Exponential stability for laminated beams with a frictional damping

We study a laminated beam which consists of two identical layers of uniform thickness, taking into account that an adhesive of small thickness is bonding the two surfaces thereby producing an interfacial slip. We show that when the frictional damping acts on the effective rotation angle there is no need for any other kind of internal or boundary control to produce exponential stability for the system.     

树脂基复合材料粘接的优化设计

本文在试验数据和理论分析的基础上,提出树脂基复合材料单搭接的优化设计的原则,胶粘剂的选择、被粘物的设计,粘接长度的选择、胶层厚度的选择等.认为通过优化设计可以提高粘接强度,减轻产品的重量,提高其质量.     

Bending of a two-layer beam with non-rigid contact between the layers

The bending, under plane stress state conditions, of a two-layer beam-strip with identical isotropic linearly elastic layers with non-rigid contact between them is considered. The effect of the contact interaction between the layers, simulated by an elastic or elastoplastic gasket of negligibly small thickness with a finite shear stiffness, on the deflection of the beam is studied. Absolute slippage and rigid contact between the layers are the two limiting values of the shear stiffness. The values of the flexural stiffness of the beam differ by a factor of four in these limiting situations. The problem is reduced to a one- dimensional problem in the case of harmonic external load and an asymptotic solution is constructed for it. In the case of a load of general form, the Kirchhoff - Love hypotheses are used to construct an approximate solution and the problem is reduced to a one-dimensional problem. The difficulties which arise in simulating of the interaction forces between the layers using Coulombic dry friction forces are discussed.     

基于粘弹性本构模型的双搭接胶结接头应力分析

采用广义Maxwell（麦克斯韦尔）粘弹性本构模型表征胶黏剂的时间相关力学特性,采用Yeoh本构模型描述橡胶材料的超弹性,建立了钢-橡胶双搭接胶结接头的有限元计算模型.在此基础上分析了加载时间对接头粘接界面剪切应力的影响.计算结果表明,剪切应力绝对值随着加载时间的增长而减小.此外,分析了胶层厚度对接头粘接界面剪切应力的影响,随着胶层厚度的增加,剪切应力绝对值呈现明显的增大趋势.     

Mathematical Modeling of the Stress-Strain State of Adhesive Layers in Sandwich Structures

The studies on theoretical modeling of a sandwich shell (SS) and sandwich beam (SB) are presented in this paper. The displacements of adhesive layers are computed in the whole SS. The Euler-Ostrogradskii equations are used to derive the equations of equilibrium, which contain six 16th-order differential equations. The three-point bending of a sandwich beam is considered and the behavior of the adhesive layer of the SB is calculated.     

Influence of Different Factors on the Stiffness and Strength of Multilayer Composite Elements

In the paper, the bending stiffness and strength of multilayer structural elements in relation to the mechanical properties of layers and their number layout and sizes are investigated and the corresponding correlations are established. It is found that the most rational structure of a multilayer element in bending is a symmetric three-layer structure formed from two materials with the thickness of the core less than the half-thickness of the element. The values of normal stresses in the layers of a multilayer beam in bending depends on its bending stiffness and the position of layers relative to the neutral axis. The influence of the number of layers on the stiffness of the structural element and on the magnitude of normal stresses is insignificant.     

Modeling the moisture and temperature dependent material behavior of adhesive bonds

Although bonding has been known for a long time, the mechanical behavior of adhesive bonded joints comes more and more into the focus of scientific attention. During usage, adhesives are exposed to environmental influences like temperature, moisture and radiation. Due to the fact that adhesives usually consist of polymers, these influences change their mechanical behavior. In the presented work, a viscoelastic cross-linked polyurethane that behaves incompressible is investigated. A three-dimensional mechanical model is presented, which takes into consideration influences of changes in temperature as well as in the moisture concentration inside the adhesive layer and its thickness on the mechanical behavior. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational model for reinforced concrete beams strengthened by epoxy bonded steel plates

This paper presents a nonlinear finite element model for the flexure-shear response of reinforced concrete (RC) beams strengthened externally by epoxy bonded steel plates. The model includes a special interface element to simulate the thin epoxy adhesive layer and which allows for the metamorphosis of failure mode from plate yielding to separation as the plate thickness t_p is increased. The numerical results show close correlation to experimental data available for an RC beam strengthened by plates of various thickness.     

