A director theory for visco-elastic folding instabilities in multilayered rock

A model for finely layered visco-elastic rock proposed by us in previous papers is revisited and generalized to include couple stresses. We begin with an outline of the governing equations for the standard continuum case and apply a computational simulation scheme suitable for problems involving very large deformations. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. The standard continuum solution becomes unstable for extreme values of the shear/normal viscosity ratio. The instability is a consequence of the neglect of the bending stiffness/viscosity in the standard continuum model. We suggest considering these effects within the framework of a couple stress theory. Couple stress theories involve second order spatial derivatives of the velocities/displacements in the virtual work principle. To avoid C-1 continuity in the finite element formulation we introduce the spin of the cross sections of the individual layers as an independent variable and enforce equality to the spin of the unit normal vector to the layers (-the director of the layer system-) by means of a penalty method. We illustrate the convergence of the penalty method by means of numerical solutions of simple shears of an infinite layer for increasing values of the penalty parameter. For the shear problem we present solutions assuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. For high values of the ratio of the normal-to the shear viscosity the deformation concentrates in thin bands around to the layer surfaces. The effect of couple stresses on the evolution of folds in layered structures is also investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.

Petrodentine in derived dipnoan tooth plates

Most lungfish tooth plates, that are arranged in radiating ridges derived from the fusion of separate cusps in young juveniles, are based on a framework of enamel, mantle dentine and bone that encloses a mass of specialized dentines forming the occlusal surface. In most taxa, the specialized dentines are interdenteonal and circumdenteonal dentine, but a few derived genera have petrodentine as well. Petrodentine, as originally defined, describes a specific form of hypermineralized dentine in adult tooth plates of the Recent African lungfish Protopterus. The ontogeny of fossil and Recent lungfish tooth plates demonstrates that petrodentine is derived by continuous enhancement of the hard tissue of the primary core of the initially isolated cusps of the tooth plate, and that interdenteonal dentine with denteons of circumdenteonal dentine is a secondary development in the tooth plate around and below the first formed cusps of the ridges. In dipnoans that lack petrodentine in adults the primary core of the cusps is not enhanced, but is removed by wear. The hard tissues of the dipnoan tooth plate provide useful characters for defining dipnoan taxa, as do the differing arrangements of the tissues in each species. Details of the arrangement of the enclosed specialized dentines are surprisingly variable among genera, and are significant for the structure and function of the tooth plate. Little regularity of structure is discernible in the histology of tooth plates of early dipnoans, but derived genera have more predictable structure. Consistent with other uniquely dipnoan characters, like the composition of the dermal skull, an evolutionary progression is evident within the group in the fine structure of the dentition, and, as with the bones of the dermal skull, little similarity is demonstrable between the dentines of dipnoans and tetrapods.

Analysis of acousto-ultrasonic characteristics for contact-type transducers coupled to composite laminated plates

The acousto-ultrasonic (AU) input-output characteristics for contact-type transmitting and receiving transducers coupled to composite laminated plates are considered in this paper. Combining a multiple integral transform method, an ordinary discrete layer theory for the laminates and some simplifying assumptions for the electro-mechanical transduction behaviour of the transducers, an analytical solution is developed which can deal with all the wave processes involved in the AU measurement system, i.e, wave generation, wave propagation and wave reception. The spectral response of the normal contact pressure sensed by the receiving transducer due to an arbitrary input pulse excited by the transmitting transducer is obtained. To validate the new analytical-numerical spectral technique in the low-frequency regime, the results are compared with Mindlin plate theory solutions. Based on the analytical results, numerical calculations are carried out to investigate the influence of various external parameters such as frequency content of the input pulse, transmitter/receiver spacing and transducer aperture on the output of the measurement system. The results show that the presented analytical-numerical procedure is an effective tool for understanding the input-output characteristics of the AU technique for laminated plates. (C) 2001 Elsevier Science Ltd. All rights reserved.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

