Numerical simulation of brittle fracture of thin-walled structures1

The model of brittle material, allowing for the determination of initiation and growth of cracks in thin-walled structures up to their destruction, is offered. Solutions of some problems are submitted: destruction of a plate at a homogeneous stress state; destruction of a beam at a pure bending; dynamic deformation and destruction of a plate with the concentrated mass having various initial speeds. Destruction of part of the material of the plate is shown to result in dynamic loss of stability of the solution.     

Laboratory-scale techniques for the measurement of a material response to an explosive blast

Laboratory-scale experiments were performed to measure the deformation of thin plates in response to varying explosive impulse. Experiments were conducted with a known explosive mass suspended in air at a known distance from an aluminum witness plate clamped in a “shock-hole” fixture. Through the use of well-characterized PETN and TATP explosive charges, the explosive impulse applied to each witness plate was determined a priori. The witness-plate response was measured using high-speed digital cameras to determine time-resolved, three-dimensional surface motion and maximum plate deformation. The results show that the maximum dynamic plate deformation is a straightforward function of applied explosive impulse, as determined from the explosive characterization. The experimental trend is the same despite the two different explosives used, highlighting that explosive impulse, determined through a blast characterization, is the controlling parameter in material blast response. A new experimental technique is used here to measure the dynamic blast response and the experimental errors are documented. Ultimately, applications of laboratory-scale explosive testing to computational code validation, material response scaling, and high-speed material property definition are discussed.     

热环境中功能梯度圆板的非线性动力响应分析

研究了热环境中功能梯度圆板在横向简谐激励作用下的非线性动力响应和动应力问题。针对陶瓷-金属功能梯度圆板, 考虑几何非线性、材料物理性质参数随温度变化及材料组分沿厚度方向按幂律分布的情况, 应用虚功原理给出了热载荷与横向简谐载荷共同作用下的非线性振动偏微分方程。在固支无滑动的边界条件下, 利用伽辽金法得到了达芬型非线性强迫振动方程。通过数值算例, 给出了关于体积分数指数的分岔图, 相图、Poincare映射等响应图以及动应力变化规律图, 讨论了材料体积分数指数和温度场对功能梯度圆板非线性动力响应的影响。结果表明: 热环境中功能梯度圆板随体积分数指数的变化可使系统出现周期响应、倍周期响应和混沌响应。功能梯度圆板中心处动应力在系统发生分岔或出现混沌响应时出现大幅变化, 而且在混沌响应时具有不可预测性。      

非线性弹性矩形板的自由振动精确解研究

板作为工程结构中的基本单元得到了人们的广泛研究,板在承受动力荷载作用下的动力响应问题受到了普遍关注.对非线性弹性矩形板的自由振动进行了研究,考虑了材料非线性和面内静载对板动力特性的影响,并根据半序空间的不动点理论求得该矩形板在自由振动时各阶模态的精确解,描绘了其自由振动的全过程.通过算例指出材料非线性和面内静载都对板的自由振动产生一定影响,在不同模态间可能出现"跳阶"现象.     

粘弹性层状地基上板的动力响应及其参数识别方法

本文系统地研究了粘弹性层状地基上板的动力响应及其结构材料参数识别方法。在一次样条半解析法求解粘弹性地基动力柔度系数[1]的基础上,应用子结构法求解了粘弹性层状地基上板的动力响应。应用快速富利叶变换将落锤式弯沉仪(FWD)所记录的荷载和时程反应曲线转化为频域内的一系列稳态振动[2],[3]。进而利用系统识别技术在频率域内反演结构材料参数。数值分析结果表明,该方法能有效地识别结构参数,从而为进一步研究FWD在混凝土道面的无损检测和承载力评价提供了基础。     

Sensitivity of Dynamic Response of a Simply Supported Functionally Graded Magneto-electro-elastic Plate to its Elastic Parameters

