Showing papers on "Plate theory published in 2001"
TL;DR: In this paper, a finite element formulation based on the classical laminated plate theory is presented for the shape and vibration control of the functionally graded material (FGM) plates with integrated piezoelectric sensors and actuators.
407 citations
TL;DR: A review of displacement and stress based refined theories for isotropic and anisotropic laminated plates is presented in this paper, together with their merits and demerits, where exact elasticity solutions for the plate problems are cited.
Abstract: A review of displacement and stress based refined theories for isotropic and anisotropic laminated plates is presented. Various equivalent single layer and layerwise theories for laminated plates are discussed together with their merits and demerits. Exact elasticity solutions for the plate problems are cited, wherever available. Various critical issues related to plate theories are presented, based on the literature reviewed.
342 citations
TL;DR: In this article, the dynamic response of initially stressed functionally graded rectangular thin plates subjected to partially distributed impulsive lateral loads and without or resting on an elastic foundation is investigated, and the formulations are based on classical small deflection plate theory, and account for the plate-foundation interaction effects by a two-parameter model.
304 citations
TL;DR: In this paper, three-dimensional thermomechanical deformations of simply supported, functionally graded rectangular plates are studied by using an asymptotic method, and the locally effective material properties are estimated by the Mori-Tanaka scheme.
Abstract: Three-dimensional thermomechanical deformations of simply supported, functionally graded rectangular plates are studied by using an asymptotic method. The locally effective material properties are estimated by the Mori–Tanaka scheme. The temperature, displacements and stresses of the plate are computed for different volume fractions of the ceramic and metallic constituents, and they could serve as benchmark results to assess two-dimensional approximate plate theories.
289 citations
TL;DR: In this article, an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models.
Abstract: The objective of this study is to model the diagnostic transient waves in an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models. PZT ceramic disks are surface mounted on an aluminum plate acting as both actuators and sensors to generate and collect A0 mode Lamb waves. Mindlin plate theory is adopted to model the propagating waves by taking both transverse shear and rotary inertia effects into account. Actuator and sensor models are both proposed. The interaction between an actuator and the host plate is modeled based on classical lamination theory. The converse piezoelectric effect of the actuator is treated as an equivalent bending moment applied to the host plate. The sensor acts as a capacitor that converts the sensed strain change into a voltage response. An analytical expression for the sensor output voltage in terms of the given input excitation signal is derived, and then experimental work is performed to verify the accuracy of the analytical model. Experimental results show that single-mode Lamb waves in the plate can be successfully generated and collected through the integrated PZT disks. The experiment also shows that the predicted sensor output for both amplitude and phase agrees well with experimentally collected data.
178 citations
01 Feb 2001
TL;DR: In this paper, a general closed-form model for predicting the critical thrust force at which delamination is initiated at different ply locations is presented, and good correlation is observed between the model and the experimental results.
Abstract: Among the various forms of material damage, delamination due to drilling is one of the major concerns in machining a composite laminate. The thrust force has been cited as the primary cause of the delamination. The analysis for multidirectional composite laminates is based on linear elastic fracture mechanics (LEFM), classical bending plate theory and the mechanics of composites. This paper presents a general closed-form mechanical model for predicting the critical thrust force at which delamination is initiated at different ply locations. Good correlation is observed between the model and the experimental results.
113 citations
TL;DR: In this article, the influence of hygrothermal effects on the postbuckling of shear deformable laminated plates subjected to a uniaxial compression was investigated using a micro-to-macro-mechanical analytical model.
112 citations
TL;DR: In this paper, the authors established the differences between the Mindlin and Reissner plate theories by deriving bending relationships between the two theories for a general plate problem and specialized them for the cases of rectangular plates with (1) all sides simply supported, (2) two opposite edges simply supported with the other two edges free.
91 citations
TL;DR: A liquid crystal display having a wide viewing angle, a large contrast ratio, and little nonuniformity of display, is formed by a pair of substrates, and a liquid crystal layer interposed between the pair of substrate.
Abstract: Anexact solution isobtainedforthethree-dimensional deformationsofsimplysupported laminated rectangular thick plates with embedded shear mode piezoelectric actuators, subjected to mechanical and electrical loading on the upper and lower surfaces. Each layer of the laminate is made of either an orthotropic elastic material or a piezoelectric material whose poling direction lies in the plane of the plate, with perfect bonding between the adjoining layers. The exact displacements and stresses for a homogeneous piezoelectric plate for various lengthto-thickness ratios are compared with those obtained by the erst-order shear deformation theory. Results are also presented for asandwich plateconsistingofashearmodepiezoelectriccoresandwiched between twoelastic layers. A comparison of the stresses with those in the corresponding surface-mounted extension actuation cone guration shows that for the same transverse deeection of the plate centroid, the maximum longitudinal stress within the actuator is signie cantly smaller for the shear actuation mechanism. The exact results presented here can be used to assess the accuracy of different plate theories and/or for validating enite element codes.
