Showing papers on "Plate theory published in 2005"
TL;DR: In this paper, the impact of the core thickness, relative to the total thickness of the plate, on the critical buckling load and the eigenfrequencies of the vibration natural frequency is investigated.
399 citations
TL;DR: In this paper, a theoretical method is developed to investigate vibration characteristics of initially stressed functionally graded rectangular plates made up of metal and ceramic in thermal environment, where material properties are assumed to be temperature dependent, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents.
270 citations
TL;DR: In this paper, a postbuckling analysis for a simply supported, shear deformable functionally graded plate with piezoelectric actuators subjected to the combined action of mechanical, electrical and thermal loads is presented.
138 citations
TL;DR: In this article, the exact closed form characteristic equations are given within the validity of the Mindlin plate theory for plates having two opposite sides simply supported, and the effect of boundary conditions, aspect ratios and thickness ratios on the eigenfrequency parameters and vibratory behavior of each distinct cases are studied in detail.
138 citations
TL;DR: Several numerical solution are obtained using a Runge-Kutta algorithm for high-order initial value problems for 1 ⩽ a ⦽ 2 and a = 2 for flat-plate flow in fluid mechanics.
136 citations
TL;DR: In this article, the authors presented the highly accurate numerical calculation of the natural frequencies and buckling loads for thick elastic rectangular plates with various combinations of boundary conditions. But the results obtained by both shear deformation theories are compared with those obtained by the classical thin plate's theory and with published results.
132 citations
TL;DR: In this article, the effect of randomness on the elastic buckling of FGM rectangular plates which are resting on an elastic foundation and subjected to uniform in-plane edge compressions is investigated.
127 citations
TL;DR: In this paper, the buckling behavior of rectangular functionally graded plates with geometrical imperfections is studied and the critical buckling load of a sample plate is obtained and compared with the results of perfect functionally graded and imperfect isotropic plates.
Abstract: Buckling behavior of rectangular functionally graded plates with geometrical imperfections is studied in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under in-plane compressive loading. Simultaneous solving of the stability and compatibility equations in conjunction with the equilibrium equations leads to the buckling relation of the plate. The critical buckling load of a sample plate is obtained and compared for different geometrical ratios. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates.
115 citations
TL;DR: In this paper, the authors discussed the FEM use of Murakami zig-zag function (MZZF) in the two-dimensional modeling of multilayered plates.
113 citations
TL;DR: In this article, the authors investigated the stochastic bending response of moderately thick, compositionally graded plates with uncertainties of low variability and subjected to lateral load and uniform temperature change and found that the response sensitivity of the plate is very much dependent on the material composition.
108 citations
TL;DR: In this article, an active diagnostic system with a linear array of actuators/sensors is used to excite/receive the lowest mode of flexural waves in the laminate.
Abstract: Migration technique, which is normally used in geophysical prospecting, is proposed to locate and image multiple delamination damages in a laminated composite plate. In this simulation study, an active diagnostic system with a linear array of actuators/sensors is used to excite/receive the lowest mode of flexural waves in the laminate. The wavefield scattered from the damages and sensor array data are synthesized using a two-dimensional explicit finite difference scheme to model wave propagation in the laminate based on the Mindlin plate theory. A prestack reverse-time migration technique is then adopted to interpret the synthetic sensor array data and to visualize the damages. The phase and group velocities of flexural waves in the composite plate are derived from the dispersion relations, and subsequently an excitation-time imaging condition specifically for migration of waves in the plate is introduced based on ray tracing and group velocity. Then the prestack reversetime migration is performed using the same finite difference scheme to back-propagate the scattered energy to the damages. During the migration process, the laminate is imaged in terms of velocity of the transverse deformation. The locations and dimensions of the damages can be visually displayed. Simulated results demonstrate that multiple delamination damages can be successfully identified and the resulting image correlates well with the target damages.
TL;DR: In this paper, a closed-form solution based on the Mindlin-Reissner plate theory is presented to describe the behavior of corrugated-core sandwich plate bending with various boundary conditions.
TL;DR: In this paper, the free flexural vibration of symmetric rectangular honeycomb panels having simple support boundary conditions is investigated using the classical plate theory, Mindlin's improved plate theory and Reddy's third-order plate theory.
TL;DR: In this article, a unified compact formulation of theories for multilayered structures analyses is extended to study the response of composites and sandwich plates subjected to localized distribution of transverse pressure and to point loadings.
