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This study investigates the electromechanical performance of piezoelectric sandwich plates both numerically and experimentally. The effect of different inner design parameters, namely the length-to-thickness, core-to-face thickness, boundary conditions and aspect ratio on both the eigenfrequency and electric potential attributes is assessed. Moreover, vibration amplitude-dependent effects are investigated. Polymer-based, sandwich plates are additively manufactured (AM) and commercially available PZT layers are surface-bonded and experimentally probed. AM smart plates are found to yield comparable eigenfrequency properties with the ones reported for fiber-reinforced smart sandwich composites. Low length-to-thickness, low core-to-face, and rectangular rather than square designs favor the electric potential performance. [ABSTRACT FROM AUTHOR]

AbstractThis article proposes a rigorous mathematical justification of the derivation of the governing equations of any beam and plate theory by the three three-dimensional (3D) elasticity equations. This is done by the application of the integration by part theorem via weight residual-like methods. The Fis polynomials (subscripts i and s denote the i-direction and the generic s-term of the displacement expansion uis, respectively) related to a given beam/plate theory are used as weight functions for each of the displacement unknown. To show how the method works a number of simple problems are discussed. These are related to the equilibrium equations and boundary conditions of bending beams according to shear deformation theory. Three methods for obtaining these equations are compared in some detail. The first two are the well-known methods used in mechanics of deformable bodies: (1) use of the Principle of Virtual Displacements; (2) use of the six cardinal ‘Newton’ equations of statics. The third method coincides with the one proposed and rigorously justified in this paper which is (3) the direct integration of the equations of 3D elasticity. Beam theories based on Lagrange polynomials are used as well. The latter makes it possible to immediately develop theories for layered beams and obtain so-called ‘layer-wise’ models, which are only applied here to the case of sandwich structures. Three appendixes discuss: A – The problem in which the derivative of one of the unknowns appears among the unknowns, as is the case with the Euler–Bernoulli theory; B – The extension to dynamics; C-Simple derivation of constitutive equations and related closed-form solution via Navier method. [ABSTRACT FROM AUTHOR]

In this present study, we are interested in the use of a precise theory of shear deformation for the buckling analysis of plates with functional gradation simply supported such as the refined theory of plates with four variables. Several parameters of comparison have been used, dimensional and nondimensional. The displacement field is compatible with this study, the nonuse of shear correction factors is satisfied, and the choice of material is very precise in such a way are variable according to the thickness of the plate and on the other hand to make comparison with other researcher and confirms that this study gives precise results and converges. The transverse shear stresses vary through the thickness, the results found is also studied and discussed. [ABSTRACT FROM AUTHOR]

The three-dimensional bending behavior of a viscoelastic functionally graded material (FGM) layer embedded between piezoelectric layers and subjected to an electric field as well as a uniform transverse pressure is studied. An analytical solution is computed for a simply supported viscoelastic smart FGM plate using the state space technique along the thickness direction and a Fourier expansion along the in-plane coordinates. The governing differential equations in the time domain are transformed to the Laplace domain, solved in the Laplace domain, and transformed back to the time domain using the inverse Laplace transform. In the present study, the relaxation modulus of the FGM layer is assumed in the form of a Prony series, and it varies according to the power law in the thickness direction. The validity of the proposed approach is assessed by comparison of the numerical results of the approach with those of published works in the literature. The effects of geometric dimensions, electromechanical loads, and relaxation time constant on the behavior of the smart plate are investigated. [ABSTRACT FROM AUTHOR]

It is shown that the classical theories of micropolar plates and shells can be obtained using the Carrera Unified Formulation (CUF) approach as a special case of approximation. The theory of micropolar plates and shells based on the hypotheses of Timoshenko–Mindlin and Kirchhoff–Love is considered in detail. The stress and strain tensors, as well as the displacement and rotation vectors are presented as linear expansion along the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including the generalized Hooke's law) were transformed into the corresponding equations for the expansion coefficients in the coordinates of the shell thickness. All equations of the theory of micropolar plates and shells based on the hypotheses of Timoshenko–Mindlin and Kirchhoff–Love are presented here. Micropolar plates in Cartesian and polar coordinates, as well as micropolar shells of cylindrical, conical, spherical and shallow geometry are considered in detail. The equations obtained can be used to calculate the stress-strain state and simulate thin-walled structures at the macro, micro and nanoscale, taking into account the micropolar stresses and the effects of rotation. [ABSTRACT FROM AUTHOR]

