Solution of a thermoelasticity problem for layered plates according to a more precise model

An applied theory is constructed for layered plates taking into account deformations due to transverse shear in a stationary thermal field. Equilibrium equations and boundary conditions are derived. It is shown that for plates of average thickness, consideration of transverse shear deformations and thermal expansion in the transverse direction leads to results significantly differing from those calculated according to the classical theory.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 25–29, 1989.     

Effect of random system properties on bending response of thermo-mechanically loaded laminated composite plates

In this paper, effect of random variation in system properties on bending response of geometrically linear laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modeled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behavior of the composite plate. A C⁰ finite element method in conjunction with the first order perturbation technique procedure developed earlier by authors for the plate subjected to lateral loading is employed to obtain the second order response statistics (mean and variance) of the transverse deflection of the plate. Typical numerical results for the second order statistics of the transverse central deflection of geometrically linear composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and linearly varying temperature distribution are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The performance of the stochastic laminated composite model is demonstrated through comparison of mean transverse central deflection with those results available in literature and standard deviation of the deflection with an independent Monte Carlo simulation.     

A solution for the local plane strain problems using elliptic integrals of Cauchy type

We consider a parallel fiber‐reinforced periodic elastic composite that present an imperfect contact of spring type between the fiber and the matrix. We use the elliptic integral of Cauchy type for solving the plane strain local problems that arise from the asymptotic homogenization method. Several general conditions are assumed, which include that the fibers are disposed of arbitrary manner in the local cell, that all fibers present contact perfect with different constants of imperfection, and that their cross section is a smooth closed arbitrary curve. We find that there are infinity solutions for these problems, and we find relations between these solutions and effective coefficients of the composite. Finally, we obtain analytic formulae for the circular fiber case and show some numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

The heat conductivity problem in a thin plate with contrasting fiber inclusions

Based on the asymptotic analysis of an elliptic boundary value problem in a thin domain, a homogenized model of the heat distribution in a composite plate of small relative thickness h ∈ (0,1] is constructed under the assumption that thermal conductivity of the fiber and that of the filler contrast very much. Namely, the plate is assumed to contain several periodic families of fibers, the diameters of the fibers and the distances between the fibers being of the same order h. Fibers in each family have the same thermal conductivity; the values of thermal conductivity of fibers in different families may vary, but should be of the same order in h. Thermal conductivity of the filler is one order smaller in h. The asymptotics is constructed by means of matching the classical asymptotic ansatz for thin plates and fibers. The periodic structure of the composite is crucially used to construct the asymptotic expansion which consists of terms of the following two types: a periodic solution of the three-dimensional problems in the periodicity cell and a solution to a two-dimensional homogenized problem in the longitudinal cross-section of the plate. The asymptotic procedure provides a simple algorithm to compute coefficients in the homogenized second-order differential operator. The asymptotics obtained is justified using the weighted Friedrichs inequality and the error estimates are asymptotically sharp.     

Thermoelastic homogenization of periodic composites using an eigenstrain-based micromechanical model

This paper presents a study on effective thermoelastic properties of composite materials with periodic microstructures. The overall elastic moduli and coefficients of thermal expansion of such materials are evaluated by a micromechanical model based on the Eshelby equivalent inclusion approach. The model employs Fourier series in the representation of the periodic strain and displacement fields involved in the homogenization procedures and uses the Levin's formula for determining the effective coefficients of thermal expansion. Two main objectives can be highlighted in the work. The first of them is the implementation and application of an efficient strategy for computation of the average eigenstrain vector which represents a crucial task required by the thermoelastic homogenization model. The second objective consists in a detailed investigation on the behavior of the model, considering the convergence of results and efficiency of the strategy used to obtain the approximate solution of the elastic homogenization problem. Analyses on the complexity of the eigenstrain fields in function of the inclusion volume fractions and contrasts between the elastic moduli of the constituent phases are also included in the investigation. Comparisons with results provided by other micromechanical methods and experimental data demonstrate the very good performance of the presented model.     

Effect of curvature of the reinforcement on the mechanical and thermophysical properties of a composite

The elastic constants and thermal expansion coefficients of a composite consisting of a matrix with low elastic properties and exceptionally stiff fibers have been experimentally determined. The curvature of the reinforcement in the specimens has been investigated. The results of the experiments are compared with the corresponding theoretical characteristics. The calculations are based on a model with an ideal arrangement of the fibers [4] and a model that takes the curvature of the reinforcement into account [5, 6].Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1036–1039. November–December, 1971.     