Modelling of Lamb waves in composite laminated plates excited by interdigital transducers

The technique of permanently attaching interdigital transducers (IDT) to either flat or curved structural surfaces to excite single Lamb wave mode has demonstrated great potential for quantitative non-destructive evaluation and smart materials design, In this paper, the acoustic wave field in a composite laminated plate excited by an IDT is investigated. On the basis of discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the surface velocity response of the plate due to the IDTs excitation. In this approach, the frequency spectrum and wave number spectrum of the output of IDT are obtained directly. The corresponding time domain results are calculated by applying a standard inverse fast Fourier transformation technique. Numerical examples are presented to validate the developed method and show the ability of mode selection and isolation. A new effective way of transfer function estimation and interpretation is presented by considering the input wave number spectrum in addition to the commonly used input frequency spectrum. The new approach enables the simple physical evaluation of the influences of IDT geometrical features such as electrode finger widths and overall dimension and excitation signal properties on the input-output characteristics of IDT. Finally, considering the convenience of Mindlin plate wave theory in numerical computations as well as theoretical analysis, the validity is examined of using this approximate theory to design IDT for the excitation of the first and second anti-symmetric Lamb modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Single mode Lamb waves in composite laminated plates generated by piezoelectric transducers

The technique of permanently attaching piezoelectric transducers to structural surfaces has demonstrated great potential for quantitative non-destructive evaluation and smart materials design. For thin structural members such as composite laminated plates, it has been well recognized that guided Lamb wave techniques can provide a very sensitive and effective means for large area interrogation. However, since in these applications multiple wave modes are generally generated and the individual modes are usually dispersive, the received signals are very complex and difficult to interpret. An attractive way to deal with this problem has recently been introduced by applying piezoceramic transducer arrays or interdigital transducer (IDT) technologies. In this paper, the acoustic wave field in composite laminated plates excited by piezoceramic transducer arrays or IDT is investigated. Based on dynamic piezoelectricity theory, a discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the input impedance characteristics of the transducer and the surface velocity response of the plate. The method enables the quantitative evaluation of the influence of the electrical characteristics of the excitation circuit, the geometric and piezoelectric properties of the transducer array, and the mechanical and geometrical features of the laminate. Numerical results are presented to validate the developed method and show the ability of single wave mode selection and isolation. The results show that the interaction between individual elements of the piezoelectric array has a significant influence on the performance of the IDT, and these effects can not be neglected even in the case of low frequency excitation. It is also demonstrated that adding backing materials to the transducer elements can be used to improve the excitability of specific wave modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

The effect of latent heat of fusion on heat transfer in fluidized-bed coating of thin plates

This paper presents a numerical study of fluidized-bed coating on thin plates using an orthogonal collocation technique. Inclusion of the latent heat of fusion term in the boundary conditions of the mathematical model accounts for the fact that some polymer powders used in coating may be partially crystalline. Predictions of coating thickness on flat plates were made with actual polymers used in fluidized-bed coating. Reasonably good agreement between numerical predictions of the coating thickness and experimental coating data of Richart was obtained for steel panels preheated to 316 degreesC. A good agreement was also obtained between numerical predictions and our coating thickness data for nylon-11 and polyethylene powders. Predicted coating thickness for polyethylene powder on flat plates were obtained with values of heat transfer coefficient closer to those obtained from our experiments. (C) 2002 Elsevier Science B.V. All rights reserved.

Dental and skeletal pathology in lungfish jaws and tooth plates

Many lungfish of the tooth plated lineage, both fossil and living, are affected by dental and skeletal pathologies including dental caries, abscesses and cysts within the bone or tooth plate, osteopenia, bone hypertrophy, and malocclusion. These conditions, while influenced in part by structural relationships of soft and hard tissues in the tooth plates, jaw bones and surrounding oral tissues, can also be used as indicators of the kind of environment inhabited by the fish. The disease processes have specific structural consequences, related either to the pathology or to attempts to heal the damage, and usually alter the form and function of the tooth plate or bone. Consequently they can be distinguished from postmortem diagenetic or taphonomic effects, which alter the structure in less specific ways and show no sign of healing. Dental caries, the most common pathological condition in dipnoan dentitions, is recognisable in lungfish from the Devonian of Western Australia, the Tertiary of South Australia and the Northern Territory and from living lungfish in south east Queensland. Other pathologies have a more sporadic occurrence.