Starting from the variational principle of virtual power for the three-dimensional equations of the micropolar theory of elasticity and using generalized series in terms of the plate thickness coordinates a new higher order models of orthotropic micropolar plates have been developed here for the first time. Following carrera unified formulation, the stress and strain tensors, as well as the vectors of displacements and rotation, have been expanded into series in terms of the plate thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the series expansion on the plate thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the series expansion of the plate thickness coordinates have been obtained in the same way as in the classical theory of elasticity. All equations for the higher order theory of micropolar plates have been developed and presented here. The case of complete linear expansion has been considered in detail and compared with the theories based on shear deformation and Kirchhoff hypothesis. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

Starting from the variational principle of virtual power for the 3-D equations of the micropolar theory of elasticity in orthogonal curvilinear coordinates and using generalized series in terms of the plate thickness coordinates a new higher order model of orthotropic micropolar plates and shells have been developed here. Following Carrera Unified Formulation (CUF), the stress and strain tensors, as well as the vectors of displacements and rotation, have been expanded into series in terms of the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the series expansion on the plate thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the series expansion of the shell thickness coordinates have been obtained in the same way as in the classical theory of elasticity. All equations for the higher order theory of micropolar plates and shells have been developed and presented here. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

New higher-order models of orthotropic micropolar plates and shells have been developed using Carrera Unified Formulation (CUF). Here, a complete linear expansion case (CLEC) has been considered in detail. The stress and strain tensors, as well as the vectors of displacements and rotation, have been presented as linear expansion in terms of the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the expansion on the shell thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the expansion of the shell thickness coordinates has been obtained. All equations for the case of CLEC theory of micropolar plates and shells have been developed and presented here. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

The dynamics of elastic functionally graded waveguides with symmetric through-thickness structure is considered on the background of the new formulation of the Nth-order plate theory. The general plate model is based on the Lagrangian formalism of analytical dynamics and the dimensional reduction approach combined with the biorthogonal expansion technique applied to the spatial distribution of the displacement vector field. The use of compact basis is shown, the normal wave propagation in a plane waveguide is modeled, and the convergence is analyzed using the isotropic homogeneous plate as a test example. Finally, the same formulation is used to model the normal wave dispersion in functionally graded plates. The proposed method is a base for the investigation of the effect of uncertainties and for the solution of inverse coefficient problems for functionally graded thin-walled structures. [ABSTRACT FROM AUTHOR]

A recently proposed tuning method for resistive-inductive (RL) shunts is implemented in a commercial finite element (FE) code (ANSYS®). A main result of the paper is therefore the consistent formulation of the tuning method in terms of variables directly available as solutions in any commercial FE code: The two natural frequencies associated with short- and open-circuit (SC and OC) electrodes and a modal charge obtained as the electrical SC reaction force. An alternative method is based on quasi-static solutions with SC and OC electrodes, convenient for both numerical analysis and experiments. The proposed shunt tuning method is suitable for implementation in any commercial FE software supporting electromechanical analysis and ANSYS® has been used to assess its accuracy for a piezoelectric smart plate benchmark problem. The method is finally extended to multiple piezoceramic patches, placed symmetrically on the structure and shunted to a single RL network, whereby more vibration modes can be effectively controlled for the specific plate problem. [ABSTRACT FROM AUTHOR]

This work is devoted to the bending analysis of functionally graded piezoelectric (FGP) material plate by using a simple quasi-3D sinusoidal shear deformation theory under simply supported edge conditions. The governing equations and boundary conditions are derived by using the principle of virtual work. The impact of piezoelectric, electric loading, and gradient index on the displacement, electric displacement, electric potential, and stresses are explored numerically presented and discussed in detail. To check the accuracy and validity of bending results obtained from this analysis of FGP plates, results are compared with the analytical solution obtained by 3D, quasi-3D, and higher order shear deformation theories. Parametric studies are then performed to examine the effects of the thickness of the plate and the electric field on the overall electro-mechanical response of the FGP plates. The presented results are useful in design processes of smart structures and analysis from piezoelectric materials. [ABSTRACT FROM AUTHOR]