Dynamic response sensitivity of a simply supported functionally graded magneto-electro-elastic plates have been studied by combining analytical method with finite element method. The functionally graded material parameters are assumed to obey exponential law in the thickness direction. A series solution of double trigonometric function agreed with the simply supported boundary condition is adopted in the plane of the plate and finite element method is used across the thickness of the plate. The finite element model is established based on energy variational principle. The coupled electromagnetic dynamic characteristics of a simply supported functionally graded magneto- electro-elastic plate are decided by its dynamics differential equation into which displacement components, electric potential and magnetic potential as nodal degree of freedom are incorporated. Dynamic response sensitivity is defined as a partial differential of dynamic response with respect to material parameter. Sensitivity of dynamic response of a simply supported functionally graded magneto-electro-elastic plate to its elastic parameters has been studied. The influence of the different exponential factor on dynamic response sensitivity has also been investigated.     

DEM simulations and experiments for projectile impacting two-dimensional particle packings including dissimilar material layers

The dynamic response of a two-dimensional ordered particle packing composed of nylon-66 spheres 6.35 mm in diameter impacted by a spherical projectile was investigated both experimentally and numerically using the discrete element method (DEM). First, the influence of the number of layers in the particle packing on wave propagation and post-impact movement were examined. As the number of layers increased, the contact forces reaching the base plate decreased together with the rebound velocity of the projectiles. Next, the effects of dissimilar material layers were examined. The spheres in one or two layers of the particle packing were replaced with spheres made of dissimilar materials, that is, alumina ceramic (Al₂O₃) or steel, and it was found that the scattering of the nylon spheres above the dissimilar material layers increased. The experimental results obtained using force sensors at the base plate showed that the dissimilar material layers reduced the contact forces at the base plate. Furthermore, as the mass of the dissimilar material spheres increased, the magnitude of the contact forces at the base plate decreased, and the rebound velocity of the projectile increased.     

Fundamental thermo-elasticity equations for thermally induced flexural vibration problems for inhomogeneous plates and thermo-elastic dynamical responses to a sinusoidally varying surface temperature

Equations of motion governing thermally induced vibration of plates with inhomogeneous material properties through the thickness direction are presented. Equations of motion for thermally induced flexural vibration for inhomogeneous rectangular plates in which the material properties are given in the form of a power of the thickness coordinate are derived from the above-mentioned fundamental equations. An exact solution of the one-dimensional temperature change is presented for an inhomogeneous plate in which one surface is exposed to a sinusoidally varying temperature, and the other is kept at zero temperature change. The associated quasi-static and dynamic solutions pertinent to deflection and thermal stresses in the inhomogeneous rectangular plate are derived under the condition of simply supported edges. Numerical calculations are performed, and the effects of material inhomogeneity such as Young’s modulus, coefficient of linear thermal expansion, and mass density, angular frequency in cyclic heating, and aspect ratio on the thermo-elastic response of the rectangular plate are shown in graphical form. Comparing the dynamic solutions with quasi-static ones, the effect of inertia on the thermo-elastic response of the inhomogeneous rectangular plate is evaluated.     

Numerical analysis of dynamic buckling of rectangular plates subjected to intermediate-velocity impact

This paper numerically investigates the dynamic buckling of thin imperfect rectangular plates subjected to intermediate-velocity impact loads. From numerical results obtained, a dynamic buckling and a dynamic yielding critical condition are defined, and the corresponding critical dynamic loads are estimated. Numerical model employed in the present study is validated by experimental data reported earlier. Results from parametric study indicate that initial imperfection and load duration have significant influence on the dynamic buckling of the plates. The smaller the initial imperfection and the load duration, the higher the dynamic buckling critical loads of the plates. Moreover, different hardening ratios of plate material also affect the elastic–plastic dynamic buckling properties of the plates. If the plate buckles plastically, the dynamic buckling load increases as the hardening ratio of plate material increases. Unlike thin plates under high-velocity impact that buckling always occur after load application, plates under intermediate-velocity impact analyzed in the present study all buckle during the loading phase.     