TL;DR: In this paper, a study of the transverse normal strain effect on the static thermoelastic response of homogeneous and multilayered plates is presented, and numerical evaluations have been given for classical, refined, and advanced zig-zag plate theories.
Abstract: A study of the transverse normal strain effect on the static thermoelastic response of homogeneous and multilayered plates is presented. Numerical evaluations have been given for classical, refined, and advanced zig-zag plate theories. Constant, linear, and higher-order forms of temperature profile in the plate thickness direction have been accounted for. Basic assumptions of the considered theories are quoted. The related governing equations are not given because these were derived from a unified formulation that was described elsewhere. Closed-form solutions are discussed by addressing three plate problems: a homogeneous plate made of an isotropic layer; a two-layered plate consisting of two layers made of different isotropic materials; a multilayered composite plate made of three cross-ply layers. It has been confirmed that any refinements of classical models are generally meaningless, unless the effects of transverse shear and normal strains are both taken into account in a plate theory. Furthermore, it has been found that transverse normal strains cannot be discarded even though thin plates are considered and the accurate description of the temperature profile in the plate thickness direction could result to be meaningless, unless transverse normal strains are taken into account, and vice versa.
TL;DR: In this article, a variational-asymptotic method was used to construct a Reissner-Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions.
TL;DR: In this article, the authors analyzed transient heat conduction in a thick functionally graded plate by using a higher-order plate theory and a meshless local Petrov-Galerkin (MLPG) method.
Abstract: We analyze transient heat conduction in a thick functionally graded plate by using a higher-order plate theory and a meshless local Petrov-Galerkin (MLPG) method. The temperature field is expanded in the thickness direction by using Legendre polynomials as basis functions. For temperature prescribed on one or both major surfaces of the plate, modified Lagrange polynomials are used as basis and additional terms are added to these expansions to exactly match the given temperatures. Partial differential equations for the evolution of the coefficients of the Legendre polynomials are reduced to a set of coupled ordinary differential equations (ODEs) in time by a MLPG method. The ODEs are integrated by the central-difference method. The time history of evolution of the temperature at the plate centroid and through-the-thickness distribution of the temperature computed with the fifth-order plate theory are found to agree very well with those obtained analytically.
TL;DR: In this paper, a four-node finite element based on the efficient higher-order cubic zigzag plate theory of laminated composite plates with multiple delaminations is developed to refine the prediction of frequencies, mode shape, and time response.
TL;DR: A combined analytical and experimental study for flexural-torsional buckling of pultruded fiber-reinforced plastic (FRP) composite open channel beams is presented in this article.
TL;DR: In this article, the effect of shape memory alloy (SMA) fibers on the critical temperature, thermal postbuckling deflection, natural frequency and critical dynamic pressure of the SMA composite plate was investigated.
Abstract: It is investigated that the composite plate embedded with shape memory alloy (SMA) fibers is subject to the aerodynamic and thermal loading in the supersonic region. The nonlinear finite element equations based on the first-order shear deformation plate theory (FSDT) are formulated for the laminated composite plate embedded with SMA fibers (SMA composite plate). The von Karman strain–displacement relation is used to account for the large deflection. The incremental method considering the influence of the initial deflections and initial stresses is adopted for the temperature-dependent material properties of SMA fibers and composite matrix. The first-order piston theory is used for modeling aerodynamic loads. This study shows the effect of the SMA on the critical temperature, thermal post-buckling deflection, natural frequency and critical dynamic pressure of the SMA composite plate.
TL;DR: In this article, an improved high-order theory is presented to investigate the dynamic behavior of thin and thick fiber-reinforced plastic (FRP) plates with a soft viscoelastic flexible core.
Abstract: An improved high-order theory is presented to investigate the dynamic behavior of thin and thick fiber-reinforced plastic (FRP) plates with a soft viscoelastic flexible core. Shear deformation theory is used for the face sheets while three-dimensional elasticity theory is used for the soft core. The analysis permits nonlinear distortions of the cross-sectional plane of the core as well as changes in its height. The analysis determines the damped natural frequencies, loss factors, and local and global mode shapes of plates. Some of the results are hitherto not reported in the literature based on a higher-order plate theory (HSAPT). Transverse shear and rotary inertia effects of face sheets are taken into consideration. For simply supported boundary condition, closed-form solutions are obtained by Navier’s technique. Numerical results are presented and compared with the experimental and theoretical results found in literature.
TL;DR: In this article, the nonlinear vibration and dynamic response of simply supported shear deformable cross-ply laminated plates with piezoelectric actuators subjected to mechanical, electrical and thermal loads are investigated.