89 citations
TL;DR: In this paper, thermal postbuckling analysis for a simply supported, shear deformable laminated plate subjected to a uniform temperature rise and resting on an elastic foundation is presented.
82 citations
TL;DR: In this paper, an exact 3D state space solution is obtained for the static cylindrical bending of simply supported laminated plates with embedded shear mode piezoelectric actuators, and subjected to mechanical and electric loading on the upper and lower surfaces.
Abstract: An exact three-dimensional state space solution is obtained for the static cylindrical bending of simply supported laminated plates with embedded shear mode piezoelectric actuators, and subjected to mechanical and electric loading on the upper and lower surfaces. Each layer of the laminate is made of either an orthotropic elastic material or a piezoelectric material whose poling direction lies in the plane of the plate, with perfect bonding between the adjoining layers. The displacements and stresses for a homogeneous piezoelectric plate for various length-to-thickness ratios are compared with those obtained by the first-order shear deformation theory. Results are also presented for a hybrid laminate with a shear mode piezoelectric core sandwiched between two elastic layers. A comparison of stresses with those in the corresponding surface-mounted extension actuation configuration shows that the longitudinal and shear stresses within the actuator are significantly smaller for the shear actuation mechanism. The analytical results can be used to assess the accuracy of different plate theories and/or validating finite element codes.
TL;DR: In this paper, the behavior of buckling driven thin-film blisterings using von Karman's plate theory was studied and upper and lower bounds for the elastic energy were established.
Abstract: We consider the behavior of buckling driven thin-film blisterings using von Karman’s plate theory. Our focus is on the setting where the blistered region is the unit square with clamped boundary conditions at the vertical sides and periodic ones along the horizontal sides. In this setting, we prove rigorous upper and lower bounds for the elastic energy which are of the same order as the film thickness. We also present a convincing argument for the necessity of branching of folds near the boundary as has been observed in experiments.
TL;DR: In this article, a differential quadrature analysis of free vibration of plates with eccentric stiffeners is presented, where the plate and the stiffeners are treated separately and simultaneously governing differential equations are derived from the plate dynamic equilibrium, the stiffener dynamic equilibrium and equilibrium and compatibility conditions along the interface of a plate segment and a stiffener.
TL;DR: In this article, a new approach for the analysis of transient waves propagating in anisotropic composite laminates is presented, where the wavelet transform (WT) using the Gabor wavelet is applied to the time-frequency analysis of dispersive flexural waves in these plates.
Abstract: A new approach is presented for the analysis of transient waves propagating in anisotropic composite laminates. The wavelet transform (WT) using the Gabor wavelet is applied to the time-frequency analysis of dispersive flexural waves in these plates. It can be shown that the peaks of the magnitude of WT in a time-frequency domain is related to the arrival times of the group velocity. Experiments were performed using a lead break as the simulated acoustic emission source on the surface of unidirectional and quasi-isotropic laminates. A method was developed to obtain the group velocity of the flexural mode as a function of frequency. Theoretical predictions were made using the Mindlin plate theory, which includes the effects of shear deformation and rotatory inertia. Our predictions on the dispersion of the flexural mode showed good agreement with the experimental results.
TL;DR: In this article, the authors considered the elastic/plastic buckling of thick plates of rectangular and circular shapes and derived elastic and plastic stability criteria for uniaxially and equibiaxially loaded rectangular plates with two opposite edges simply supported.
TL;DR: Based on the Mindlin/Reissner plate theory, two refined triangular thin/thick plate elements, the conforming displacement element DKTM with one point quadrature for the part of shear strain and the element RDKTM with the re-constitution of the shear force, are proposed in this paper.
Abstract: Based on the Mindlin/Reissner plate theory, two refined triangular thin/thick plate elements, the conforming displacement element DKTM with one point quadrature for the part of shear strain and the element RDKTM with the re-constitution of the shear strain, are proposed. In the formulations the exact displacement function of the Timoshenko's beam is used to derive the element displacements of the refined elements. Numerical examples are presented to show that the present models indeed possess properties of high accuracy for thin and thick plates, is capable of passing the patch test required for Kirchhoff thin plate elements, and does not exhibits extra zero energy modes. The element RDKTM is free of locking for very thin plate analysis and its convergence can be ensured theoretically. However, the element DKTM is not free of shear locking when the thickness/span ratios less than 10−2. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this paper, a structural health monitoring system (SHMS) with a linear array of actuators/sensors is proposed to detect and image multiple damages in a plate-like structure.
