Solution of nonstationary problems in the mechanics of anisotropic bodies by the method of dynamic photoelasticity

The results obtained in developing and applying the method of dynamic photoelasticity to two-dimensional problems in the mechanics of anisotropic bodies are reviewed. The theory behind the method and its engineering implementation are described. The capabilities of the method are illustrated by solving specific nonstationary problems: dynamic stress concentration, diffraction of longitudinal and transverse waves by free and reinforced holes, dynamic fracture of orthotropic plates with holes and cracks under impulsive and explosive loads     

定向断裂控制爆破的空孔效应实验分析

采用新型数字激光动态焦散线实验系统, 对爆炸荷载作用下空孔周围的动应力场分布及空孔对爆生主裂纹扩展行为的影响进行了研究。研究结果表明, 在空孔周围强应力场的影响下, 2条相向扩展的爆生主裂纹逐渐向空孔处偏转, 并在空孔处贯通; 空孔附近的主应力方向与炮孔连心线夹角基本稳定在约12°, 增大空孔尺寸对空孔附近的主应力方向影响不明显; 爆炸应力波与空孔相互作用, 产生反射拉伸波, 改变了主裂纹尖端的应力场, 降低了主裂纹的扩展速度, 且空孔直径越大, 主裂纹的扩展速度越低; 当爆生主裂纹扩展到空孔附近时, 主裂纹尖端动态应力强度因子再次出现上升的趋势。     

Diffraction of stress waves by a free or reinforced hole in an orthotropic plate

Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves propagate __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 73–78, July 2007.     

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.     

含孔平板弹性波散射问题的复变函数方法

本文采用平板弯曲波动理论及复变函数方法，对平板开孔弹性波的散射及动应力集中问题进行了分析研究，得到了传播急剧记波时此种平板弯曲波动问题的分析解。若同时采用保角射技术，就为主解平板任意形状开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。作为算例，本文给出了平板开圆孔和椭圆孔附近的动应力集中系数的数值结果，并对其进行了讨论。     

Electromagnetoelastic problem for an infinite plate with known electrical potentials at hole boundaries

The plane electromagnetoelastic problem for an infinite plate with cracks and holes for known electrical potentials at the boundaries of the cracks and holes is solved using generalized complex potentials and conformal mapping, series, and least squares methods. The electromagnetoelastic state and variation of the stress intensity coefficient versus the geometric and physicomechanical properties of the material was studied for plates with two circular holes, a crack and a circular hole, or two cracks.     

Nonlinear dynamic response and fatigue damage evolution for piezoelectric laminated plates with matrix cracks

Based on the Talreja’s damage model with tensor valued internal state variables, considering the effects of piezoelectricity, geometrical nonlinearity and the constitutive relations of the composite uni-ply plate with matrix cracks, the nonlinear dynamic equations of piezoelectric laminated plates with damage are established and the problems are solved by using the finite difference method. In numerical calculating examples, the nonlinear dynamics responses and the fatigue damage evolution curves of the plates are obtained, and the effects of piezoelectric materials, damage and external load on the nonlinear dynamic response and fatigue damage evolution of the plates are discussed.     

集中力作用下含尖孔无限域的反平面剪切问题

论文采用了一种新的方法求解含孔元发域的反平面剪切问题，以闭合形式导出了在集中力作用下，孔口尖点的应力强度因子表达式。同时，给出了对称翼状尖孔、内摆线状尖孔、震状尖孔及圆孔径向边裂纹的应力强度因子，其结果在理论上和应用中都具有重要的意义。     

Spontaneous Mixed-Mode Fracture in Bonded Similar and Dissimilar Materials

In this paper, we report on an experimental study of spontaneous, mixed-mode, crack propagation in weakly bonded similar and dissimilar materials. A unique experimental configuration is proposed to induce spontaneous crack growth events along the interfaces. The cracks nucleate from tiny circular holes and are triggered by an exploding wire. They subsequently propagate under the action of a constant, far-field load. Dynamic photoelasticity in conjunction with high speed photography is used to capture the real-time isochromatics associated with crack propagation. In the case of identical materials, crack propagation is anti-symmetric with respect to the crack nucleation point while strong asymmetry is observed for the case of dissimilar materials. In both cases, cracks propagate at constant velocity from the initiation point. The time histories of dynamic stress intensity factors and of energy release rates of the propagating cracks along the bonded similar materials are also reported.     

含偏置裂纹三点弯曲梁的动态断裂行为研究

采用动态焦散线方法，对含偏置裂纹三点弯曲梁承受横向冲击的弯曲断裂行为进行了一系列动态断裂力学实验研究，分析了无量纲量ａ／ｌ的改变（ａ——初始裂纹偏离梁中心线的距离；ｌ——梁长度的一半）对于裂纹动态扩展行为（裂纹起始状态、裂纹尖端的复合应力强度因子、裂纹扩展速度、裂纹扩展轨迹）的影响，并借助动态光弹性应力分析，对应力波与扩展裂纹的相互作用以及应力波传播规律进行探讨．给出了裂纹尖端复合应力强度因子、裂纹扩展速度的变化、裂纹曲裂轨迹以及方向与梁中应力波传播的相互关系     

Reciprocal theorem method for the forced vibration of elastic thick rectangular plates

I.IntroductionTheproblelllsofthefol.cedvibrationofelasticthickrectallgularplatestobesolvedareofgreattheoreticalsignificanceandpractical\7altle.Asthevibratinggoverningequationofthethickplateismorecomplicatedthallthatofthinplate.itisdil'ficulttoso]\'einmathematics.Manyscholarshat,eresearchedintotheseproblemsalldadvancedvariousspecialapproximations.Suchassuperpositionmethod.initialfLinctiollnletllod.thecombinedseriesot'theeigenftlnctionsofdeepbeamabouttilecorrespondillgboulldarycollditions.eller…     

