Asymptotic simulation of imperfect bonding in periodic fibre-reinforced composite materials under axial shear

An asymptotic approach for simulation of the imperfect interfacial bonding in composite materials is proposed. We introduce between the matrix and inclusions a flexible bond layer of a volume fraction c⁽³⁾ and of a non-dimensional rigidity λ⁽³⁾, derive a solution for such three-component structure, and then set c⁽³⁾→0, λ⁽³⁾→0. In the asymptotic limit depending on the ratio λ⁽³⁾/c⁽³⁾ different degrees of the interface's response can be simulated. A problem of the axial shear of elastic fibre-reinforced composites with square and hexagonal arrays of cylindrical inclusions is considered. The performed analysis is based on the asymptotic homogenization method, the cell problem is solved using the underlying principles of the boundary shape perturbation technique. As a result, we obtain approximate analytical solutions for the effective shear modulus and for the stress field on micro level depending on the degree of the interfacial debonding. Developed solutions are valid for all values of the components’ volume fractions and properties. In particular, they work well in cases of rapid oscillations of local stresses (e.g., in the case of densely packed perfectly rigid inclusions), while many of other commonly used methods may face computational difficulties.     

Asymptotic homogenization modeling and analysis of effective properties of smart composite reinforced and sandwich shells

General micromechanical models for smart composite shells with periodically arranged actuators and varying thickness are developed using the asymptotic homogenization techniques. The models make it possible to determine both local fields, i.e., stresses, strains and displacements, and effective elastic and piezoelectric coefficients of the smart composite shells. It is shown that the original boundary value problem decouples into a set of simpler problems, known as unit cell problems. In particular, it is the solution of these unit cell problems that yields the aforesaid effective coefficients. These coefficients are universal in nature and may be used to study a wide variety of boundary value problems associated with a given smart composite structure. The derived models and the expressions for the effective coefficients are illustrated by means of four examples pertaining to hexagonal honeycomb sandwich structures and rectangular-reinforced, diagonally restrained and triangular-reinforced smart wafer shells. These structures are endowed with piezoelectric carrier layers made of orthotropic material and isotropic core or wafer. It is shown that the derived models can be used to tailor the effective properties of such smart composite structures to meet the requirements of particular applications of interest.     

Nonlinear free vibration of laminated composite plates on elastic foundation with random system properties

The present investigation is concerned with free vibration analysis of laminated composite plates resting on elastic foundation undergoing large amplitude oscillation with random system properties. The lamina material properties and foundation stiffness parameters are modeled as basic random variables for accurate prediction of the system behavior. The basic formulation of the problem is based on higher-order shear displacement theory including rotatory inertia effects and von Karman-type nonlinear strain displacement relations. A C⁰ finite element is used for descretization of the laminate. A direct iterative method in conjunction with first-order Taylor series based perturbation technique procedure is developed to solve random nonlinear generalized eigenvalue problem. The developed probabilistic procedure is successfully used for the nonlinear free vibration problem with a reasonable accuracy. Typical numerical results (second-order statistics) are obtained for the composite plates resting on Winkler and Pasternak elastic foundations with different support conditions, side-to-thickness ratio, aspect ratio, oscillation amplitude ratio, stacking sequences and foundation parameters for symmetric and anti-symmetric cross-ply and angle-ply laminates. The results are validated with existing available results and independent Monte Carlo simulation.     

Rolling cylinder on an elastic half-plane with harmonic oscillations in normal force and rotational speed. Part I: Solution of the partial slip contact problem

We study the effect of harmonic oscillations during the steady rolling of a cylinder on a plane in partial slip contact conditions in the limit of small oscillations. The solution is an extension of that given in Barber et al. [1] for infinitely large coefficient of friction. Here, the effect of varying normal load and hence contact area is investigated in detail by analyzing the first order variation of the tangential force and the corresponding relative displacements.In particular, the solution is given in terms of an explicit length scale d in the Flamant solution used as a Green function. Appropriate choice of values of d allows to treat both two-dimensional problems and three-dimensional ones having elliptical contact area sufficiently elongated in the direction of the rotation axis.Also, this analysis can be used as starting point for corrugation calculations in railway tracks, where oscillations in time of the normal forces can result in non-uniform wear and hence in amplification of the corrugation.