Bounds for the effective properties of heterogeneous plates

This paper presents new bounds for heterogeneous plates which are similar to the well-known Hashin–Shtrikman bounds, but take into account plate boundary conditions. The Hashin–Shtrikman variational principle is used with a self-adjoint Green-operator with traction-free boundary conditions proposed by the authors. This variational formulation enables to derive lower and upper bounds for the effective in-plane and out-of-plane elastic properties of the plate. Two applications of the general theory are considered: first, in-plane invariant polarization fields are used to recover the “first-order” bounds proposed by Kolpakov [Kolpakov, A.G., 1999. Variational principles for stiffnesses of a non-homogeneous plate. J. Meth. Phys. Solids 47, 2075–2092] for general heterogeneous plates; next, “second-order bounds” for n-phase plates whose constituents are statistically homogeneous in the in-plane directions are obtained. The results related to a two-phase material made of elastic isotropic materials are shown. The “second-order” bounds for the plate elastic properties are compared with the plate properties of homogeneous plates made of materials having an elasticity tensor computed from “second-order” Hashin–Shtrikman bounds in an infinite domain.     

Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach

This paper presents an analytical investigation on the buckling analysis of symmetric sandwich plates with functionally graded material (FGM) face sheets resting on an elastic foundation based on the first-order shear deformation plate theory (FSDT) and subjected to mechanical, thermal and thermo-mechanical loads. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. An analytical approach is used to reduce the governing equations of stability and then solved using an analytical solution which is named as power series Frobenius method for symmetric sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of the plate aspect ratio, side-to-thickness ratio, loading type, sandwich plate type, volume fraction index, elastic foundation coefficients and boundary conditions on the buckling response of FGM sandwich plates. This has not been done before and serves to fill the gap of knowledge in this area.     

The skidding of an elliptic plate on a wet surface

A viscous fluid separates a massed, sliding, free elliptic plate and a smooth bottom plate. Due to the weight, the gap width between the plates decreases. The increased viscous drag eventually stops the skidding. The Navier-Stokes equations are expanded in terms of a small squeeze number. It is found that the gap width decrease as (time)^–1/2 and the maximum skidding distance depends on five nondimensional groups. An example shows it is easier for the elliptic plate to side longitudinally than laterally.     

基于新修正偶应力理论的Mindlin层合板热稳定性分析

以新修正偶应力理论为基础,首次提出了机械载荷与热载荷共同作用下的微尺度Mindlin层合板热稳定性模型,该模型只引入一个材料尺度参数,通过虚功原理推导出了控制方程和边界条件,以四边简支方板为例,进行了热稳定性分析,应用纳维叶解法得到解析解。结果表明,所建模型可以捕捉到尺度效应。材料尺度参数值越大,屈曲临界温度越高;当跨厚比增大时,屈曲临界温度下降;随着板几何参数的增大,模型将退化为宏观模型;温度变化量越大,考虑热载荷作用下的屈曲临界载荷越大,尺度效应体现越显著。     

Metal sandwich plates subject to intense air shocks

Recent results on fluid–structure interaction for plates subject to high intensity air shocks are employed to assess the performance of all-metal sandwich plates compared to monolithic solid plates of the same material and mass per area. For a planar shock wave striking the plate, the new results enable the structural analysis to be decoupled from an analysis of shock propagation in the air. The study complements prior work on the role of fluid–structure interaction in the design and assessment of sandwich plates subject to water shocks. Square honeycomb and folded plate core topologies are considered. Fluid–structure interaction enhances the performance of sandwich plates relative to solid plates under intense air shocks, but not as significantly as for water blasts. The paper investigates two methods for applying the loading to the sandwich plate—responses are contrasted for loads applied as a time-dependent pressure history versus imposition of an initial velocity.     

Low-energy impact response of composite and sandwich composite plates with piezoelectric sensory layers

An efficient model reduction based methodology is presented for predicting the global (impact force, plate deflection and electric potential) and through-thickness local (interfacial strains and stresses) dynamic response of pristine simply-supported cross-ply composite and sandwich composite plates with piezoelectric sensory layers subjected to low-energy impact. The through-thickness response of the laminate is modelled using coupled higher-order layerwise displacement-based piezoelectric laminate theories. Linearized contact laws are implemented for simulating the impactor–target interaction during impact. The stiffness, mass, piezoelectric and permittivity matrices of the plate are formulated from ply to structural level and reduced by applying a Guyan reduction technique to yield the structural system in state space. This reduction technique enables the formulation of a plate–impactor structural system of minimum size (1 term per vibration mode for composite plates – 2 terms for sandwich plates) and reduces computational cost, thus facilitating applicability for real-time impact and vibration control.     