正交各向异性平板开孔弹性波的衍射与动应力集中

采用各向异性平板弯曲波动方程及摄动方法，对正交各向异性无限平板开孔弹性波的衍射及动应力集中的问题进行了分析研究，得到了在稳态波作用下此种忆边界条件波动问题的渐近形式分析解。同时采用复变函数方法及保角映射技术，为求解正交各向异性无限平板开孔弹性波的衍射及动力集中问题提供了一种统一规范的分析方法。     

孔结构金属复合夹芯板抗爆炸冲击响应及吸能特性研究

采用有限元方法研究爆炸载荷下四边固支孔结构金属复合夹芯板的动力响应及吸能特性，给出了孔结构金属复合夹芯板的动力响应过程，得到夹芯板的变形模式，比较了孔结构金属复合夹芯板与非孔结构金属复合夹芯板的抗爆炸冲击性能，同时讨论了孔大小、间距、排布方式和面板质量分布等因素对孔结构金属复合夹芯板抗爆炸冲击性能的影响。研究结果表明，迎爆面外面板的孔设计使爆炸冲击波穿过孔洞直接作用在芯材上，增强了芯材的压缩，从而提高了夹芯板的能量吸收能力。同等面密度情况下，内外面板厚度比大于1的孔结构金属复合夹芯板变形挠度小于内外面板厚度比小于1的孔结构金属复合夹芯板。进一步研究发现，通过合理设计内外面板的质量分布，可以使孔结构金属复合夹芯板的抗爆炸冲击性能最优。     

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

I. INTRODUCTION The composite material and the composite structure are liable to generate damage during manufactureand under load, which will lead to a decrease of the material and structure’s mechanical properties.It is accepted that there exist four…     

Asymptotic analysis of perforated plates and membranes. Part 2: Static and dynamic problems for large holes

Static and dynamic problems for the elastic plates and membranes periodically perforated by holes of different shapes are solved using the combination of the singular perturbation technique and the multi-scale asymptotic homogenization method. The problems of bending and vibration of perforated plates are considered. Using the asymptotic homogenization method the original boundary-value problems are reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. In the present paper the perforated plates with large holes are considered, and the singular perturbation method is used to solve the pertinent unit cell problems. Matching of limiting solutions for small and large holes using the two-point Padé approximants is also accomplished, and the analytical expressions for the effective stiffnesses of perforated plates with holes of arbitrary sizes are obtained.     

Response of composite plates to blast loading

The transient response of composite plates, with and without central circular holes, to blast loading is studied. The modal-analysis approach has been used in the computation of numerical results, which have been obtained for isotropic and orthotropic plates, with and without holes. In order to verify the theoretical results, experiments have been conducted on aluminum and unidirectionally reinforced E-glassepoxy plates, using a shock tube as the loading device. The experimental peak dynamic strains (normalized with respect to the pressure) are compared with the theoretical values. The strain-time history is also shown for a particular gage location in the composite plate. Finally, a comparison of dynamic-amplification factors, defined as the ratio of the peak dynamic strains to the static strains, has been made between the isotropic and the composite plates.     

横向爆炸载荷下开孔板的动应力集中因子

基于ANSYS 5.7/LS-DYNA程序,对3 m3 m0.25 m四边固支和简支、中心具有0.3 m0.3 m方孔的开孔板和无孔板对应点在两种下三角爆炸载荷作用下的应力响应进行了分析;由开孔板和无孔板边对应点的主应力时程曲线,对提出的能量密度时间分布函数的绝对值平方进行变上限积分,按其比值确定动应力集中因子,该方法简单易行。     

不同倾角预制裂纹缺陷与运动裂纹的相互作用

为了研究运动裂纹与不同倾角预制裂纹缺陷之间的作用机制,采用数字激光动态焦散线方法对含不同倾角预制裂纹缺陷的三点弯曲梁进行冲击实验。研究结果表明,在冲击载荷作用下,预制裂纹缺陷尖端均产生了次生裂纹;当运动主裂纹与预制裂纹缺陷贯通时,次生裂纹不会立即起裂,而是经过0~10 μs的能量积蓄后,次生裂纹才起裂;运动主裂纹应力强度因子峰值与次裂纹起裂时的应力强度因子值均随预制裂纹倾角的增大而增大。     

Strain and failure analysis of graphite/epoxy plates with cracks

The objective of this investigation was to study the deformation and failure of uniaxially loaded graphite/epoxy plates with cracks and to determine the influence of notch size on failure. The specimens were quasi-isotropic laminates with cracks of various lengths. They were instrumented with strain gages, photoelastic coatings and moiré grids. Strains near the crack tip show two distinct points of rate change at strain levels of 0.002 and 0.006, the latter corresponding to the ultimate strain of the 90-deg plies. Failure near the crack tip takes the form of a damage zone consisting of ply subcracking along fibers, local delamination and fiber breakage. Failure occurs when this damage zone reaches some critical value. Measured maximum strains at failure exceeded twice the ultimate strain of the unnotched laminate. The average stress over a characteristic distance (5 mm) from the crack tip was used as a criterion to describe the influence of crack length on failure. Comparison of results with those from similar specimens with circular holes showed that strength was nearly independent of notch geometry in this case, i.e., specimens with holes and cracks of the same size had nearly the same strength.     

Stability and fracture of plates with two edge cracks under tension

The paper presents experimental results on the deformation, local buckling, and fracture of D16AT plates with two parallel edge cracks under tension. The distribution of strains and deflections over typical cross-sections and buckling modes are determined. The influence of the crack length and the distance between the cracks on the local buckling stresses and breaking stresses is studied. The effect of local buckling on the strength of the plate is evaluated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 121–125, November 2006.