Uncertainty quantification in non-linear dynamic response of functionally graded materials plate

This study deals with the stochastic non-linear dynamic response of functionally graded materials (FGMs) plate with uncertain system properties subjected to time-dependent uniformly distributed transverse load in thermal environments. System properties, such as material properties of each constituent's material, volume fraction index, and transverse load, are taken as uncorrelated random input variables. Material properties are assumed as temperature dependent (TD). The formulation is based on higher-order shear deformation theory (HSDT) with von-Karman non-linear strain kinematics using modified C° continuity. A Newton–Raphson-based non-linear finite element method along with a first-order perturbation technique (FOPT) and Monte Carlo sampling (MCS) is outlined to examine the second-order statistics (mean, standard deviation (SD), and probability density function (PDF)) of the non-linear dynamic response of the FGM plate. The governing dynamic equation is solved by Newmark's time integration scheme. The effects of volume fraction index, load parameters, plate thickness ratios, and temperature changes with random system properties are examined through parametric studies. The present outlined approach is validated with the results available in the literature and by MCS.     

Experimental investigation of the efficiency of dynamic damping of transverse oscillations of a plate

We present the results of experimental investigation of transverse oscillations of a plate with dynamic damper whose elastodamping element is made of a polymeric material. We determine the frequencies of free oscillations of the plate with dynamic damper, plot the amplitude-frequency characteristics of this system for various values of its parameters, and compare the results of experimental and theoretical investigations. Samarkand State University, Samarkand, Uzbekistan. Translated from Problemy Prochnosti, No. 4, pp. 153–159, July–August, 1997.     

热环境下混凝土矩形薄板在弹性地基上的振动

基于刚性板的小挠度理论，考虑混凝土的材料非线性，推导了双参数弹性地基上混凝土矩形薄板热弹性问题的动力方程。采用级数法，导出了热环境下双参数弹性地基上四边简支混凝土矩形薄板的固有频率计算公式和强迫振动下的挠度函数。为便于工程应用，给出了双参数弹性地基上四边简支混凝土矩形薄板在恒向变温和温度均匀变化时的固有频率和均布荷载作用下的挠度函数。针对Winlder弹性地基的情况，讨论了板的材料弹性常数、几何尺寸（长宽比）、相对厚度、刚度系数k和温度对薄板固有频率和挠度函数的影响，从而为工程结构中热环境下弹性地基上混凝土矩形薄板的振动计算提供了理论依据。     

Dynamic constitutive behavior of Ti/TiB FGM under thermo-mechanical loading

An experimental investigation is conducted to evaluate the thermo-mechanical constitutive behavior of a functionally graded material (FGM) under dynamic loading. Cylindrical specimens are machined from a titanium/titanium mono-boride (Ti/TiB)-layered FGM plate using electrical discharge machining (EDM). A Split Hopkinson Pressure Bar (SHPB) apparatus with infrared (IR) spot heaters is used to investigate the effect of temperature on mechanical response of the FGM material. A series of experiments are conducted at different temperatures and the stress–strain relation for different temperatures is obtained. The material showed high thermal softening at elevated temperatures resulting in a large reduction in compressive strength and an increase in failure strain.     

Analysis of the aluminum alloy resistance to the penetration of a steel rod at impact velocities of up to 500 m/s

The penetration of a steel rod into aluminum alloy plates of various thicknesses is examined. The resistance to penetration at its initial stages prior to the rod fracture is found to be determined by the dynamic strength of the plate material, its viscous component (proportional to the plastic strain rate) prevailing at impact velocities of up to 500 m/s. The depth of penetration varies with the velocity and is conditioned by wave processes in the plate, their scale being dependent on its thickness. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 106–110, September–October, 1998.     