In this work we study, from the numerical point of view, a thermoelastic problem involving a microstretch plate. The variational problem is written as a linear system composed of parabolic equations written in terms of the velocity field, the microrotations speed, the microstretch speed and the temperature. Then, a fully discrete approximation is introduced by using the finite element method and an Euler scheme. A priori error estimates are proved and the linear convergence of the algorithm is shown. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the solution. [ABSTRACT FROM AUTHOR]

This study investigates the applicability of an emergent learning algorithm called Gaussian process regression (GPR) algorithm to predict damage in plate-like structures as an inverse problem. The presented method is based on static responses and static strain energy as input parameters to GPR model. The performance of the presented methods has been evaluated using two numerical examples, namely, four fixed and cantilever plates. Also, an examination has been performed in which only translational DOFs are selected as measured DOFs. In another work, the effect of noise in static data has been investigated. The model results were compared using mean square errors. The obtained results show the effectiveness of GPR in damage detection and estimation of plate-like structures using static data which may be noisy. [ABSTRACT FROM AUTHOR]

Destructive identification approaches are no longer in favor since the advent of nondestructive evaluation approaches, as they are accurate, rapid, and cheap. Researchers are devoted to improving the accuracy, rate of convergence, and cost of such approaches, which depend greatly on the types of vibrational experiments conducted and the types of forward and inverse methods used in numerical section. Therefore, this article presents a review on the development of nondestructive vibrational evaluation approaches in identifying the elastic constants of composite plates, in experimental and numerical manners in order to enlighten researchers with the current trends of nondestructive vibrational approaches. [ABSTRACT FROM PUBLISHER]

In this article various sinusoidal shear deformation theories are used for the buckling analysis of functionally graded sandwich plates. The theories may account for through-the-thickness deformations and/or zig-zag effect. The governing equations and boundary conditions are derived using the Principle of Virtual Work under a generalization of Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions. A numerical investigation has been conducted on the buckling analysis of sandwich plates with functionally graded skins. The influence of the thickness stretching and the zig-zag effects on these problems is investigated. Numerical results demonstrate the accuracy of the present approach. [ABSTRACT FROM AUTHOR]

The following article serves three purposes: (i) it presents a simple semi-implicit numerical formulation for nonlinear structural dynamics problems, which is computationally inexpensive and simple to use in nonlinear dynamics and chaos simulations; (ii) it serves as an introduction to numerical studies of nonlinear structural dynamics for engineering students; and (iii) it formulates a nonlinear structural dynamical system for studies of nonlinear dynamics and chaos. Numerical formulations along with results are presented for nonlinear oscillators, beams, Föppl–von Kármán plates, and thin shallow shells. [ABSTRACT FROM AUTHOR]

In this paper, the development of a new proof of plate capacity under combined in-plane loads for ship design and classification is described. The new proof is based on an improved understanding of plating collapse obtained from an extensive series of non-linear buckling analyses using the finite element method and covering the full range of structural configurations and load combinations relevant for the shipbuilding industry. Compared to existing proofs, the new proof incorporates a more physically based approach towards tensile stress effects on plate capacity and better captures the influences of both plate slenderness and aspect ratio under compressive biaxial loads. Moreover, the new proof can be solved without the need for iterations and may be used directly with stresses obtained from finite element analyses, thereby eliminating the need for a correction of stresses due to Poisson effects. [ABSTRACT FROM AUTHOR]

Best theory diagrams (BTDs) are reported in this article for the static analysis of metallic and laminated composite plates. A BTD is a curve that provides the minimum number of unknown variables of a structural theory for a fixed error. The error is related to a given variable with respect to an exact or quasi-exact solution. The theories that belong to the BTD have been obtained by means of the axiomatic/asymptotic technique, and a genetic algorithm has been employed to obtain the BTD. The Carrera Unified Formulation (CUF) has been employed to obtain refined models, since the CUF can generate automatically, and in a unified manner, any type of plate model. Equivalent single layer (ESL) and layer-wise (LW) kinematics are discussed. Closed-form, Navier-type solutions have been employed, and attention has therefore been restricted to simply-supported plates. The influence of various geometries, material properties, and layouts has been considered, and their influence on the BTD has been evaluated. Furthermore, some known theories have been evaluated and compared with the BTD curve. The results suggest that the BTD and the CUF can be considered as tools to evaluate the accuracy of any structural theory against a reference solution in a systematic manner. [ABSTRACT FROM PUBLISHER]

