Solid Circular Plate Research Articles

The effect of different functionalities of FGM and FGPM layers on free vibration analysis of the FG circular plates integrated with piezoelectric layers

The present paper deals with the free vibration analysis of the functionally graded solid and annular circular plates with two functionally graded piezoelectric layers at top and bottom subjected to an electric field. Classical plate theory (CPT) is used for description of the all deformation components based on a symmetric distribution. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness direction of the plate. The properties of plate core can vary from metal at bottom to ceramic at top. The effect of non homogeneous index of functionally graded and functionally graded piezoelectric sections can be considered on the results of the system. <TEX>$1^{st}$</TEX> and <TEX>$2^{nd}$</TEX> modes of natural frequencies of the system have been evaluated for both solid and annular circular plates, individually.

Thermal buckling analysis of porous circular plate with piezoelectric sensor-actuator layers under uniform thermal load

This study presents the thermal buckling analysis of solid circular plate made of porous material bounded with piezoelectric sensor-actuator patches. The porous material properties vary through the thickness with specific function. The general mechanical nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of piezoelectric porous plate. Thermal buckling load is derived for solid circular plates under uniform temperature load for the clamped edge condition. In recent paper the effects of porous plate’s thickness, porosity, porous thermal expansion coefficient, piezoelectric thickness, piezoelectric thermal expansion coefficient, and feedback gain on thermal stability of the plate are investigated.

Thermal Postbuckling of Imperfect Circular Functionally Graded Material Plates: Examination of Voigt, Mori–Tanaka, and Self-Consistent Schemes

Thermal postbuckling of solid circular plates made of a through-the-thickness functionally graded material (FGM) is analyzed in this paper. Initial imperfection of the plate is also taken into account. Each thermomechanical property of the plate is assumed to be a function of the temperature and thickness coordinate. Equivalent properties of the FGM media are obtained based on three different homogenization schemes, namely, Voigt rule, Mori–Tanaka scheme, and self-consistent estimate. Temperature profile is assumed to be through-the-thickness direction only. The solution of the heat conduction equation is obtained using an iterative central finite difference scheme. Various types of thermal loadings, such as uniform temperature rise, temperature specified at surfaces, and heat flux, are considered. Nonlinear equilibrium equations of the plate are obtained by means of the conventional Ritz method. Solution of the resulting nonlinear equilibrium equations and temperature distribution are obtained simultaneously at each step of heating. It is shown that response of a perfect clamped FGM plate is of the bifurcation type of buckling with stable postbuckling equilibrium branch, whereas imperfect clamped and perfect/imperfect simply supported FGM plates do not reveal the bifurcation type of instability through the nonuniform heating process. Furthermore, amplitude of initial imperfection is an important factor on the equilibrium path of FGM circular plates, especially for simply supported ones.

Thermal Buckling Analysis of Circular Plates Made of Piezoelectric and Saturated Porous Functionally Graded Material Layers

AbstractThis study presents the thermal buckling of a radially solid sandwich circular plate made of a piezoelectric actuator and porous material. The porous material properties vary through the thickness of the plate for a specific function. The general thermoelastic nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The geometrical nonlinearities are considered along with the higher-order shear deformation plate theory. The problem is simplified to an axisymmetric one, and then closed-form solutions for circular plates subjected to temperature load are obtained. The buckling temperatures that are derived for solid circular plates under uniform temperature rise through the thickness for an immovable clamped edge of the boundary conditions. The effects of the porous plate thickness, piezoelectric thickness, applied actuator voltage, and variation of porosity on the critical temperature loa...

Thermal and mechanical stability of a circular porous plate with piezoelectric actuators

In this study, thermal and mechanical stability of solid circular plate which is made of saturated and unsaturated porous material with piezoelectric actuators is investigated. The edge of the plate is clamped, and the plate is assumed to be geometrically perfect. The effect of porosity on mechanical and thermal buckling loads is investigated in this study. The results show that the effect of porosity on thermal and mechanical stability is different and depends on some parameters. Effects of fluid thermal expansion and piezoelectric thermal expansion on critical thermal buckling load are investigated for a porous plate. The effects of porous, piezoelectric layers thicknesses, and applied electrical field on thermal and mechanical buckling load of the plate are investigated, too. Mechanical and thermal equilibria are derived based on classic plate theory. Thermal and mechanical critical loads are obtained for all the cases, and finally, there is a comparison between the result of this paper and previous literature.

