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.

Hyaline tissue of thermally unaltered conodont elements and the enamel of vertebrates

Comparison of the ultrastructure of the hyaline tissue of conodont elements and the enamel of vertebrates provides little support for a close phylogenetic relationship between conodonts and vertebrates. Transmission and scanning electron microscopy shows that the mineralised component of the hyaline tissue of Panderodus and of Cordylodus elements consists of large, flat, oblong crystals, arranged in layers that run parallel to the long axis of the conodont. Enamel in the dentition of a living vertebrate, the lungfish Neoceratodus forsteri, has crystals of calcium hydroxyapatite, arranged in layers, and extending in groups from the dentine-enamel junction; the crystals are slender, elongate spicules perpendicular to the surface of the tooth plate, Similar crystal arrangements to those of lungfish are found in other vertebrates, but none resembles the organisation of the hyaline tissue of conodont elements, The crystals of hydroxyapatite in conodont hyaline tissue are exceptionally large, perpendicular or parallel to the surface of the element, with no trace of prisms, unlike the protoprismatic radial crystallite enamel of fish teeth and scales, or the highly organised prismatic enamel of mammals.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

An investigation of the effect of powder on the impact characteristics between a ball and a plate using free falling experiments

The study of the mechanisms of mechanical alloying requires knowledge of the impact characteristics between the ball and vial in the presence of milling powders. In this paper, foe falling experiments have br cn used to investigate the characteristics of impact events involved in mechanical milling. The effects of milling conditions, including impact velocity, ball size and powder thickness. on the coefficient of restitution and impact force are studied. It is found that the powder has a significant influence on the impact process due to its porous structure. This effect can be demonstrated using a modified Kelvin model. This study also confirms that the impact force is a relevant parameter for characterising the impact event due to its sensitivity to the milling conditions. (C) 1998 Elsevier Science S.A.

FRA10B structure reveals common elements in repeat expansion and chromosomal fragile site genesis

A common mechanism for chromosomal fragile site genesis is not yet apparent. Folate-sensitive fragile sites are expanded p(CCG)n repeats that arise from longer normal alleles. Distamycin A or bromodeoxyuridine-inducible fragile site FRA16B is an expanded AT-rich similar to 33 bp repeat; however, the relationship between normal and fragile site alleles is not known. Here, we report that bromodeoxyuridine-inducible, distamycin A-insensitive fragile site FRA10B is composed of expanded similar to 42 bp repeats. Differences in repeat motif length or composition between different FRA10B families indicate multiple independent expansion events. Some FRA10B alleles comprise a mixture of different expanded repeat motifs. FRA10B fragile site and long normal alleles share flanking polymorphisms. Somatic and intergenerational FRA10B repeat instability analogous to that found in expanded trinucleotide repeats supports dynamic mutation as a common mechanism for repeat expansion.

Evolution of three-dimensional folds for a non-Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

Large amplitude folding in finely layered viscoelastic rock structures

We analyze folding phenomena in finely layered viscoelastic rock. Fine is meant in the sense that the thickness of each layer is considerably smaller than characteristic structural dimensions. For this purpose we derive constitutive relations and apply a computational simulation scheme (a finite-element based particle advection scheme; see MORESI et al., 2001) suitable for problems involving very large deformations of layered viscous and viscoelastic rocks. An algorithm for the time integration of the governing equations as well as details of the finite-element implementation is also given. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered plate. The domain is compressed along the layer axis by prescribing velocities along the sides. First, for the viscous limit we consider the response to a series of harmonic perturbations of the director orientation. The Fourier spectra of the initial folding velocity are compared for different viscosity ratios. Turning to the nonlinear regime we analyze viscoelastic folding histories up to 40% shortening. The effect of layering manifests itself in that appreciable buckling instabilities are obtained at much lower viscosity ratios (1:10) as is required for the buckling of isotropic plates (1:500). The wavelength induced by the initial harmonic perturbation of the director orientation seems to be persistent. In the section of the parameter space considered here elasticity seems to delay or inhibit the occurrence of a second, larger wavelength. Finally, in a linear instability analysis we undertake a brief excursion into the potential role of couple stresses on the folding process. The linear instability analysis also provides insight into the expected modes of deformation at the onset of instability, and the different regimes of behavior one might expect to observe.