Asymptotic evaluation of effective complex moduli of fibre‐reinforced viscoelastic composite materials

We propose an asymptotic approach for the evaluation of effective complex moduli of viscoelastic fibre‐reinforced composite materials. Our method is based on the homogenization technique. We start with a non‐trivial expansion of the input plane‐strain boundary value problem by ratios of visco‐elastic constants. This allows to simplify the governing equations to forms analogous to the complex transport problem. Then we apply the asymptotic homogenization method, coming from the original problem on multi‐connected domain to the cell problem, defined on a unit cell of the periodic structure. For the analytical solution of the cell problem we apply the boundary perturbation technique, the asymptotic expansion by a distance between two neighbouring fibres and the method of two‐point Padé approximants. As results we derive uniform analytical representations for effective complex moduli, valid for all values of the components volume fractions and properties.     

翘曲空间曲线梁自然坐标精确解

基于现有空间曲线梁理论,考虑与扭转有关的翘曲变形和横向剪切变形的影响,建立了自然标架下空间曲线梁的内力和变形的解析解答．将该解答应用于受均布扭矩和竖向分布荷载的平面曲线梁的分析,将所得结果与Heins解答进行比较,证明了理论的正确．并应用该理论分析了解析式中翘曲和横向剪切变形项的影响．     

The consistent equations of the theory of plane curvilinear rods for finite displacements and linearized problems of stability

Based on a previously constructed, consistent version of the geometrically non-linear equations of elasticity theory, for small deformations and arbitrary displacements, and a Timoshenko-type model taking into account transverse shear and compressive deformations, one-dimensional equations of an improved theory are derived for plane curvilinear rods of arbitrary type for arbitrary displacements and revolutions and with loading of the rods by follower and non-follower external forces. These equations are used to construct linearized equations of neutral equilibrium that enable all possible classical and non-classical forms of loss of stability (FLS) of rods of orthotropic material to be investigated, ignoring parametric deformation terms in the equations. These linearized equations are used to find accurate analytical solutions of the problem of plane classical flexural-shear and non-classical flexural-torsional FLS of a circular ring under the combined and separate action of a uniform external pressure and a compression in the radial direction by forces applied to both faces.     

Computation of thermal residual stresses in optic fibers

We propose an analytic method of determining all the components of the residual stress tensor in optic fibers. The method is based on solving a plane problem for a cylindrical structure with singular stresses. We obtain closed-form solutions of the problem in the case of a piecewise-constant distribution of free deformations that model the presence of inclusions in the fiber with different values of the thermal coefficient of expansion. We also consider inclusions with cross sections in the shape of a circle, a central ellipse and a central annular sector. We describe the results obtained on this basis in the computation of residual thermal stresses.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 79–83.     

A Linear,First-order Shell Model for Transverse Isotropic Material under a Uniform Change of Temperature

A first-order shell model is derived for describing the behaviour of a thin, arbitrarily curved structure made from homogeneous, transverse isotropic material under the influence of a uniform change of temperature. Transverse isotorpy means that the elastic behaviour and the thermal expansion is isotropic in in-plane directions but different in thickness direction. The influence of the different thermal expansion is incorporated by equivalent stress couples and bending moments. Thus, a higher-order approximation in thickness direction is not necessary. However, the so-called ‘second approximation of shell theory’ must be used which deals with more accurate constitutive relations than the standard theory. Further the question is investigated in which cases a stress-free transverse isotropic thermal deformation exists.     

Asymptotic behavior of the correlation coefficients of transverse momenta in the model with string fusion

In the framework of the model with fusion of quark–gluon strings on the transverse lattice, we find the asymptotic behavior of the correlation coefficients between observables in separated rapidity intervals with a high string density in a realistic case with an inhomogeneous distribution of strings in the impact parameter plane. We calculate the asymptotic forms for three types of correlations: between the average transverse momenta of particles with rapidity in these intervals, between the average transverse momentum of particles in one rapidity interval and the multiplicity of particles in another, and also between the multiplicities of charged particles in these intervals. We show that the previously found independence of the asymptotic form of the correlation coefficient between the average transverse momenta from the variance in the number of particles produced in string fragmentation holds only in the case of a uniform distribution of strings in the transverse plane. We also show that the found general expressions for the long-range correlation coefficients in the particular case with a uniform distribution of strings in the transverse plane become the formulas previously obtained by another method applicable only in this simple case.     