Thermal buckling analysis of porous circular plate with piezoelectric actuators based on first order shear deformation theory

Abstract This study presents the thermal buckling of radially solid circular plate made of porous material with piezoelectric actuator layers. Porous material properties vary through the thickness of plate with a specific function. The porous plate is assumed of the form where pores are saturated with fluid. The general thermoelastic nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of piezoelectric porous plate. The geometrical nonlinearities are considered along with the first order shear deformation plate theory (FST). Then, closed form solution for the circular plates subjected to temperature load is obtained. Buckling temperatures are derived for solid circular plates under uniform temperature rise through the thickness for immovable clamped edge of boundary conditions. The effects of porous plate thickness, pores distribution, piezoelectric thickness, applied actuator voltage and variation of porosity on the critical temperature load are investigated. It has also been investigated the effect of different thermal expansion coefficient of porous and piezolectric plate on stability of plate.

A Nonclassical Model for Circular Mindlin Plates Based on a Modified Couple Stress Theory

A nonclassical model for circular Mindlin plates subjected to axisymmetric loading is developed using a modified couple stress theory. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation based on Hamilton's principle. The new model contains a material length scale parameter and can capture the size effect, unlike existing circular Mindlin plate models based on classical elasticity. In addition, both the stretching and bending of the plate are considered in the formulation. The current plate model reduces to the classical elasticity-based Mindlin plate model when the material length scale parameter is set to be zero. Additionally, the new circular Mindlin plate model recovers the circular Kirchhoff plate model as a special case. To illustrate the new model, the static bending problem of a clamped solid circular Mindlin plate subjected to an axisymmetrically distributed normal pressure is analytically solved by directly applying the new model and using the Fourier–Bessel series. The numerical results show that the deflection and rotation angle predicted by the new model are smaller than those predicted by the classical Mindlin plate model. It is further seen that the differences between the two sets of predicted values are significantly large when the plate thickness is small, but they are diminishing with the increase of the plate thickness.

Thermal Buckling Analysis of Functionally Graded Thin Circular Plate Made of Saturated Porous Materials

This study presents the buckling analysis of thermal loaded solid circular plate made of porous material. It is assumed that the material properties of the porous plate vary across the thickness. The edge of the plate is clamped and the plate is assumed to be geometrically perfect. The geometrical nonlinearities are considered in the Love–Kirchhoff hypothesis sense. Equilibrium and stability equations, derived through the variational formulation, are used to determine the prebuckling temperatures and critical buckling temperatures. The equations are based on the Sanders non-linear strain-displacement relation.The porous plate is assumed of the form where pores are saturated with fluid. Also, the effect of pores distribution and thermal distribution on the critical buckling temperature is investigated.

Buckling analysis of a porous circular plate with piezoelectric sensor–actuator layers under uniform radial compression

This study presents the buckling analysis of a solid circular plate made of porous material bounded with piezoelectric sensor–actuator patches. The porous material properties vary through the thickness direction of the plate following a given function. The general mechanical nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The buckling load is derived for solid circular plates under uniform radial compressive loading for the clamped edge condition. The effects of piezoelectric layers on the buckling load of the plate, piezoelectric layer-to-porous plate thickness ratio, feedback gain, and variation of porosity are investigated. The results are verified with the known results in the literature.

Semi-Analytical Solution for the Static Analysis of 2D Functionally Graded Solid and Annular Circular Plates Resting on Elastic Foundation

The effects of two-parameter linear elastic foundations on axisymmetric response of two directionally functionally graded circular plates are investigated by using a differential quadrature method. The state equations are derived based on 3D theory of elasticity, and assuming the modulus of elasticity varies continuously throughout the thickness and radius directions in the form of an exponential function, and the Poisson's ratio is constant. The stresses and displacements distribution are obtained by solving these state equations. The influences of gradient indices, thickness to radius ratio, foundation stiffness, and edge supports on the static behavior of a plate are studied in the numerical examples.

Buckling analysis of porous circular plate with piezoelectric actuator layers under uniform radial compression

This study presents the buckling analysis of radially solid circular plate made of porous material bounded with the layers of piezoelectric actuators. Porous material properties vary through the thickness of plate with a specific function. The general mechanical non-linear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of piezoelectric porous plate. Buckling load is derived for solid circular plates under uniform radial compressive loading, for the clamped edge condition. The effects of piezoelectric layers on the buckling load of plate, piezoelectric layer-to-porous plate thickness ratio, and variation of porosity are investigated. The results are verified with the known results in the literature.