This work analyzes the influence of edge-boundary conditions on the static and dynamic behavior of isotropic and cross-ply plates in cylindrical bending conditions. The main concern of the analysis is addressed to dynamic problems (free vibrations) along with certain boundary conditions that seem to be mainly responsible for a low convergence of the eigenvalues to the exact values. The interest on the static behavior comes from the inherent sensitivity of related quantities, which can both be compared with previous studies and can better elucidate such a low convergence. The analysis is carried out within the frame of the three-dimensional theory by using different variational formulations based both on assumed displacements and/or stresses along with the attempt to unify the comparison of the different formulations. The numerical results/performance of such formulations are also compared to those achieved through alternative models. [ABSTRACT FROM PUBLISHER]

Recently, severe plastic deformation (SPD) techniques have been gaining wide popularity in developing nano/ultrafine grained (UFG) structured materials for a wide variety of applications. Among SPD techniques, there are a few techniques that are specially used to process metallic sheets and plates. Repetitive corrugation and straightening (RCS) is one such promising technique, which can produce fine grained structures in metallic sheets or plates in bulk. The process was introduced to develop UFG metallic sheets and plates nearly a decade ago and is now gaining great interest in the material processing field. The aim of the present review is to give a comprehensive summary of the state-of-the-art of the process in developing fine grained structured sheets. Emphasis has been given to discuss different material systems processed by RCS. The mechanism behind the grain refinement during RCS, promising applications, and future perspectives in developing UFG structured sheets or plates by RCS are also discussed. [ABSTRACT FROM PUBLISHER]

Some models for axially moving orthotropic thin plates are investigated analytically via methods of complex analysis to derive estimates for critical plate velocities. The linearized Kirchhoff plate theory is used, and the energy forms of steady-state models are considered with homogeneous and inhomogeneous tension profiles in the cross direction of the plate. With the help of the energy forms, some limits for the divergence velocity of the plate are found analytically. In numerical examples, the derived lower limits for the divergence velocity are analyzed for plates with small flexural rigidity. [ABSTRACT FROM PUBLISHER]

In this article, a general solution for moment distribution around a circular/elliptical/triangular shaped hole in a laminated composite plate subjected to a bending/twisting moment at infinity is presented. The numerical results are obtained for graphite/epoxy, glass/epoxy, boron/epoxy, etc. The effect of loading factor, stacking sequence, material parameters, and hole geometry on moment distribution is studied for cross ply and angle ply laminates. The results are compared with existing literature and found to be in good agreement. [ABSTRACT FROM PUBLISHER]

Solids that possess negative Poisson's ratio are termed auxetic materials. This article considers the effect of auxeticity, i.e., the negative extent of Poisson's ratio on thermal stresses in plates, shells, and other solids. Results show that in cases where temperature gradient is in the through-thickness of a fully-clamped plate or when the temperature gradient is in the radial direction of fully-clamped shells, the thermal stresses can be significantly reduced by using auxetic materials. The same result applies to spheres and cylinders with radial temperature gradient. The maximum thermal stress is minimized if the selected material possesses Poisson's ratio of –1. However, the use of auxetic material is not always advantageous, nor does the use of materials with Poisson's ratio of –1 always minimize the maximum thermal stresses. It is herein suggested that, in addition to the use of materials with lower modulus and lower coefficient of thermal expansion, the use of auxetic materials offers an alternative route for lowering thermal stresses in some cases. [ABSTRACT FROM AUTHOR]

Porous cobalt oxide (Co3O4) microplates have been successfully synthesised via a facile thermal decomposition from plate-like cobalt oxalate complex precursors. The microstructures and morphologies of the obtained Co3O4 materials are characterised by X-ray diffraction, scanning electron microscopy, transmission electron microscopy and N2 adsorption-desorption techniques. The characterisation results show that the obtained Co3O4 microplates are composed of plate-like polycrystalline nanoparticles with lengths of ∼20 nm and widths of ∼10 nm. In addition, these nanoplates aggregate each other to form the porous network with an average pore size of ∼18·9 nm. The obtained porous Co3O4 microplates exhibit high discharge-charge capacities and good rate performances, suggesting a promising application as anode materials for Li ion batteries. [ABSTRACT FROM AUTHOR]