Prediction of the deformation properties of a polymeric composite with a granular-fibrous filler

Conclusion A variant of calculation of the characteristics of the deformation properties of a hybrid composite containing a complex disperse filler in the form of granular particles and short fibers was proposed. The effect of aggregation of the granular filler, the statistical distributions of the fibers by lengths and orientation in the material, and the anisotropy of the fibers are taken into consideration in the calculation. The statistical distribution of the orientation of the fibers is given by a function proportional to the distance from the center to the surface of a triaxial ellipsoid in the corresponding direction. The uniform random distribution of the fibers in bulk and in the plane is a special case of this distribution. The results of the analysis of the effect of the parameters of the statistical distributions of the length and orientation of short fibers on the elasticity characteristics of a composite are reported. The dependence of the creep of the composite on the ratio of the concentration of the components of the complex filler was determined, and the efficiency of partial replacement of a granular filler by a short-fiber filler to inhibit creep of the composite was demonstrated. The possibilities of predicting the long-term creep were experimentally confirmed on the example of LDPE filled with ground limestone and short glass fibers.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 898–909, September–October, 1987.     

Transverse spectral instabilities in Konopelchenko–Dubrovsky equation

We study the transverse spectral stability of the one-dimensional small-amplitude periodic traveling wave solutions of the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) equation. We show that these waves are transversely unstable with respect to two-dimensional perturbations that are periodic in both directions with long wavelength in the transverse direction. We also show that these waves are transversely stable with respect to perturbations which are either mean-zero periodic or square-integrable in the direction of the propagation of the wave and periodic in the transverse direction with finite or short wavelength. We discuss the implications of these results for special cases of the KD equation—namely, KP-II and mKP-II equations.     

非齐次小周期复合材料稳态热问题的多尺度渐近展开和收敛性分析

利用多尺度渐近展开和均匀化思想讨论了小周期复合材料的稳态热问题,得到了非齐次边界条件下二阶椭圆型方程的渐近解,并给出了原始解与渐近解之间的误差估计,数值结果表明了结论的正确性.     

空心球复合材料热弹性性质的一些精确结果

本文基于所提出的基体均匀场方法研究了空心球增强复合材料的热弹性性质·导出了均匀边界条件激发的局部热场和力学场量的关系，并进而得到了复合材料等效热弹性性质之间的精确关系·对于具有某种特定内外径比的空心球所构成的宏观各向同性复合材料，如果基体和空心球的热膨胀系数相同，可以证明其等效体积模量和线膨胀系可以精确地确定·     

带状区域中渐近周期曲率流方程的整体解

该文研究了具有渐近周期系数的曲率流方程的Neumann边值问题.首先,考虑一列初值问题及其相应的全局解,通过一致的先验估计取一个收敛子列,得到其极限就是一个整体解的结论.其次,向负无穷时间方向进行重整化,使用强极值原理证明了整体解的唯一性.最后,为了研究整体解的ω-和α-极限,再次使用重整化方法,通过构造拉回函数、进行...     

横向非均升温下弹性梁的热过屈曲

基于轴向可伸长梁的几何非线性理论和打靶法,研究了两端不可移简支弹性梁在横向非均匀分布升温场作用下的热弹性屈曲响应。着重分析了横向升温变化对热过屈曲变形的影响,给出了相应的特性曲线。数值结果表明,由于横向温度改变会产生热弯曲内力,因此过屈曲平衡路径与有初始变形梁的过屈曲平衡路径相似。     

Temperature and displacement fields in brake and clutch systems with thermoelastic instabilities

In brake and clutch systems kinetic energy is converted into thermal energy. Experiments show that the corresponding temperature field can develop unstable periodic structures. The temperature field couples to the displacement field by thermal expansion. Local pressure maxima in the frictional plane and the corresponding maxima in heat generated cause thermoelastic instabilities (TEI). A model describing both effects covers layers of thermoelastic materials for all necessary mechanical components of the system. The set of field equations of each layer can analytically be solved by separation of constants. These solutions must fulfill the boundary conditions e.g. in the sliding plane. A stability discussion yields whether TEI appear or not. As a study a brake system is analyzed comprising two pads pressed against a rotating disk with cooling channels inside. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures

This paper deals with free vibration analysis of functionally graded composite shell structures reinforced by carbon nanotubes. Uniform and three distributions of carbon nanotubes which are graded in the thickness direction of the structure are considered. The effective material properties are determined via a micro-mechanical model using some efficiency parameters. The equations of motion are developed based on a discrete double directors shell finite element formulation which introduces the transverse shear deformations via a higher-order distribution of the displacement field. Comparison studies are carried out for various functionally graded composite shell structures reinforced by carbon nanotubes in order to highlight the applicability and the efficiency of the proposed model in the prediction of the vibrational behavior of such shell structures.