A new Bernoulli–Euler beam model incorporating microstructure and surface energy effects

A new Bernoulli–Euler beam model is developed using a modified couple stress theory and a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equation and complete boundary conditions for a Bernoulli–Euler beam. The new model contains a material length scale parameter accounting for the microstructure effect in the bulk of the beam and three surface elasticity constants describing the mechanical behavior of the beam surface layer. The inclusion of these additional material constants enables the new model to capture the microstructure- and surface energy-dependent size effect. In addition, Poisson’s effect is incorporated in the current model, unlike existing beam models. The new beam model includes the models considering only the microstructure dependence or the surface energy effect as special cases. The current model reduces to the classical Bernoulli–Euler beam model when the microstructure dependence, surface energy, and Poisson’s effect are all suppressed. To demonstrate the new model, a cantilever beam problem is solved by directly applying the general formulas derived. Numerical results reveal that the beam deflection predicted by the new model is smaller than that by the classical beam model. Also, it is found that the difference between the deflections predicted by the two models is very significant when the beam thickness is small but is diminishing with the increase of the beam thickness.     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

Influence of fixation conditions and material anisotropy on the frequency spectrum of laminated beams

To accurately determine the influence of fixation conditions and material anisotropy of laminated beams on their dynamic properties, a new method for analyzing their stress is used. The theoretical model takes into account the transverse shear and normal deformations of layers and the nonlinear variation of in-plane displacements across the thickness of each layer. The stress-strain state in the region of fixation of a beam and its influence on the bending stiffness of the beam is examined. The frequency spectrum of laminated beams is also analyzed in relation to the anisotropic mechanical properties of layers and the configuration of the fixation unit.     

Investigations of chaotic dynamics of multi-layer beams taking into account rotational inertial effects

We propose a novel mathematical model of a vibrating multi-layer Timoshenko-type beam. We show that the introduced model essentially changes the type of partial differential equations allowing inclusion of rotational inertial effects. We illustrate and discuss the influence of boundary conditions, the beam layers and parameters of the external load on the non-linear dynamics of this composite beam including a study of its regular, bifurcation and chaotic behavior.The originally derived infinite problem is reduced to the finite one using either Finite Difference Method (FDM) or Finite Element Method (FEM) which guarantees validity and reliability of the obtained numerical results. In addition, a comparative study is carried out aiming at a proper choice of the efficient wavelet transform. In particular, scenarios of transition into chaos are studied putting emphasis on novel phenomena. Charts of the system dynamical regimes are also constructed with respect to the control parameters regarding thickness and composition of the beam layers.     

Convergence to a propagating front in a degenerate Fisher-KPP equation with advection

We consider a Fisher-KPP equation with density-dependent diffusion and advection, arising from a chemotaxis–growth model. We study its behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We analyze, for small times, the emergence of transition layers induced by a balance between reaction and drift effects. Then we investigate the propagation of the layers. Convergence to a free boundary limit problem is proved and a sharp estimate of the thickness of the layers is provided.     

Modeling of flow in a very small surface separation

When a fluid flows in a very small surface separation, the very thin boundary layer physically adhering to the solid surface will participate in the flow, while between the two boundary layers is a continuum fluid flow. An analysis is here presented for this multiscale flow. The continuum fluid is treated as Newtonian. The physical adsorbed boundary layer is treated as non-continuum across the layer thickness. The interfacial slippage can occur on the adsorbed layer-solid surface interface, while it is absent on the adsorbed layer-fluid interface. Three flow equations are derived respectively for the two adsorbed layers and the intermediate continuum fluid. They together govern the multiscale flow in such a small surface separation.     

