influence of load biaxiality on the stress field and fracture behavior of a cracked plate is investigated. Considered is a square plate containing a central through the thickness crack and subjected to a biaxial loading perpendicular and parallel to the crack plane. The stress field of the plate is analyzed by a finite element code based on incremental plasticity and the von Mises yield condition. A method based on the strain energy density theory is used to determine the critical stress for crack initiation. It was found that the equi-biaxial loading mode induces the smallest plastic zones, while the critical applied stress for crack initiation becomes maximum. Quite the contrary happens for the shear loading system which causes the largest plastic zones and the minimum applied stress values fro crack growth. Results showing the dependence of the above quantities on the biaxiality of the applied stress are presented in graphical form.     

裂缝分析的比例边界有限元与有限元耦合的虚拟结构面模型

比例边界有限元法SBFEM(Scaled Boundary Finite Element Method)是一种半解析数值方法,在裂缝分析特别是强度因子计算上具有相当高的精度。本文提出了一种用于裂缝分析的基于虚拟结构面的SBFEM与常规FEM的耦合分析方法。首先选取裂缝周边一定范围的计算域,并将结构分成不含裂缝区域和含裂缝区域两部分。然后,对不含裂缝区域,采用FEM进行网格离散;对含裂缝区域,采用SBFEM进行网格离散;两者相互独立,在这两个域内,分别采用各自相应的位移模式。最后通过在SBFEM网格的外边界设置虚拟耦合结构面的模式,实现有限元网格和比例边界有限元网格的耦合。通过两个经典的含裂缝平板的算例研究,探讨了本文方法在I型开裂和混合型开裂分析中,影响应力强度因子精度的因素。算例表明,SBFEM具有的降维和半解析性质,使本文方法在裂缝分析中的前处理简单易行,且计算结果具有相当高的计算精度。     

A crack bridging model for bonded plates subjected to tension and bending

A crack bridging model is presented for analysing the tensile stretching and bending of a cracked plate with a patch bonded on one side, accounting for the effect of out-of-plane bending induced by load-path eccentricity inherent to one-sided repairs. The model is formulated using both Kirchhoff–Poisson plate bending theory and Reissners shear deformation theory, within the frameworks of geometrically linear and nonlinear elasticity. The bonded patch is represented as distributed springs bridging the crack faces. The springs have both tension and bending resistances ; their stiffness constants are determined from a one-dimensional analysis for a single strap joint, representative of the load transfer from the cracked plate to the bonded patch. The resulting coupled integral equations are solved using a Galerkin method, and the results are compared with three-dimensional finite element solutions. It is found that the formulation based on Reissners plate theory provides better agreement with finite element results than the classical plate theory.     

Experimental and numerical investigation of a cracked transversely graded plate subjected to in plane bending

The variation of stress intensity factor along the thickness in a cracked transversely graded plate subjected to in plane bending is investigated in this study. A transversely graded plate having elastic modulus varying continuously along the thickness was prepared by embedding glass beads in epoxy resin. An edge crack in this plate was subjected to in plane bending and the crack tip displacement field on the surfaces of the plate was measured using digital image correlation (DIC). Using the recently reported asymptotic displacement fields for cracked transversely graded plates (Wadgaonkar, S.C., Parameswaran, V., 2009. Structure of near tip stress field and variation of stress intensity factor for a crack in a transversely graded material, Journal of Applied Mechanics 76 (1), 011014), the stress intensity factor (SIF) on the surfaces of the plate was calculated from the experimental data. The results of this part of the study indicated that the extent of variation of the SIF across the plate thickness is nearly the same as that of the elastic modulus. An expression to calculate the variation of the SIF through the plate thickness was developed assuming simple bending of the plate. The predicted variation of SIF was verified through finite element calculations. Further, the behavior of the SIF near the intersection of the crack front and the plate surfaces, the extent of dominance of the corner singular field and the exponent of the corner singularity were also investigated in detail. Finally, the effect of gradation strength and gradation type on the SIF was also studied.     

Elastic-plastic analytical solutions for an eccentric crack loaded by two pairs of anti-plane point forces

IntroductionTheelastic_plasticanalysisforacrackedplatewithfinitedimensionsisoneofthemostdifficultfieldsofelastic_plasticmechanics .Thenearcracklineanalysismethod ,whichwasfirstproposedbyAchenbachetal.[1,2 ] ,hasbeenimprovedbyYiinRefs.[3,4 ].InRefs.[3,4 ],…     

Numerical modeling of PZT-induced Lamb wave-based crack detection in plate-like structures

This paper presents the numerical modeling and simulations of PZT-induced Lamb wave propagation in plate-like structures by using the spectral finite element method. A novel spectral plate finite element, which can efficiently model the three-dimensional (3D) behavior of Lamb waves, is proposed. In the formulation, linear displacement distributions in the thickness direction are assumed for both the PZT layer and the base plate. A way to avoid the thickness locking is proposed and used in the formulations. Two examples, one for the validation of the proposed two-dimensional (2D) spectral finite element and the other for the demonstration of crack detection in plates, are presented and discussed. The contact between the two faces of crack is considered. Numerical results show that (1) only the anti-symmetric mode is prone to thickness locking thus remedy should be made only on this part, (2) the proposed 2D spectral finite element can adequately model the Lamb wave propagation in plate-like structures and the complex scattering for the crack, and (3) crack location can be well determined by a PZT-induced Lamb wave-based diagnosis algorithm.