Abstract: An approach to detect and image multiple damages in a platelike structure is presented. A structural health monitoring system (SHMS) with a linear array of actuators/sensors is proposed. The integrated actuators/sensors are used to activate/receive lowest-order antisymmetric A0 mode Lamb waves. A migration technique used in geophysical exploration and seismic prospecting is adopted to interpret the backscattering wave e eld and to image thee awsinthestructure.Theproposed approachismodeledbya two-dimensional explicite nitedifferencemethod both in simulating the ree ection waves and in implementing the prestack migration. An analytical solution based on Mindlin plate theory (Mindlin, R. D., “ Ine uence of Rotary Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates,” Journal of Applied Mechanics , Vol. 18, No. 1, 1951, pp. 31 ‐38) is derived to verify the accuracy of the numerical algorithm. An excitation-time imaging condition specie cally for the migration of waves in a plate is introduced based on a ray tracing concept, and prestack reverse-time migration is proceeded to propagate the ree ection energy back to the damages. The plate is imaged in terms of the velocity of transverse deformation after migration,thus, thelocations, dimensions, and seriousness of thee awscan bevisually displayed. Numerical results show that multiple damages can be successfully detected and the image of the damages correlate well with the target damages. The conclusion is that prestack migration can be a prospective technique in SHMS applications.
TL;DR: In this article, the authors report on modeling, numerical simulation, and experimental investigation of plates subjected to impulsive loading using the Chaboche and Bodner-Partom constitutive laws.
TL;DR: In this paper, the authors used the large deflection orthotropic plate approach to develop the ultimate strength formulations for steel stiffened panels under combined biaxial compression/tension and lateral pressure loads, considering the overall grillage buckling collapse mode.
Abstract: This paper uses the large deflection orthotropic plate approach to develop the ultimate strength formulations for steel stiffened panels under combined biaxial compression/tension and lateral pressure loads, considering the overall (grillage) buckling collapse mode. The object panel has a number of one-sided small stiffeners in either one or both orthogonal directions. The stiffened panel is then modeled as an equivalent orthotropic plate, for which the various elastic constants characterizing structural orthotropy are determined in a consistent systematic manner using classical theory of elasticity. The panel edges are considered to be simply supported. The influence of initial deflections is taken into account. The membrane stress distribution inside the panel under combined uniaxial loading (in either longitudinal or transverse direction) and lateral pressure is analyzed by solving the nonlinear governing differential equations of large deflection orthotropic plate theory. It is presumed that the panel collapses when the most highly stressed boundary location yields, resulting in closed-form expressions for the ultimate strength of the stiffened panel. Based on the insights previously developed through numerical studies, the panel ultimate strength interaction formulation between biaxial loads, with lateral pressure regarded as a secondary load component is then proposed as a relevant combination of the two sets of panel ultimate strength formulations, i.e. one for combined longitudinal axial load and lateral pressure and the other for combined transverse axial load and lateral pressure. The validity of the proposed ultimate strength formulations is verified by a comparison with nonlinear finite element and other numerical solutions.
TL;DR: In this article, the free and forced vibration analysis for Reissner-Mindlin plates with four free edges resting on a Pasternak-type elastic foundation is presented, considering the first order shear deformation effect and including the plate-foundation interaction and thermal effects.
TL;DR: In this article, the authors demonstrate a feasibility study of applying migration, which is widely used as an advanced data processing technique in geophysical exploration, to detect damage in a plate, and suggest a scheme that may build a real-time, in situ, and quantitative health monitoring system.
Abstract: This paper demonstrates a feasibility study of applying migration,which is widely used as an advanced data processing technique in geophysical exploration,to detect damage in a plate. This technique suggests a scheme that may build a real time, in situ,and quantitative health monitoring system. A linear actuator/sensor array is placed along a horizontal central axis on a square homogeneous isotropic plate. A technique is proposed to utilize piezoelectrics as both actuators and sensors to generate and collect the flexural waves in the plate. Migration technique is then adopted to interpret the recorded data and image the damage that formed in the plate. The wave field reflected from the damage is synthesized by using a two-dimensional explicit finite difference method to model the plate using Mindlin plate theory. A one-way version of flexural wave equation is derived. The one-way wave equation based poststack reverse-time migration is then used to back-propagate the synthetic wave field to their secondary sources,and the damage is imaged by applying appropriate imaging condition. The data pre-processing procedures before migration,such as muting direct arrival,deconvolution and stacking,are also discussed. The satisfactory determination of the locations and dimensions of the damages in several numerical simulation examples validates the feasibility of proposed monitoring system.
