New Conservation Laws of Energy and C-D Inequalities in Continua Without Microstructure

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Stability of sandwich plates by mixed,higher-order analytical formulation

A unified mixed, higher-order analytical formulation has been presented in this paper to predict general buckling as well as wrinkling of a general multi-layer, multi-core sandwich plate having any arbitrary sequence of stiff layers and cores. Assumptions of thin stiff layers and anti-plane core, which are usually made in the analysis of sandwiches, have been eliminated in the present formulation. Displacements as well as the transverse stress continuities have been enforced in the formulation by incorporating them as the degrees-of-freedom. The modal transverse stresses have been obtained directly as eigen vectors and thus their separate calculations have been advantageously avoided. Two sets of mixed models have been proposed on the basis of individual layer as well as equivalent single layer (ESL) theories by selectively incorporating non-linear components of Green’s strain tensor. Solutions from the models have been shown to be in excellent agreement with the available three-dimensional elasticity solutions as well as with the available experimental results. It has been demonstrated that the ESL theories cannot accurately evaluate the overall buckling as well as the wrinkling loads of sandwiches. Limitations of the typical simplifying assumptions have also been highlighted.     

On mechanics of saturated granular materials

A continuum theory of saturated granular materials is formulated. The basic balance laws for the solid phase as well as for the fluid phase are presented. The constitutive equations are derived and the basic equations of motion of the solid and fluid continua are obtained. Several cases of interest, such as incompressible granules saturated with liquids are discussed. It is shown that the theory contains, as its special cases, the Mohr-Coulomb criterion for a granular material as well as Darcy's law of flow through porous media.     

MOIRÉ INTERFEROMETRY WITH ENHANCED RESOLUTION

The implementation of this method is relatively simple. It does not require any modification to interferometric systems already in use. It can be used in the analysis of large as well as very small fields, including measurements under a microscope.
A fringe pattern with a carrier is recorded in a single exposure, just as in the standard procedure. As a consequence, any possible instability of the interferometer does not affect the accuracy of the measurements. Further, the spatial resolution of the measurements is not compromised.
Since only one exposure is needed for a given displacement component this method can be applied to dynamic as well as static measurements.
It should be emphasized that even though the number of electronically generated fringes can be arbitrary, the sensitivity is the same as in ordinary moire interferometry as long as the data are taken at the lines of minimum intensity. The improvement is in the increase of the number of data points taken at the locations of maximum resolution. In other words, all the data are taken at the maximum resolution.
This method applies not only to moire interferometry but to any experimental technique based on two-beam interference, as long as the fringe pattern has good contrast.     

Streak interferometric measurements of transient displacements

A program was designed to demonstrate and evaluate the use of streak interferometry as a method for collecting temporally and spatially resolved transient-deformation data on the surfaces of metallic solids. The study has shown that the technique can resolve displacement histories with times as short as 70 nsec and measure surface velocities as large as 80 ips. These capabilities appear adequate for the intended applications. Representative data are shown and analyzed.     

四面体无定型无氢非晶碳膜的制备及其摩擦学性能研究

采用磁过滤阴极真空弧系统分别在硅片[Si(100)]、W18Cr4V高速钢和Cr18Ni9不锈钢基体上沉积了一系列sp3键含量较高的四面体无定型无氢非晶碳膜(ta-C),研究了所合成薄膜的结构、硬度、附着强度和摩擦磨损性能,考察了基体和薄膜厚度对薄膜摩擦系数的影响,简要分析了相应ta-C膜的失效机理.结果表明,在高速钢基体上沉积的ta-C膜的显微硬度为76 GPa,结合力Lc值达42 N,具有优良的摩擦学性能,其摩擦系数为0.12,且摩擦系数可以在16 000 r范围内保持稳定.     

Numerical computations of internal flows for axisymmetric and two-dimensional nozzles

MacCormack's explicit time-marching scheme is used to solve the full Navier–Stokes unsteady, compressible equations for internal flows. The requirement of a very fine grid to capture shock as well as separated flows is circumvented by employing grid clustering. The numerical scheme is applied for axisymmetric as well as two-dimensional flows. Numerical predictions are compared with experimental data and the qualitative as well as the quantitative agreement is found to be quite satisfactory. © 1997 John Wiley & Sons, Ltd.     

Drained and Undrained Poroelastic Properties of Healthy and Pathological Bone: A Poro-Micromechanical Investigation

Poro-micromechanics allows for the quantification of poroelastic properties such as the Biot and Skempton coefficients, once a continuum micromechanics model for the material under consideration has been developed and validated. Employing such a model for the transversely isotropic elasticity of cortical and trabecular bone, we determine the tensors of Biot and Skempton coefficients as functions of the volume fractions of mineral, collagen, and the micropore space (Haversian and Volkmann canals, and the inter-trabecular space). Increase of microporosity, as experienced in osteoporosis, as well as decrease of mineral content, as experienced in osteomalacia, lead to an increase of Biot and Skempton coefficients, i. e. to magnification of the mechanical role of the marrow filling the micropore space. For quantification of the marrow pressure rise upon downfall, undrained conditions are appropriate, as can be shown by model predictions of non-destructive impact experiments.     

