S.A. Meguid

Nonlinear analysis of functionally graded plates and shallow shells

In this paper, an analytic solution is provided for the coupled large deflection of plates and shallow shells made of functionally graded materials (FGMs) under transverse mechanical loads and a temperature field. The material properties of the functionally graded shells are assumed to vary continuously through the thickness of the shell, according to a power law distribution of the volume fraction of the constituents. The fundamental equations for thin rectangular shallow shells of FGM are obtained using the von Karman theory for large transverse deflection, and the solution is obtained in terms of Fourier series. The effect of material properties, shell geometry and thermomechanical loading on the stress field are determined and discussed. The results reveal that thermomechanical coupling effects play a major role in dictating the response of the functionally graded shell.

Three—dimensional dynamic finite element analysis of shot-peening induced residual stresses

This investigation is devoted to the modelling and simulation of the residual stress field resulting from the shot-peening process. In this dynamic elasto-plastic analysis, single and twin spherical indentations were examined using the finite element method. The contact between the shots and the target was modelled using contact elements of the penalty function type. Attention was devoted to three related issues. The first is concerned with the effect of the shot velocity, size and shape upon the plastic zone development and growth, and unloading residual stresses. The second with the effect of the separation distance between two impinging shots upon the equivalent stress trajectories and unloading residual stresses. Finally, the study examines the effect of the strain-hardening rate of the target upon the development and the spread of the plastic zone. The results reveal the important role played by the shot and target characteristics upon the quality of the treatment, as measured by the mechanically induced residual stresses.

3D FE analysis of peening of strain-rate sensitive materials using multiple impingement model

In spite of its importance to the aerospace and automobile industries, little or no attention has been devoted to the accurate modelling of the shot-peening process. It is therefore the purpose of this study to conduct dynamic elasto-plastic finite element analysis of the process using a realistic multiple impingement model using a rate sensitive material. In this analysis, we implement a novel “symmetry cell” approach to examine the impact effect of a large number of rigid and deformable shots on a high-strength steel target made from AISI 4340. A number of convergence tests, which account for element size and stiffness of contact elements, were carried out. In addition, efforts were devoted to determine the appropriate material damping parameters needed to dampen unwanted numerical oscillations associated with the explicit solver of LS-DYNA for this class of problems. The model was used to predict the effect of peening intensity and coverage upon the mechanically induced residual stress field and the plastic zone development for different classes of materials.

Tunneling resistance and its effect on the electrical conductivity of carbon nanotube nanocomposites

In this paper, we examined the effect of electron tunneling upon the electrical conductivity of carbon nanotube (CNT) polymer nanocomposites. A CNT percolating network model was developed to account for the random distribution of the CNT network using Monte Carlo simulations, where the tunneling resistance between CNTs was established based on the electron transport theory. Our work shows several novel features that result from this tunneling resistance: (i) direct contact resistance is the result of one-dimensional electron ballistic tunneling between two adjacent CNTs, (ii) the nanoscale CNT-CNT contact resistance should be represented by the Landauer-Buttiker (L-B) formula, which accounts for both tunneling and direct contact resistances, and (iii) the difference in contact resistance between single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs) can be modeled by the channel number in the L-B model. The model predictions reveal that the contact resistance due to electron tunneling effects in nanoc...

FE modelling of deformation localization in metallic foams

In this paper, we employ a modi!ed and representative unit cell model to study the crush behaviour of closed-cell metallic foams with varying spatial density distribution. The mean through-thickness density variation was assumed to be a function of the casting process of the foam, while the in-plane variation was assumed to follow a statistical probability distribution of the Gaussian type. A multiple cell !nite element model, utilizing the modi!ed unit cell, was developed. The model exhibits deformation localization patterns similar to those observed in compression testing for both transverse and in-plane crushing. The nominal � –� curve obtained from quasistatic crushing of the foam was compared with experimental !ndings and was found to be in good agreement only if the appropriate density distribution is taken into account. ? 2001 Elsevier Science B.V. All rights reserved.

On the electroelastic behaviour of a thin piezoelectric actuator attached to an infinite host structure

In this paper, we examine the coupled electromechanical behaviour of a thin piezoceramic actuator embedded in or bonded to an elastic medium under inplane mechanical and electrical loadings. The actuator is characterized by an electroelastic line model with the poling direction being perpendicular to its length. The theoretical formulations, governing this electromechanically coupled problem, are based upon the use of singular integral equations in terms of an interfacial shear stress. A square-root singularity of the resulting shear stress is found at the tips of the actuator. A new shear stress singularity factor (SSSF) was then obtained by solving these singular integral equations using Chebyshev polynomial expansions. Typical examples are provided to show the effect of the geometry of the actuator, the material combination and interfacial debonding upon the shear stress singularity factor.

Finite element modelling of shot-peening residual stresses

Abstract Shot-peening is a cold working process used to impart compressive residual stresses in the exposed surface layers. Despite its importance to the aerospace and automobile industries, little or no attention has been devoted to the accurate modelling of the process. It is therefore the purpose of this study, which is part of an extensive research program, to conduct dynamic elasto-plastic analysis of the process using a single shot. Specifically, it is desired to evaluate the effect of shot velocity, size and shape upon the time variations of the contact force, the velocity history, the plastic zone development and its growth and unloading residual stresses.

On the dynamic propagation of a finite crack in functionally graded materials

This article provides a comprehensive theoretical investigation of the singular behaviour of a propagating crack in a functionally graded material (FGM) with spatially varying elastic properties under plane elastic deformation. The analytical formulations are developed in terms of Fourier transforms and the solution of the resulting singular integral equations by using Chebyshev polynomials. In this study, we examine the effect of the gradient of material properties and the speed of crack propagation upon the stress intensity factors, the strain energy release rate and the crack opening displacement. The results reveal that although the singular stress field around the tip of a crack in this FGM is governed by the traditional square root singularity, significant discrepancy in the local stress field exist between it and a homogeneous solid. This indicates that the presence of a gradient in the mechanical properties affects the local stress distribution significantly and, ultimately, the fracture behaviour of the solid.

Interfacial debonding of a circular inhomogeneity in piezoelectric materials

A generalized and mathematically rigorous model is developed to treat the partially-debonded circular inhomogeneity problem in piezoelectric materials under antiplane shear and in plane electric field using the complex variable method. The principle of analytical continuation and the complex series expansion method were employed to reduce the formulations into Riemann-Hilbert problems. This enabled the explicit determination of the complex potentials inside the inhomogeneity and the matrix. The resulting closed form expressions were then used to obtain the energy release rate for several interesting cases involving partial-debonding at the inhomogeneity-matrix interface.

On the dynamic crack propagation in an interface with spatially varying elastic properties

This article provides a comprehensive theoretical treatment of a finite crack propagating in an interfacial layer with spatially varying elastic properties under antiplane loading condition. The theoretical formulations governing the steady state solution are based upon the use of an integral transform technique. The resulting dynamic stress intensity factor of the propagating cracks is obtained by solving the appropriate singular integral equations, using Chebyshev polynomials, for different inhomogeneous materials. Numerical examples are provided to verify the technique and to show the effect of the thickness of the interfacial layer and the material properties upon the dynamic stress intensity factor of the crack and the associated singularity transition.