This article investigates the effect of auxeticity on the thermal stresses of isotropic plates. The thermal stress is non-dimensionalized against the coefficient of thermal expansion, the change in temperature and at least one of the moduli so as to express the dimensionless thermal stresses solely in terms of Poisson's ratio of the plate material. Results show that increasing auxeticity leads to mild and significant drop in the thermal stresses under the conditions of constant Young's modulus and constant shear modulus, respectively. However, increasing auxeticity causes increase in the thermal stress under the condition of constant bulk modulus. It is also shown that increasing auxeticity under the condition of constant product of all the three moduli reduces the thermal stress if Poisson's ratio falls within a wide range of −1 and 0.303. These results suggest that, under most circumstances, the replacement of conventional plate materials with auxetic solids is useful for reducing thermal stresses therein. The use of auxetic materials, therefore, provides an additional choice for the reduction of thermal stresses in plates other than selecting materials of lower modulus and low coefficient of thermal expansion. [ABSTRACT FROM PUBLISHER]

Simple intuitive formulas, to calculate the large amplitude vibration frequencies, have been recently developed for the beams and square plates. The basis for development of these formulas is the master formula, obtained for the initially loaded structural members. These basic formulas, for the initially loaded beams and square plates, are modified to obtain the ratios of the nonlinear frequency (undergoing moderately large amplitude vibrations), for a given amplitude ratio, to the linear frequency parameters. Though, these intuitive formulas give a quick and accurate estimation for large amplitude vibrations, it is necessary to show that these formulas can be obtained through the rigorous formulation such as, the energy formulation. This is the main objective of the present study, where in it is demonstrated that the intuitive formulas, for the large amplitude vibrations of beams and square plates, are exactly the same with those derived by the rigorous energy formulation, for the s-s-s-s and c-c-c-c square plates, where s and c stand for the simply supported (hinged for beams) and clamped end/edge conditions. This study is further extended to beams and square plates with different boundary conditions, other than h-h and c-c boundary conditions for beams and s-s-s-s and c-c-c-c boundary conditions for square plates. The numerical results presented give the required confidence to the structural engineers and researchers, to use the simple intuitive formulas, whenever required. [ABSTRACT FROM PUBLISHER]

This article addresses the static deformations and free vibration analysis of laminated composite and sandwich plates by collocation with radial basis functions, according to a layerwise formulation. The present layerwise approach accounts for through-the-thickness deformations. The equations of motion and the boundary conditions are obtained by the Carrera’s Unified Formulation, and further interpolated by collocation with radial basis functions. [ABSTRACT FROM PUBLISHER]

A study of static deformations and free vibration of shear flexible isotropic and laminated composite plates is presented, using a layerwise theory. The analysis is based on a new numerical scheme based on a local collocation scheme with radial basis functions and finite differences to produce highly accurate results. Numerical results for symmetric laminated composite and sandwich plates are presented and discussed. [ABSTRACT FROM PUBLISHER]

An application of a meshless technique for the static and vibration analysis of plates is presented in this paper. The method is based on the radial basis functions-QR (RBF-QR) algorithm. Static deformations and free vibration analysis of plates are obtained by Gaussian RBF-QR technique, previously proposed by Fornberg and Piret (2007) for interpolation problems. Circular and square plates are analyzed considering free-edge, simply-supported, and fully-clamped boundary conditions. The presented technique can be applied to any geometry and node sets embedded in the 2D unitary disk. The RBF-QR approach is stable for decreasing values of the shape parameter, corresponding to flat RBFs and the conversion to polar coordinates brings an extra improvement in precision. The method produces highly accurate displacements, natural frequencies, and modes of vibrations. [ABSTRACT FROM AUTHOR]

Elastic and functionally graded (FGM) Kirchhoff plates are investigated in this study. Meshless approximate methods are employed for solution of plate equations. For static analysis, uniformly distributed load and clamped boundaries are assumed. Galerkin's method is used to solve the partial differential equation of plates. In addition, vibration characteristics of simply supported FGM plates are studied by using the Ritz method. The Poisson's ratios of plates are assumed to be constant, but Young's modulus varies functionally. The effective Young's modulus of the plates, made of isotropic ceramic and metal constituents with volume contents varying only in the thickness direction, is computed using the Mori–Tanaka homogenization technique. The objective here is to investigate the influence of volume fractions and the component materials on mechanical behavior of super elliptical plates. [ABSTRACT FROM AUTHOR]