Optimization of Dynamic Plastic Deformation of Plates with a Complex Contour

A method for studying dynamic deformation of ideal rigid–plastic plates with a complex contour on a viscoelastic foundation is proposed. The method allows one to optimize the process of pulsed forming. The optimization parameters are the amplitude of the pulsed load, viscoelastic damping coefficients of the foundation, the surface density of the plate material, and the shape and supporting conditions of the edges. Numerical examples of simply– and doubly–connected plates are given. It is shown that different combinations of the control parameters of the process can ensure the same final shape of the plate formed.     

包覆板材料为陶瓷时平板装药的防护性能

运用口径36mm的精密成型装药实验,研究了等效厚度相同的碳化硅和氧化铝陶瓷平板装药的防护性能,并与包覆材料为钢的平板装药进行了对比。运用LS-DYNA3D软件,对平板装药与聚能装药的作用过程进行了三维数值模拟。实验结果显示,对于此结构的平板装药,碳化硅和氧化铝陶瓷平板装药使聚能装药侵彻能力分别下降了88%和82%,优于钢板的防护性能。数值模拟结果显示,陶瓷包覆板从边缘至中心依次出现断裂和粉碎现象,钢板与射流后部作用为断续干扰,而陶瓷板为连续干扰。     

基于复合面/背板的平板装药防护性能

采用实验和数值模拟方法研究了橡胶复合板作为爆炸反应装甲面、背板时的防护性能,分析了两种反应装甲结构的防护机理,并与面密度相同的钢反应装甲进行了对比。实验结果表明:爆炸反应装甲面板或背板为橡胶复合板时的防护性能优于钢反应装甲,其中橡胶复合板作为背板时效果最优。数值模拟结果表明:橡胶复合板在爆炸驱动下外层钢板速度相比于钢反应装甲飞板提高16%,橡胶复合板的界面效应及其飞板间隙可以有效减小逃逸射流的长度。     

Experimental research on heat transfer of natural convection in vertical rectangular channels with large aspect ratio

This work presents the experimental research on the steady laminar natural convection heat transfer of air in three vertical thin rectangular channels with different gap clearance. The much higher ratio of width to gap clearance (60–24) and the ratio of length to gap clearance (800–320) make the rectangular channels similar with the coolant flow passage in plate type fuel reactors. The vertical rectangular channels were composed of two stainless steal plates and were heated by electrical heating rods. The wall temperatures were detected with the K-type thermocouples which were inserted into the blind holes drilled in the steal plates. Also the air temperatures at the inlet and outlet of the channel were detected. The wall heat fluxes added to the air flow were calculated by the Fourier heat conduction law. The heat transfer characteristics were analyzed, and the average Nusselt numbers in all the three channels could be well correlated with the Rayleigh number or the modified Rayleigh number in a uniform correlation. Furthermore, the maximum wall temperatures were investigated, which is a key parameter for the fuel’s integrity during some accidents. It was found that even the wall heat flux was up to 1500 W/m², the maximum wall temperature was lower than 350 °C. All this work is valuable for the plate type reactor’s design and safety analysis.     

Vibration of continuous circular plates

The general development of the theory given here considers the material to be orthotropic and continuous over (n ? 1) elastic or rigid supports. The effect of rotatory inertia and in-plane loads are also included while formulating the equations of motion. Double and triple series solutions are given for orthotropic continuous plates. By matching the continuity conditions at the intermediate supports and satisfying the boundary conditions at the outer edge, the frequency determinant is obtained. For the purpose of numerical computations, an isotropic plate continuous over an intermediate-rigid or elastic-support and free and with no in-plane loads at the outer edge is considered. It is found that the influence of Poisson's ratio on the frequency parameter is significant only for the first symmetric or asymmetric modes. The rotatory inertia influences the frequency parameter when the radius to thickness ratio is less than 80, viz, when the plate is thick. Moreover, the elasticity of the support influences considerably the free vibration of plates.     

Theoretical study of the effect of liquid desiccant mass flow rate on the performance of a cross flow parallel-plate liquid desiccant-air dehumidifier

A computer simulation using MATLAB is investigated to predict the distribution of air stream parameters (humidity ratio and temperature) as well as desiccant parameters (temperature and concentration) inside the parallel plate absorber. The present absorber consists of fourteen parallel plates with a surface area per unit volume ratio of 80 m²/m³. Calcium chloride as a liquid desiccant flows through the top of the plates to the bottom while the air flows through the gap between the plates making it a cross flow configuration. The model results show the effect of desiccant mass flow rate on the performance of the dehumidifier (moisture removal and dehumidifier effectiveness). Performance comparisons between present cross-flow dehumidifier and another experimental cross-flow dehumidifier in the literature are carried out. The simulation is expected to help in optimizing of a cross flow dehumidifier.     