TL;DR: This study uses the first-order Mindlin plate theory with the precise thickness-shear frequency, which is normalized to one, to find corresponding wavenumbers and solves the coupled frequency equation for exact coupling points in a crystal plate of AT-cut quartz.
Abstract: It is well understood that the strong coupling of thickness-shear and flexural vibrations in piezoelectric crystal plates only occurs at specific length at which the vibration mode conversion, like the flexural mode gradually converting to thickness-shear mode while the thickness-shear mode converting to higher-order flexural mode, happens. It is important to avoid the strong coupling of modes in a crystal resonator that uses thickness-shear vibrations to enhance the energy trapping. To achieve such a design goal, the length of a crystal blank should be carefully chosen such that the coupling is at its weakest, which usually is in the middle of two strong coupling points. Through a closer examination of the frequency spectra, or the frequency-length relationship in this study, we can see that the strong coupling points appear periodically. This implies that we can find exact locations with the plate theory that predicts the resonance frequency. Based on this observation, we first use the first-order Mindlin plate theory with the precise thickness-shear frequency, which is normalized to one, to find corresponding wavenumbers. Then the length as a variable is solved from the coupled frequency equation for exact coupling points in a crystal plate of AT-cut quartz. The optimal length of a crystal blank in the simplest resonator model is calculated for the coupled thickness-shear, flexural, and extensional vibrations. The solutions and the method will be important in the determination of optimal length of a crystal blank in the resonator design process.
TL;DR: In this article, structural eigensolutions for the out-of-plane modes and sound radiation from the modal vibration of a thick annular disk with free-free boundaries have been calculated using both thick and thin plate theories.
TL;DR: In this article, the authors used a higher order shear and normal deformable plate theory of Batra and Vidoli and the finite element method to analyze free vibrations and stress distribution in a thick isotropic and homogeneous plate.
TL;DR: In this paper, the nonlinear random vibration of a simply supported cross-ply laminated composite plate is treated as a random process and the material properties and the external excitations are treated as random process.
TL;DR: In this article, the displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory, which is used to perform free-vibration analysis of a simply supported functionally graded thick plate.
Abstract: The displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory. This trigonometric shear deformation plate theory is used to perform free-vibration analysis of a simply supported functionally graded thick plate. Lame's coefficients and density for the material of the plate are assumed to vary in the thickness direction only. Effects of rotatory inertia are considered in the present theory and the vibration natural frequencies are investigated. The results obtained from this theory are compared with those obtained from a 3D elasticity analysis and various equivalent theories that are available. A detailed analysis is carried out to study the various natural frequencies of functionally graded material plates. The influences of the transverse shear deformation, plate aspect ratio, side-to-thickness ratio and volume fraction distributions are investigated.
TL;DR: In this paper, a homogeneous isotropic plate is examined with a surfacemounted linear array of piezoelectric ceramic (PZT) disks, which function as actuators to excite flexural waves and also as sensors to receive the waves scattered from structural damage in the plate.
Abstract: This article presents the experimental results of adopting a geophysical migration technique to interpret the ultrasonic flexural wave signals for the purpose of realizing quantitative damage identification in structures. In this study, a homogeneous isotropic plate is examined with a surfacemounted linear array of piezoelectric ceramic (PZT) disk. The piezoelectric disks function as actuators to excite flexural waves and also as sensors to receive the waves scattered from the structural damage in the plate. A prestack reverse-time migration technique, which is an advanced technique in geophysics to reverse the reflection wavefield and to image the Earth’s interior, is then used to back-propagate the scattering waves and to image damage in the plate. The configuration of the experimental setup is presented and its capability of accurately generating and receiving flexural waves is validated by comparing the collected signals with an analytical solution of transient response of a narrowband signal in a piezoelectric sensor/actuator integrated plate using Mindlin plate theory. Finally, the migration results from the scattering waves of an artificial damage are presented. It is shown that the existence of the damage is correctly revealed through migration process in the experiment as it has been shown using synthetic data.
TL;DR: In this article, a spline and semi-analytical finite strip method for predicting the postbuckling response of rectangular composite laminated plates with initial imperfections, when subjected to progressive end shortening is presented.
TL;DR: In this article, a new spectrally formulated plate element is developed to study wave propagation in composite structures, which is based on the classical lamination plate theory and has an exact dynamic stiffness matrix, as it uses the exact solution of the governing elastodynamic equation of plate in frequency-wavenumber domain as the interpolating functions.