Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders

This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoclasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work. (C) 2003 Elsevier Science Ltd. All rights reserved.

Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading

In this paper, we examine the postbuckling behavior of functionally graded material FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, in-plane forces, and constant applied actuator voltage. A Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations. To account for the transverse shear strains, the Reddy higher-order shear deformation plate theory is employed. The bifurcation-type thermo-mechanical buckling of fully clamped plates, and the postbuckling behavior of plates with more general boundary conditions subject to various thermo-electro-mechanical loads, are discussed in detail. Parametric studies are also undertaken, and show the effects of applied actuator voltage, in-plane forces, volume fraction exponents, temperature change, and the character of boundary conditions on the buckling and postbuckling characteristics of the plates. (C) 2003 Elsevier Science Ltd. All rights reserved.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.

Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates

This paper presents a large amplitude vibration analysis of pre-stressed functionally graded material (FGM) laminated plates that are composed of a shear deformable functionally graded layer and two surface-mounted piezoelectric actuator layers. Nonlinear governing equations of motion are derived within the context of Reddy's higher-order shear deformation plate theory to account for transverse shear strain and rotary inertia. Due to the bending and stretching coupling effect, a nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the plate that is subjected to uniform temperature change, in-plane forces and applied actuator voltage. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed FGM laminated plates are derived. A semi-analytical method that is based on one-dimensional differential quadrature and Galerkin technique is proposed to predict the large amplitude vibration behavior of the laminated rectangular plates with two opposite clamped edges. Linear vibration frequencies and nonlinear normalized frequencies are presented in both tabular and graphical forms, showing that the normalized frequency of the FGM laminated plate is very sensitive to vibration amplitude, out-of-plane boundary support, temperature change, in-plane compression and the side-to-thickness ratio. The CSCF and CFCF plates even change the inherent hard-spring characteristic to soft-spring behavior at large vibration amplitudes. (C) 2003 Elsevier B.V. All rights reserved.

A relative gradient theory for layered materials

It is possible to remedy certain difficulties with the description of short wave length phenomena and interfacial slip in standard models of a laminated material by considering the bending stiffness of the layers. If the couple or moment stresses are assumed to be proportional to the relative deformation gradient, then the bending effect disappears for vanishing interface slip, and the model correctly reduces to an isotropic standard continuum. In earlier Cosserat-type models this was not the case. Laminated materials of the kind considered here occur naturally as layered rock, or at a different scale, in synthetic layered materials and composites. Similarities to the situation in regular dislocation structures with couple stresses, also make these ideas relevant to single slip in crystalline materials. Application of the theory to a one-dimensional model for layered beams demonstrates agreement with exact results at the extremes of zero and infinite interface stiffness. Moreover, comparison with finite element calculations confirm the accuracy of the prediction for intermediate interfacial stiffness.

Finite-difference time-domain-based studies of MRI pulsed field gradient-induced eddy currents inside the human body

In modern magnetic resonance imaging (MRI), patients are exposed to strong, rapidly switching magnetic gradient fields that, in extreme cases, may be able to elicit nerve stimulation. This paper presents theoretical investigations into the spatial distribution of induced current inside human tissues caused by pulsed z-gradient fields. A variety of gradient waveforms have been studied. The simulations are based on a new, high-definition, finite-difference time-domain method and a realistic inhomogeneous 10-mm resolution human body model with appropriate tissue parameters. it was found that the eddy current densities are affected not only by the pulse sequences but by many parameters such as the position of the body inside the gradient set, the local biological material properties and the geometry of the body. The discussion contains a comparison of these results with previous results found in the literature. This study and the new methods presented herein will help to further investigate the biological effects caused by the switched gradient fields in a MRI scan. (C) 2002 Wiley Periodicals, Inc.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Thermal effects in the evolution of initially layered mantle material

A simplified model for anisotropic mantle convection based on a novel class of rheologies, originally developed for folding instabilities in multilayered rock (MUHLHAUS et al., 2002), is extended ¨ through the introduction of a thermal anisotropy dependent on the local layering. To examine the effect of the thermal anisotropy on the evolution of mantle material, a parallel implementation of this model was undertaken using the Escript modelling toolkit and the Finley finite-element computational kernel (DAVIES et al., 2004). For the cases studied, there appears too little if any effect. For comparative purposes, the effects of anisotropic shear viscosity and the introduced thermal anisotropy are also presented. These results contribute to the characterization of viscous anisotropic mantle convection subject to variation in thermal conductivities and shear viscosities.