TL;DR: In this paper, a finite strip method for predicting buckling stresses of rectangular sandwich plates is described. But this method is based on a B-spline finite strip model and is not suitable for the case of composite laminates.
TL;DR: In this paper, the authors present the results of a thermal buckling analysis for clamped, rectangular plates based on energy considerations, which reveals that both of the edge length to thickness ratios (a / h, b / h ) are independent parameters, i.e. fixing the aspect ratio (a/ b ) is not sufficient to ensure a unique problem.
TL;DR: In this article, a simply supported, shear deformable laminated plate with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads is presented.
TL;DR: In this paper, the analysis of the elastic stiffnesses of corrugated core sandwich panels was performed in the framework of first-order shear deformation laminated plate theory and it was shown that the in-plane extensional and shear stiffness and the bending and twisting stiffnesses are dominated by the face sheets.
Abstract: The objective of this paper is to review and recast previous analytical approaches to the analysis of the elastic stiffnesses of corrugated core sandwich panels into the framework of first-order shear deformation laminated plate theory. Extensional, shear and bending stiffnesses will be determined and compared to measured data. It is shown that the in-plane extensional and shear stiffness and the bending and twisting stiffnesses are dominated by the face sheets and that calculated values agree with measured data. Transverse shear stiffnesses, however, are highly dependent on the integrity and shape of the core and the details of face-to-core bonding, and predictions were found to be highly unconservative. A major factor for the reduction in stiffnesses of the core is attributed to delamination damage of the web inflicted during the corrugation process.
TL;DR: In this article, the authors extend a layerwise higher-order shear-deformation theory to model a sandwich plate impacting with an elastic foundation at a low velocity, and derive a finite-element model based on this sandwich plate theory for performing direct transient analyses to predict the initiation and location of critical matrix crack and the threshold of impact damage.
11 Jun 2001
TL;DR: In this article, an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models.
Abstract: The objective of this study is to model the diagnostic transient waves in an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models. PZT ceramic disks are surface mounted on an aluminum plate acting as both actuators and sensors to generate and collect A0 mode Lamb waves. Mindlin plate theory is adopted to model the propagating waves by taking both transverse shear and rotary inertia effects into account. Actuator and sensor models are both proposed. The interaction between an actuator and the host plate is modeled based on classical lamination theory. The converse piezoelectric effect of the actuator is treated as an equivalent bending moment applied to the host plate. The sensor acts as a capacitor that converts the sensed strain change into a voltage response. An analytical expression for the sensor output voltage in terms of the given input excitation signal is derived, and then experimental work is performed to verify the accuracy of the analytical model. Experimental results show that single-mode Lamb waves in the plate can be successfully generated and collected through the integrated PZT disks. The experiment also shows that the predicted sensor output for both amplitude and phase agrees well with experimentally collected data.
TL;DR: In this article, an extension of the 1,2-order plate theory to a higher order {3,2} theory is presented, where the displacement components at any point on the plate are approximated in terms of weighted-average quantities (displacements and rotations) that are functions of the inplane coordinates.
TL;DR: In this paper, exact relationships between the bending solutions of the two theories for beams and plates are derived using the mathematical similarity of the governing equations of the classical beam and plate theories.
TL;DR: In this paper, the authors compared the results of the classical laminated plate theory, the first-order shear deformation theory, and the analytical solution with an analytical solution for elastic plates with distributed or segmented piezoelectric layers.
Abstract: Elastic plates with distributed or segmented piezoelectric layers have been analyzed using the classical laminated plate theory, the first-order shear deformation theory, and the results are compared with an analytical solution. The plate theories and the analytical solution take into account both the direct and the converse piezoelectric effects, and assume generalized plane strain deformations. The transverse displacements from both theories are in reasonable agreement. The classical lamination theory gives a discontinuous longitudinal stress at the edges of the segments whereas the analytical solution predicts a continuous curve with steep gradients. Piezoelectric bimorphs with the axis of transverse isotropy inclined at an angle to the thickness direction are also studied using the three formulations. The displacements and stresses obtained from the first-order shear deformation theory are in very good agreement with the analytical solution even for thick plates. It is advantageous to use shear bimorphs since the stresses induced in them are smaller than those in extension bimorphs. © 2001 Elsevier Science Ltd. All rights reserved.