This paper describes the generalized finite difference method to solve second-order partial differential equation systems and fourth-order partial differential equations. This method is applied to solve the problem of thin and thick elastic plates. [ABSTRACT FROM PUBLISHER]

During the welding of steel-plated structures, geometric distortions and residual stresses are developed. The influence of welding-induced geometric distortions and residual stresses on the compressive ultimate strength in longitudinal direction of plates and stiffened panels were investigated using nonlinear finite element analyses considering a range of plate thicknesses with various levels of residual stresses. The residual stresses in plates and stiffened panels have been modelled carefully and their effects on these structures due to welding-induced imperfections only are studied. The results and insights observed from the current study are presented. [ABSTRACT FROM AUTHOR]

Driscoll and Heryudono [1] developed an adaptive method for radial basis functions method. This article addresses the adaptive analysis of composite plates in bending with radial basis multiquadric functions using Driscoll and Heryudono's technique. In this article, various laminates, thickness to side length ratios, and boundary conditions are considered. The method allows for a more natural and automatic selection of the problem grid, where the user must only define the error tolerance. The results obtained show an interesting and promising approach to the static analysis of composite laminates. [ABSTRACT FROM AUTHOR]

The performance of an electromagnetic-thermal method for nondestructive testing is investigated experimentally by eddy current thermography. The experiments concerned the detection of the crack in six circular aluminium plates at various positions and orientations. Two circular coils are employed for the excitation, C8 and C15, with outer diameter smaller (C8) and greater (C15) than the plate diameter. The coil C8 is more effective in detecting cracks perpendicular to the current flow, while C15 excels in the detection of cracks perpendicular to the heat flow. Crack detection is based not only on the thermograms but on data processing techniques as well, such as the depiction of the norm of spatial derivative of temperature and Fourier transform. The detection of cracks perpendicular to the current flow is enhanced considerably by Fourier transform (phase images). Both the norm of the spatial derivative of temperature and Fourier transform (amplitude images) give the adequate results for the cracks perpendicular to the heat flow. Notwithstanding the fact that the performance of the infrared camera is relatively low, the use of the two coils, combined to techniques of data processing, permitted for the detection of all six cracks in the plates. [ABSTRACT FROM AUTHOR]

The present work investigates the static response problem of multilayered plates and shells embedding functionally graded material (FGM) layers. Carrera's unified formulation (CUF) is employed to obtain several hierarchical refined and advanced two-dimensional models for plates and shells. The refined models are based on the principle of virtual displacements. The advanced models, based on Reissner's mixed variational theorem, permit the transverse shear and normal stresses to be 'a priori' modelled. Refined and advanced models are developed in both equivalent single layer and layer wise multilayer approaches. CUF is also employed to describe the continuous variation of elastic properties in the thickness direction for the embedded FGM layers. The numerical results, which are restricted to simply supported plates/shells loaded by a harmonic distribution of transverse pressure, show that the use of refined and advanced models, based on CUF, is mandatory with respect to the classical theories that are widely employed for isotropic and one-layered structures. Furthermore, advanced models lead to a quasi-3D description of the bending problem for FGM plates and shells. New benchmarks are considered in order to investigate the possible benefits of introducing FGM layers into common multilayered structures. It has been concluded that significant benefits can be obtained by employing opportune values for [image omitted]-hFGM parameters, where [image omitted] is the exponent of the thickness law for the FGM elastic properties and hFGM is the thickness of the embedded FGM layers. [ABSTRACT FROM AUTHOR]

This study presents a novel optimization algorithm which is a hybrid of particle swarm optimization (PSO) method and genetic algorithm (GA). Using the Ackley and Schwefel multimodal benchmark functions incorporating up to 25 variables, the performance of the hybrid is compared with pure PSO and GA and found to be far superior in convergence and accuracy. The hybrid algorithm is then used to identify multiple crack damages in a thin plate using an inverse time-domain formulation. The damage is detected using an orthotropic finite element (FE) model based on the strain energy equivalence principle. The identification is carried out using time-domain acceleration responses. The principle is to minimize the difference between the measured and theoretically predicted accelerations. Since the computational effort of identifying the use of global FE model proved prohibitive, a quarter substructure was identified which contains 72 damage variables. Using numerically simulated experiments, three cracks in a plate were reliably detected using this method in the presence of noise. While the pure particle swarm algorithm proved to be fast, the hybrid algorithm proved to be more accurate in damage prediction. GA performed worst in speed and accuracy. [ABSTRACT FROM AUTHOR]