Ultrastructure of developing tooth plates in the Australian lungfish, Neoceratodus forsteri (Osteichthyes : Dipnoi)

While the lungfish dentition is partially understood as far as morphology and light microscopic structure is concerned, the ultrastructure is not. Each tooth plate is associated with a dental lamina that develops from the inner layer of endodermal cells that form the oral epithelium. Dentines, bone and cartilage of the jaws differentiate from mesenchyme cells aggregating beneath the oral endothelium. Enamel, in the developing and in the mature form, has similarities to that of other early vertebrates, but unusual characters appear as development proceeds. Ameloblasts are capable of secreting enamel, and, with mononuclear osteoclasts, of remodelling the bone below the tooth plate. The forms of dentine, all based largely on an extracellular matrix of collagen and mineralised with biological apatite, differ from each other and from the underlying bone in the ultrastructure of associated cells and in the mineralised extracellular matrices produced. Cell processes emerging from the odontoblasts and from the osteoblasts vary in length, degree of branching and of anastomoses between the processes, although all of the cell types have large amounts of rough endoplasmic reticulum. Mineralisation of the extracellular matrices varies among the enamel, dentines and bone in the tooth plate. In addition, the development of the hard tissues of the tooth plates indicates that many of the similarities in fine structure of the dentition in lungfish, to tissues in other fish and amphibia, apparent early in development, disappear as the dentition matures. (C) 2003 Elsevier Ltd. All rights reserved.

Developmental anomalies in the tooth plates and jaw bones of lungfish

Lungfish of the tooth-plated lineage, both fossil and living, may be affected by alterations in the permanent tooth plates and associated jaw bones as they grow. In a few taxa, the unusual structures may be so common that they must be considered as normal for those species, or as a variation of the normal condition. In others the condition is rare, affecting only a few individuals. Variations, or anomalies, may appear in the growing tissues of the lungfish tooth plate at any time in the life cycle, although they usually appear early in development. Once the changes appear, they persist in the dentition. The altered structures include divided or intercalated ridges, short ridge anomaly, changes in the shape, number and position of cusps, pattern loss, and fused ridges or cusps. Criteria used to distinguish alteration from normal conditions are the incidence of the character in the population, the associated changes in the jaw bone, and the position of the altered structure in the tooth plate. The occurrence of similar changes across a wide range of different species suggests that they may have a genetic cause, especially when they are a rare occurrence in most taxa, but common enough to be a part of the normal variation in others. Prevalence of related anomalies throughout the history of the group suggests that dipnoans of the tooth-plated lineage are closely related, despite significant differences in morphology, microstructure, and function of the denfitions.

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.

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.

Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element

Based on the refined non-conforming element method for geometric nonlinear analysis, a refined nonlinear non-conforming triangular plate element is constructed using the Total Lagrangian (T.L.) and the Updated Lagrangian (U.L.) approach. The refined nonlinear non-conforming triangular plate element is based on the Allman's triangular plane element with drilling degrees of freedom [1] and the refined non-conforming triangular plate element RT9 [2]. The element is used to analyze the geometric nonlinear behavior of plates and the numerical examples show that the refined non-conforming triangular plate element by the T.L. and U.L. approach can give satisfactory results. The computed results obtained from the T.L. and U.L. approach for the same numerical examples are somewhat different and the reasons for the difference of the computed results are given in detail in this paper. © 2003 Elsevier Science Ltd. All rights reserved.

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy's third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.