Mantle convection modeling with viscoelastic/brittle lithosphere: Numerical methodology and plate tectonic modeling

The earth's tectonic plates are strong, viscoelastic shells which make up the outermost part of a thermally convecting, predominantly viscous layer. Brittle failure of the lithosphere occurs when stresses are high. In order to build a realistic simulation of the planet's evolution, the complete viscoelastic/brittle convection system needs to be considered. A particle-in-cell finite element method is demonstrated which can simulate very large deformation viscoelasticity with a strain-dependent yield stress. This is applied to a plate-deformation problem. Numerical accuracy is demonstrated relative to analytic benchmarks, and the characteristics of the method are discussed.

Effect of sodium dodecylbenzene sulfonate on the motion of three-phase contact lines on the Wilhelmy plate surface

The combined approach of the molecular-kinetic and hydrodynamic theories for description of the motion of three-phase gas-liquid-solid contact lines has been examined using the Wilhelmy plate method. The whole dynamic meniscus has been divided into molecular, hydrodynamic, and static-like regions. The Young-Laplace equation and the molecular-kinetic and hydrodynamic dewetting theories have been applied to describe the meniscus profiles and contact angle. The dissipative forces accompanying the dynamic dewetting have also been investigated. The experiments with a Wilhelmy plate made from an acrylic polymer sheet were carried out using a computerized apparatus for contact angle analysis (OCA 20, DataPhysics, Germany). The extrapolated dynamic contact angle versus velocity of the three-phase contact line for Milli-Q water and 5 x 10(-4) M SDBS solution was experimentally obtained and compared with the combined MHD models with low and moderate Reynolds numbers. The models predict similar results for the extrapolated contact angle. SDBS decreases the equilibrium contact angle and increases the molecular jumping length but does not affect the molecular frequency significantly. The hydrodynamic deformation of the meniscus, viscous dissipation, and friction were also influenced by the SDBS surfactant. (c) 2005 Elsevier Inc. All rights reserved.

Identification of novel non-autonomous CemaT transposable elements and evidence of their mobility within the C. elegans genome

We describe here two new transposable elements, CemaT4 and CemaT5, that were identified within the sequenced genome of Caenorhabditis elegans using homology based searches. Five variants of CemaT4 were found, all non-autonomous and sharing 26 bp inverted terminal repeats (ITRs) and segments (152-367 bp) of sequence with similarity to the CemaT1 transposon of C. elegans. Sixteen copies of a short, 30 bp repetitive sequence, comprised entirely of an inverted repeat of the first 15 bp of CemaT4's ITR, were also found, each flanked by TA dinucleotide duplications, which are hallmarks of target site duplications of mariner-Tc transposon transpositions. The CemaT5 transposable element had no similarity to maT elements, except for sharing identical ITR sequences with CemaT3. We provide evidence that CemaT5 and CemaT3 are capable of excising from the C. elegans genome, despite neither transposon being capable of encoding a functional transposase enzyme. Presumably, these two transposons are cross-mobilised by an autonomous transposon that recognises their shared ITRs. The excisions of these and other non-autonomous elements may provide opportunities for abortive gap repair to create internal deletions and/or insert novel sequence within these transposons. The influence of non-autonomous element mobility and structural diversity on genome variation is discussed.

Eutectic modification and microstructure development in Al-Si alloys

Recent increasing applications for cast Al-Si alloys are particularly driven by the need for lightweighting components in the automotive sector. To improve mechanical properties, elements such as strontium, sodium and antimony can be added to modify the eutectic silicon from coarse and plate-like to fine and fibrous morphology. It is only recently being noticed that the morphological transformation resulting from eutectic modification is also accompanied by other, equally significant, but often unexpected changes. These changes can include a 10-fold increase in the eutectic grain size, redistribution of low-melting point phases and porosity as well as surface finish, consequently leading to variations in casting quality. This paper shows the state-of-the-art in understanding the mechanism of eutectic nucleation and growth in Al-Si alloys, inspecting samples, both quenched and uninterrupted, on the macro, micro and nano-scale. It shows that significant variations in eutectic nucleation and growth dynamics occur in AI-Si alloys as a function of the type and amount of modifier elements added. The key role of AIP particles in nucleating silicon is demonstrated. (c) 2005 Elsevier B.V. All rights reserved.