Flow and axial dispersion simulation for traveling axisymmetric Taylor vortices

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

A simple design methodology for elliptical cross-section, transverse, asymmetric, head gradient coils for MRI

A simple design process for the design of elliptical cross-section, transverse gradient coils for use in magnetic resonance imaging (MRI) is presented. This process is based on a flexible stochastic optimization method and results in designs of high linearity and efficiency with low switching times. A design study of a shielded, transverse asymmetric elliptical coil set for use in neural imaging is presented and includes the minimization of the torques experienced by the gradient set.

A sponge/dinoflagellate association in the haplosclerid sponge Haliclona sp.: cellular origin of cytotoxic alkaloids by Percoll density gradient fractionation

Light-microscopic and electron-microscopic studies of the tropical marine sponge Haliclona sp. (Or der: Haplosclerida Family: Haliclonidae) from Heron Island, Great Barrier Reef, have revealed that this sponge is characterized by the presence of dinoflagellates and by nematocysts. The dinoflagellates are 7-10 mu m in size, intracellular, and contain a pyrenoid with a single stalk, whereas the single chloroplast is branched, curved, and lacks grana. Mitochondria are present, and the nucleus is oval and has distinct chromosomal structure. The dinoflagellates are morphologically similar to Symbiodinium microadriaticum, the common intracellular symbiont of corals, although more detailed biochemical and molecular studies are required to provide a precise taxonomic assignment. The major sponge cell types found in Haliclona sp, are spongocytes, choanocytes, and archaeocytes; groups of dinoflagellates are enclosed within large vacuoles in the archaeocytes. The occurrence of dinoflagellates in marine sponges has previously been thought to be restricted to a small group of sponges including the excavating hadromerid sponges; the dinoflagellates in these sponges are usually referred to as symbionts. The role of the dinoflagellates present in Haliclona sp. as a genuine symbiotic partner requires experimental investigation. The sponge grows on coral substrates, from which it may acquire the nematocysts, and shows features, such as mucus production, which are typical of some excavating sponges. The cytotoxic alkaloids, haliclonacyclamines A and B, associated with Haliclona sp. are shown by Percoll density gradient fractionation to be localized within the sponge cells rather than the dinoflagellates. The ability to synthesize bioactive compounds such as the haliclonacyclamines may help Haliclona sp. to preserve its remarkable ecological niche.

Analysis of pore-fluid pressure gradient and effective vertical-stress gradient distribution in layered hydrodynamic systems

A theoretical analysis is carried out to investigate the pore-fluid pressure gradient and effective vertical-stress gradient distribution in fluid saturated porous rock masses in layered hydrodynamic systems. Three important concepts, namely the critical porosity of a porous medium, the intrinsic Fore-fluid pressure and the intrinsic effective vertical stress of the solid matrix, are presented and discussed. Using some basic scientific principles, we derive analytical solutions and explore the conditions under which either the intrinsic pore-fluid pressure gradient or the intrinsic effective vertical-stress gradient can be maintained at the value of the lithostatic pressure gradient. Even though the intrinsic pore-fluid pressure gradient can be maintained at the value of the lithostatic pressure gradient in a single layer, it is impossible to maintain it at this value in all layers in a layered hydrodynamic system, unless all layers have the same permeability and porosity simultaneously. However, the intrinsic effective vertical-stress gradient of the solid matrix can be maintained at a value close to the lithostatic pressure gradient in all layers in any layered hydrodynamic system within the scope of this study.

On uniquely determining cell-wall material properties with the compression experiment

A finite element model (FEM) of the cell-compression experiment has been developed in dimensionless form to extract the fundamental cell-wall-material properties (i.e. the constitutive equation and its parameters) from experiment force-displacement data. The FEM simulates the compression of a thin-walled, liquid-filled sphere between two flat surfaces. The cell-wall was taken to be permeable and the FEM therefore accounts for volume loss during compression. Previous models assume an impermeable wall and hence a conserved cell volume during compression. A parametric study was conducted for structural parameters representative of yeast. It was shown that the common approach of assuming reasonable values for unmeasured parameters (e.g. cell-wall thickness, initial radial stretch) can give rise to nonunique solutions for both the form and constants in the cell-wall constitutive relationship. Similarly, measurement errors can also lead to an incorrectly defined cell-wall constitutive relationship. Unique determination of the fundamental wall properties by cell compression requires accurate and precise measurement of a minimum set of parameters (initial cell radius, initial cell-wall thickness, and the volume loss during compression). In the absence of such measurements the derived constitutive relationship may be in considerable error, and should be evaluated against its ability to predict the outcome of other mechanical experiments. (C) 1998 Elsevier Science Ltd. All rights reserved.