稀土铈有机配合物添加剂的制备及其摩擦学性能

采用水热合成法分别制备了含1，10-菲啰啉和油酸两种配体的稀土铈配合物，以及作为对照组的只含一种配体的配合物. 利用傅里叶变换红外光谱仪、紫外-可见分光光度仪和热重分析仪对配合物的组成及结构进行了表征和分析，利用SRV-IV型微动摩擦磨损试验机对含有不同质量分数目标产物的润滑油的摩擦学性能进行了研究. 结果表明:以Ce3+为中心离子，1，10-菲啰啉作为第一配体，油酸作为第二配体所制备的稀土有机配合物可以显著提高基础油(PAO8)的极压性能和抗磨损性能，并且使润滑油的使用寿命得以延长.      

Network Dynamics: Tools and Examples

Some mathematical tools and results are presented which may be used to study the dynamics of agents living on a network as well as the networks themselves as evolving dynamical systems. They include decomposition of differential dynamics, ergodic techniques, estimates of invariant measures, etc. Some examples are discussed as an application of the dynamical tools.     

Large deflection analysis of plates on elastic foundation by the boundary element method

A boundary element method is developed for the large deflection analysis of thin elastic plates resting on elastic foundation. The subgrade reaction may depend linearly (Winkler-type) or nonlinearly on the deflection as well as on the point coordinates (nonhomogeneous subgrade). Moderately large deflections are examined as described by the von Karman equations. The plate may have arbitrary shape and its boundary may be subjected to any type of boundary condition. The proposed method uses the fundamental solution of the linear plate theory and treats the nonlinearities as well as the subgrade reaction as unknown domain forces. Numerical results are presented to illustrate the method and demonstrate its effectiveness and accuracy.     

New Principles of Work and Energy as Well as Power and Energy Rate for Continuum Field Theories

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ℋ︁‐LU factorization in preconditioners for augmented Lagrangian and grad‐div stabilized saddle point systems

The (mixed finite element) discretization of the linearized Navier–Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as ‘grad‐div’ (GD) stabilization, as well as on the discrete side where it is known as an ‘augmented Lagrangian’ (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ??‐LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ??‐LU factorization in the preconditioners. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite element modelling of orthotropic material behaviour in pneumatic membranes

In this paper, we develop a model to describe the hyperelastic material behaviour of pneumatic membranes reinforced with roven–woven fibres. A generalized stored energy function is developed via a series of loading tests on a representative sample of this composite material. The exponents in the effective law are chosen so as to fulfil basic restrictions, discussed in the body of the paper, as well as to match certain experimental values. Numerical examples demonstrate the application of the approach to inflated rubber matrix materials, as well as laminated shells.     

Periodic motions of coupled simple pendulums with periodic disturbances

Several theorems on the existence of oscillatory, rotary, and mixed periodic motions of n, coupled simple pendulums are proved. These theorems are very general and include subharmonic and ultraharmonic type solutions as well as harmonic type solutions and cover cases of large coupling and disturbances as well as small. The results are also extended to include more general systems of nonlinear oscillators.     

A geometrically nonlinear analysis of rotational shells using B-spline function

In this paper, based on the nonlinear thin shell theory, a geometrically nonlinear formulation using the total Lagrangian approach for rotational shells, as well as rotational shells on the Winkler-type elastic foundation, is presented. The displacements of the middle surface are approached by a B-spline function. All nonlinear terms of membrane strains are reserved. Two cases in which the arc length as well as ordinate is used as the coordinate parameter along meridional direction are discussed at the same time.The project supported by National natural Science Foundation of China.     

A study of the scattered-light technique in two-dimensional problems

The scattered-light method is applied to plane-stress problems. The study gives significance to the fringe spacing perpendicular as well as parallel to the direction of light propagation. The results show that one full-field photograph is sufficient to determine the state of stress in the model as well as to calibrate the model material. Results for the case of a ring in diametrical compression are presented.     

Some general results on the stability and flow failure of rigid viscoplastic structures

The evolution of structures made of materials which obey a rigid viscoplastic constitutive law, conceived as a generalisation of the classical Bingham model, and submitted to several loading parameters, is examined here in connection with the limit analysis (or yield design) theorems. A minimum principle for the velocities is established, from which it is shown in particular that the structure remains motionless as far as the loading belongs to the domain of safe loadings, while flow failure is triggered as soon as it is loaded beyond its limit load. Such a property is illustrated on the example of a uniform layer of Bingham material flowing on an inclined plane, due to the combined action of gravity and surface shear loading, considered as two independent loading parameters.     

Measurement of the shear viscosity using a newly developed GRLDA-viscometer

A two-point laser-Doppler anemometer is used to determine velocity gradients. Measuring additionally the pressure drop in channel flow allows one to use this instrument as a viscometer. This is demonstrated by measuring two polymer solutions as well as water. Besides the velocity gradient, the system also furnishes the velocity as well as velocity fluctuations. For surfactant solutions the sudden increase in these fluctuations go hand-in-hand with the sudden shear thickening reported. This behavior thus seems to be caused by a change in type of flow field (structural turbulence) rather than a change in the rheology of the surfactant solutions.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.