Stability analysis of graphene based laminated composite sheets under non-uniform inplane loading by nonlocal elasticity

Size dependent buckling of composite laminates made of isotropic graphene layers interlaid with bonding agents is considered. Nonlocal theory of elasticity is used in the buckling analysis to reflect the size scale effects on the critical buckling loads which is discussed in detail. The method is capable of predicting the relative buckling modes for non-uniform inplane loading applied through the thickness of the laminate. All modes of buckling in which the layers may displace together or opposite one another are investigated to study their scale dependent effects. Displacement or load controls are implemented through independent parameters as constraints to form special combination of buckling modes. Each graphene sheet is considered as a Kirchhoff plate model. The interlaid bonding agent is laterally treated as Winkler elastic foundation between graphene layers while neglecting their other load carrying capacities. Various numerical results are obtained reflecting the nonlocality effects. It is observed that in cases of higher load ratios and simpler buckling modes, the effect of nonlocality tends to drastically increase. The results of simpler examples studied are verified by another reference.     

Static and dynamic stability modeling of a capacitive FGM micro-beam in presence of temperature changes

Stability of a functionally graded (FG) micro-beam, based on modified couple stress theory (MCST), subjected to nonlinear electrostatic pressure and thermal changes regarding convection and radiation, is the main purpose of this paper. It is assumed that the functionally graded beam, made of metal and ceramic, follows the volume fraction definition and law of mixtures, and its properties change as an exponential function through its thickness. By changing the ceramic constituent percent of the bottom surface, five different types of the micro-beams are investigated. The static pull-in voltages in presence of temperature changes are obtained by using step-by-step linearization method (SSLM) and, by adapting Runge–Kutta approach, the dynamic pull-in voltages are obtained numerically. Though the temperature distribution through the thickness of FG micro-beam (due to its too small measurement) is considered uniform, owing to the different thermal expansions of layers, temperature changes cause deflection in the micro-beam, and consequently affect pull-in values. Hence the profound effects of different material constituent over the pull-in voltages are illustrated and it is graphically displayed that how in some cases neglecting components of the couple stress leads to inaccurate results.     

The effective characteristics and electroelastic state of active composite elements

For rods in which the piezoelectric and elastic layers are perpendicular to the rod axis and the lamination has a periodic structure, formulae for the effective characteristics of inhomogeneous material are obtained and the equations that describe the electroelastic state are constructed by the asymptotic method of homogenization. Such active composite elements are known as stacks. As an example, the electroelastic state of stacks executing forced harmonic vibrations under the action of an electrical load is calculated, the effective characteristics of material are found, and both the slowly varying state described by the rod theory and the rapidly varying state caused by the inhomogeneity of the layered structure are calculated. The effect of the thickness of weak adhesive layers on the electromechanical coupling coefficient, characterizing the stacks as energy convertors, is investigated.     

A viscoelastic frictionless contact problem with adhesion

We consider a model for the quasistatic, bilateral, adhesive and frictionless contact between a viscoelastic body and a rigid foundation. The adhesion process on the contact surface is modeled by a surface internal variable, the bonding field, and the tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and an integro-differential equation for the bonding field. The existence of a unique weak solution for the problem is established by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space. We also consider the problem describing the bilateral contact between two viscoelastic bodies, and establish similar results.     

Theoretical studies on solid heterogenous targets thickness in muon catalyzed fusion using transport theory and its comparison with available experimental values

Muon catalyzed fusion in solid heterogeneous H/D/T layers has been studied in recent years. When a negative muon enters the protium layer with a small admixture of tritium, the muonic atom is formed. molecular ion formation is highly dependent on the energy of the muonic tritium atom, μt, and this energy itself depends on the thickness of H/T and D₂ layers. In this paper, the transport theory is used to study the effect of the thickness of different layers (H/T and D₂) on the output kinetic energy of the μt atom. The calculated thickness by the used theoretical method are compared with the available experimental values and it is shown that they are in a good and acceptable agreement, and represents the reliability of used theoretical method.