Although they furnish accurate displacements, conventional displacement-based lower order finite elements fail to predict accurate stress resultants and stresses in certain classes of plate and shell problems that involve free edges, steep stress gradients and singularities. In order to tackle such problems, a triangular higher-order shell element based on the nodal basis approach has been developed. The nodes of the element are located at optimal points and its more superior shape functions derived from orthogonal Proriol polynomials. To illustrate the improved performance of the higher-order element as compared to commonly used lower order shell elements in predicting the variations of stress resultants and stresses, three example problems involving a simply supported skew plate, a corner supported square plate, and a clamped cylindrical shell are solved. The stress resultants and the stresses furnished by the higher-order element for the problems considered are found to be accurate with the satisfaction of the natural boundary conditions and devoid of any oscillations. When compared to lower order elements, the higher-order element requires a simple mesh design and lesser degrees of freedom resulting in a considerable reduction in the computational effort, especially for large scale nonlinear analysis. [ABSTRACT FROM AUTHOR]

Data collected from ageing ships indicate that the rate of corrosion of ship's plating may increase with long periods of exposure when combined with plate flexure. The reasons for this have not been clarified. Herein, the possibility is investigated that the observed effect is due to the loss of protective rusts under high strains in the steel plating, as might be caused by high sea-states and during loading and unloading. Recently, relatively short-term exposure studies of the tensile strain-induced fracture of rusts formed on structural steels during natural marine exposure show an increase in corrosion rate of some 10-15%, but only when the strains are near and beyond the elastic limit of the steel. This has implications for ship management. An interpretation is given for the corrosion loss curves reported in the literature and it is shown that, qualitatively at least, they are consistent with earlier observations and models for the corrosion of steel in marine environments. It is proposed that the validity of the conclusions be tested using long-term exposures under corrosion and flexure conditions in actual ships. [ABSTRACT FROM AUTHOR]

The paper deals with the influence of shear stresses on bending and buckling of beams and plates of composite materials employing the hypothesis of 'straight line'. It is assumed that a set of points lying on a line perpendicular to the neutral surface (the mid-plane) before deformation remains on the line and this line is non-perpendicular to the neutral surface after a load's application. This non-orthogonality is caused by the presence of shear stresses. Thus, this approach does not require the section to be normal to the neutral surface as in the classic Kirchhoff hypothesis. It is shown that the latter is inconsistent with the existence of shear stresses. The corresponding differential equations are derived from the non-linear differential equations of the theory of elasticity in Cartesian coordinates. This allows well-founded simplification of the equations for different partial cases and also correct determination of the sections' rotation angles in the equations for buckling. Several solutions for bending and buckling of beams and plates are given while considering the effect of shear stresses. Formulae are derived for the Euler force of compressed beams and simply supported orthotropic plates, which allows calculation of the error resulting from the application of the Kirchhoff hypothesis. For example, it is shown that for h/b < 0.1 (h = plate thickness, b = dimension of smallest side) the error is smaller than 5% and it does not depend on the plate's aspect ratio. Also, a solution is found for bending strength of beams and orthotropic plates subjected to the arbitrarily distributed lateral pressure considering the effect of shear stresses. Formulae for the deflection in the plate's centre are derived as well as for calculating the error when the classic Kirchhoff hypothesis is applied. [ABSTRACT FROM AUTHOR]

We study the behaviour of thin elastic bodies of fixed cross-section and of height h, with h → 0. We show that critical points of the energy functional of nonlinear three-dimensional elasticity converge to critical points of the von Karman functional, provided that their energy per unit height is bounded by Ch4 (and that the stored energy density function satisfies a technical growth condition). This extends recent convergence results for absolute minimizers. [ABSTRACT FROM AUTHOR]