High Frequency Measurements of Viscoelastic Properties of Hydrogels for Vocal Fold Regeneration

This report describes a torsional wave experiment used to measure the viscoelastic properties of vocal fold tissues and soft materials over the range of phonation frequencies. A thin cylindrical sample is mounted between two hexagonal plates. The assembly is enclosed in an environmental chamber to maintain the temperature and relative humidity at in vivo conditions. The bottom plate is subjected to small oscillations by means of a galvanometer driven by a frequency generator that steps through a sequence of frequencies. At each frequency, measured rotations of the top and bottom plates are used to determine the ratio of the amplitudes of the rotations of the two plates. Comparisons of the frequency dependence of this ratio with that predicted for torsional waves in a linear viscoelastic material allows the storage modulus and the loss angle, in shear, to be calculated by a best-fit procedure. Experimental results are presented for hydrogels that are being examined as potential materials for vocal fold regeneration.     

Deformation of lead disks under impact

The effect of relatively low-velocity (1–3 m/sec) impact on a thin disk of imcompressible viscoplastic material placed in the gap between parallel rough surfaces is considered. The state of stress of the interlayer is assumed nearly hydrostatic during impact, the duration of which is limited by the elastic deformation of the elements of the striker system. The mathematical problem of determining the distributions of stresses, velocities, and temperatures for the axisymmetric deformation of a disk is reduced to the integration of an ordinary second-order differential equation. Numerical calculations for certain cases of impact are compared with the results of experiments on lead samples. Plane strain of an interlayer of viscoplastic material between rigid plates moving with a constant velocity is discussed in [1]. The state of stress of the interlayer for the same conditions of motion of the plates was studied in [2] for axial symmetry. In the present paper we take account of the impact nature of the loading and the elastic compression of the elements of the striker system, factors on which the deformation and the pressure developed in the impact depend.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 153–158, September–October, 1975.     

Planar Flexural Vibrations and Dissipative Heating of Laminated Rectangular Plates

The coupled thermomechanical dynamic behavior of a heterogeneous solid is investigated by an example of laminated inelastic rectangular plates subjected to forced vibration and dissipative heating. The problem is solved in two formulations: complete and approximate. The complete formulation uses generalized flow theory to describe the inelastic properties of the material. The approximate formulation employs a model based on the idea of complex moduli. Special distributions of the field variables and amplitude–frequency responses of the rectangular plate are analyzed. The effect of the loading level on the mode shape and stress distribution is studied as well. A good agreement between the results obtained in the complete and approximate formulations is pointed out.     

Optimization of two component ceramic armor for a given impact velocity

Using Florence’s model a problem of two-component ceramic-faced lightweight armors design against ballistic impact is solved. Approximate analytical formulas are derived for areal density and thicknesses of the plates of the optimal armor as functions of parameters determining the properties of the materials of the armor components, cross-section and mass of an impactor, and of the expected impact velocity.     

剪切变形对FGM圆板轴对称屈曲的影响

基于一阶剪切变形板理论，推导了功能梯度材料圆形板在边界面内均布压力作用下的轴对称屈曲方程。在推导过程中，忽略了前屈曲耦合变形。利用一阶板理论与经典板理论屈曲方程之间在数学形式上的相似性，得到了一阶板理论下功能梯度材料圆板与经典板理论下均匀圆板临界屈曲载荷之间的解析关系。利用这个解析关系，可以直接从已有的较为简单的经典理论的结果，获得一阶板理论下功能梯度材料板的临界屈曲载荷。     

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young''s moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young''s moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.     

Exact solutions for variable-thickness inhomogeneous elastic plates under various boundary conditions

In this paper, an exact solution to the governing equations of the bending of a variable-thickness inhomogeneous rectangular plate is presented. The procedure is applicable to variable-thickness inhomogeneous rectangular plates with two opposite edges simply supported. The remaining ones subjected to a combination of clamped, simply supported, and free boundary conditions and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for variable-thickness inhomogeneous orthotropic plates as for uniform-thickness homogeneous isotropic plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of the inhomogeneity, aspect ratio, thickness parameter and degree of non-uniformity on the deflections and stresses are investigated. This paper is partially supported by the Deanship of Scientific Research at King AbdulAziz University (Grant no. 172/427).