阻尼压筋板的动态力学性能研究

本文对一种船用压筋板进行了粘弹性阻尼处理，通过有限元模拟计算了阻尼结构的模态参数，用试验模态分析的结果进行了验证，二者所得结果基本一致，并进一步用有限元分析预测了阻尼材料模量、处理厚度等变化对压筋板动态力学性能参数的影响，探讨了粘弹性阻尼材料抑制结构共振响应的有效性。     

一种新型短切碳纤维增强纸基摩擦材料研究

以短切碳纤维为增强纤维,采用湿法工艺研制成功一种新型无石棉纸基摩擦材料,采用TG-DTA热分析方法、定速摩擦试验和惯量摩擦研究了摩擦材料耐热性能、摩擦性能和磨损性能.试验结果表明,新研制的炭纤维增强纸基摩擦材料的起始分解温度和失重速率等耐热性能指标优良,动摩擦系数高达0.136～0.149,且摩擦系数稳定,磨损率低,是一种理想的新型无石棉纸基摩擦材料.     

A meshfree radial point interpolation method for analysis of functionally graded material (FGM) plates

A meshfree model is presented for the static and dynamic analyses of functionally graded material (FGM) plates based on the radial point interpolation method (PIM). In the present method, the mid-plane of an FGM plate is represented by a set of distributed nodes while the material properties in its thickness direction are computed analytically to take into account their continuous variations from one surface to another. Several examples are successfully analyzed for static deflections, natural frequencies and dynamic responses of FGM plates with different volume fraction exponents and boundary conditions. The convergence rate and accuracy are studied and compared with the finite element method (FEM). The effects of the constituent fraction exponent on static deflection as well as natural frequency are also investigated in detail using different FGM models. Based on the current material gradient, it is found that as the volume fraction exponent increases, the mechanical characteristics of the FGM plate approach those of the pure metal plate blended in the FGM.     

Nonlinear vibration and dynamic response of shear deformable laminated plates in hygrothermal environments

This paper deals with hygrothermal effects on the nonlinear vibration and dynamic response of shear deformable laminated plates. The temperature field considered is assumed to be a uniform distribution over the plate surface and through the plate thickness. The material properties of the composite are affected by the variation of temperature and moisture, and based on a micro-mechanical model. The formulations are based on higher-order shear deformation plate theory and general von Kármán-type equation of motion, which includes hygrothermal effects. The equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of shear deformable antisymmetric angle-ply and unsymmetric cross-ply laminated plates. The numerical illustrations concern the nonlinear vibration and dynamic response of the shear deformable laminated plates under different sets of hygrothermal environmental conditions. Effects of temperature rise, the degree of moisture concentration, and fiber volume fraction on natural frequencies, nonlinear to linear frequency ratios and dynamic responses are studied.     

树状分形结构夹芯板动态冲击特性研究

目的 探究一种新型树状分形结构夹芯板的动态冲击特性。方法 采用Ansys Workbench建立有限元模型,选用真空注型用聚氨酯(PU)弹性体材料制备1阶分形结构夹芯板试样进行动态冲击实验,验证模型可靠性;仿真分析该结构在不同分形阶数(n)下的动态冲击特性,并与常见中空型和三角型夹芯板对比。结果 模型平均误差约为7.25%;相同条件下,2阶TFS模型的比能量吸收(SEA)分别比0阶、1阶的提高了16.71%和0.23%。平均压溃力(FS)分别比0阶、1阶提高了27.76%和11.66%。与中空型夹芯板和三角型夹芯板对比,1阶分形夹芯板动态缓冲特性较优。结论 树状分形结构应用于缓冲包装中,可以表现出优良的吸能效率,为包装设计提供了一种新思路。     

Elastic transverse impact on an orthotropic plate

The impact of a solid projectile via an elastic buffer on an orthotropic elastic plate possessing a cylindrical anisotropy has been numerically simulated. The dynamical behavior of the plate is described in terms of the Uflyand-Mindlin wave equations taking into account the rotary inertia and the transverse shear deformations. The wave equations are solved using the ray method and the matching of asymptotic expansions obtained for short times inside and outside the contact zone. The influence of the anisotropy of the plate material on the dynamic contact force and the plate inflection at the impact site has been studied.