The main focus of this paper is the study of grid stiffened plates. The plates are modeled using the finite element approach. A 2D 8-node plate element is proposed. The advantage of the proposed element is that it can model plates with stiffeners within the element. This can yield models with many fewer elements for grid structures. A parametric study is presented to study the effect of the stiffener angle on the element stiffness in an attempt to optimize the stiffener configuration. For validation purposes, three cases are considered; plain plate, plate with straight stiffeners, and plate with isogrid stiffeners. The modal frequencies and modes of the plates are calculated using the proposed model and compared with the predictions of the commercial finite element package ANSYS® as well as experimental measurements taken on three plates manufactured by stereo lithography technique. The comparisons demonstrate the validity of the proposed model and the effectiveness of the isogrid stiffeners compared to straight stiffeners of the same mass in significantly increasing the fundamental frequency. The obtained results emphasize the potential of employing isogrid stiffeners in numerous vibration and noise control applications. [ABSTRACT FROM AUTHOR]

Based on thermoelastic theory, various two-dimensional equations and solutions for plane problems have been deduced systematically and directly from thick plate theory by using Biot's solution and Lur'e method without ad hoc assumptions. These equations and solutions can be used to construct the refined theory for the plane problems. In the case of homogeneous boundary conditions, the exact governing differential equations and solutions for the plate are derived, which consist of four governing differential equations. It is important note that the refined theory is consistent with the decomposition theorem by Gregory. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order terms. The correctness of the stress assumptions in the classic plane stress problems is revised. [ABSTRACT FROM AUTHOR]

The Reissner-Mindlin plate model for calculation of functionally graded materials has been proposed in literature by using shear correction coefficient of homogeneous model. However, this use is a priori not appropriate for the gradient material. Identification of the transverse shear factors is thus investigated in this paper. The transverse shear stresses are derived by using energy considerations from the expression of membrane stresses. Using the obtained transverse shear factor, a numerical analysis is performed on a simply supported FG square plate whose elastic properties are isotropic at each point and vary through the thickness according to a power law distribution. The numerical results of a static analysis are compared with available solutions from previous studies. [ABSTRACT FROM AUTHOR]

This article deals with the study of the interaction between an elastic plate with constant thickness and an incompressible fluid when the plate is approximated by the N &ThickSpace;=&ThickSpace;0 order term of Vekua's hierarchical model. [ABSTRACT FROM AUTHOR]

A new and effective generation method for the stiffener layout pattern for plate and shell structures to achieve minimum compliance, the so-called adaptive growth technique, is suggested in this paper. The method is based on the adaptive growth rule of branch systems in nature that branches grow and branch off automatically towards such directions that can improve the global functional performance, such as the maximum absorption of sunlight or water. It is expected that a plate or shell structure can achieve good mechanical performance if the stiffeners extend by obeying a similar adaptive growing and branching rule as branch systems in nature. The stiffeners, starting from the so-called seeds, grow and branch off towards the direction with the maximum effectiveness of the global mechanical performance, which is dependent on the design sensitivity of the current structure. During the growth process, the volume increment is controlled so as to make it possible to create new branches and to eliminate degenerate branches. The validity and effectiveness of the suggested method are confirmed by some typical stiffener layout design problems. [ABSTRACT FROM AUTHOR]

Two important tectonic phases generated by African and Arabian plate movements influenced the evolution of trends in SE Turkey's oilfields. The main phase occurred during the late Cretaceous (Maastrichtian) time, while the second phase reactivated the existing trends in Miocene. Paleogeological evolutions reveal that SE Turkey was tectonically stable from Paleozoic up to the end of Cretaceous, during which the structural trends were oriented in a WSW-ENE direction, contrarily, under the influence of opening of the Red Sea area, the existing trends rotated in a counterclockwise direction and oriented in a SW-NE direction. This rotational tectonic event is evidenced by SW-NE alignments of SE Turkey's oilfields in subsurface and Karacadag basaltic expensions and appearance of major faults, like the Dead Sea fault, Adiyaman fault, and Akcakale fault, on surface. Subsurface interpretations indicate that, contrarily to the previous works, which considered the Dead Sea fault and Adiyaman fault separate tectonic features from each other and also attached them to the East Anatolian fault, the Adiyaman fault is the continuity of the Dead Sea fault through the Adiyaman, Diyarbakir and Selmo areas. The Akcakale fault, which generated the Karacadag basaltic flows, is another tectonic element and has influenced the exploration activities in SE Turkey. Moreover, detailed interpretations of well data reveal that the SW-NE structural trends also improved reservoir conditions by creating fractures and dolomitizations in reservoir rocks, and the high geothermal and potential (piezometric) gradients and porosity trends are also aligned in the same direction. [ABSTRACT FROM AUTHOR]