A Comparison between Thermal Buckling Solutions of Power-Law, Sigmoid, Exponential FGM Circular Plates

In this paper, buckling of elastic, circular plates made of functionally graded material subjected to thermal loading have been investigated. Boundary condition of the plate as immovable clamped edge is considered. The material properties of the FG plates except poisson's ratios are assumed to vary continuously throughout the thickness direction according to the volume fraction of constituents defined by power-law, sigmoid, and exponential function. The Nonlinear equilibrium equations are derived based on the classical plate theory using variational formulations. Linear stability equations are used to obtain the critical buckling of solid FG circular plate under thermal load as uniform temperature rise, linear and nonlinear temperature distribution through the thickness. The effects of P-, S-, E-FGM on buckling of plate are compared. The results are validated with the known data in the literature.

Thermoelastic Buckling Analysis of Functionally Graded Circular Plates Integrated with Piezoelectric Layers

Thermal buckling of circular plates made of functionally graded materials with surface-bounded piezoelectric layers are studied. The material properties of the FG plates are assumed to vary continuously through the plate thickness by distribution of power law of the volume fraction of the constituent materials. The general thermoelastic nonlinear equilibrium and linear stability equations for the piezoelectric FG plate are derived using the variational formulations. Buckling temperatures are derived for solid circular plates under uniform temperature rise, nonlinear and linear temperature variation through the thickness for immovable clamped edge of boundary conditions. The effects of piezo-to-host thickness ratio, applied actuator voltage, boundary condition, and power law index of functionally graded plates on the buckling temperature of plate are investigated. The results are verified with the data in literature.

Nonlinear behavior of functionally graded circular plates with various boundary supports under asymmetric thermo-mechanical loading

The equilibrium equations of the first-order nonlinear von Karman theory for FG circular plates under asymmetric transverse loading and heat conduction through the plate thickness are reformulated into those describing the interior and edge-zone problems of the plate. A two parameter perturbation technique, in conjunction with Fourier series method is used to obtain analytical solutions for nonlinear behavior of functionally graded circular plates with various clamped and simply-supported boundary conditions. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified with known results in the literature. The load–deflection curves for different loadings, boundary conditions, and material constant in a solid circular plate are studied and discussed. It is shown that the behavior of FG plates with clamped or simply-supported boundary conditions are completely different. Under thermo-mechanical loading, snap-through buckling behavior is observed in simply-supported FG plates which are immovable in radial direction. Moreover, it is found that linear theory is inadequate for analyzing FG and also homogenous plates with immovable boundary supports in radial direction and subjected to thermal loading, even for deflections that are normally considered small.

Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading

AbstractIn this paper, the static analysis of functionally graded (FG) circular plates resting on linear elastic foundation with various edge conditions is carried out by using a semi-analytical approach. The governing differential equations are derived based on the three dimensional theory of elasticity and assuming that the mechanical properties of the material vary exponentially along the thickness direction and Poisson’s ratio remains constant. The solution is obtained by employing the state space method (SSM) to express exactly the plate behavior along the graded direction and the one dimensional differential quadrature method (DQM) to approximate the radial variations of the parameters. The effects of different parameters (e.g., material property gradient index, elastic foundation coefficients, the surfaces conditions (hard or soft surface of the plate on foundation), plate geometric parameters and edges condition) on the deformation and stress distributions of the FG circular plates are investigated.

Theoretical and Test Study on Dynamic Characteristics of Thin-Layered Sandy Frozen Soil in Blasting

In order to understand the stress changes of various points in sandy frozen soil, tension-compression conversion, fissure development on the surface, the rupture process, the expansion speed and scope of frozen soil duing blasting, the dynamic characteristics of thin-layered sandy frozen soil were analyzed in this paper. The blasting process of frozen soil is regarded as a dynamic pressure operation process of gas expansion chamber under thin plate. The gas pressure in blasting chamber obtained by adiabatic gas state equation is approximate close to the actual expansion pressure. At the same time, a moment of frozen soil blasting process is regarded as a model that a peripherally-fixed solid circular plate is suffered to a concentrated force in the center of circle. Through calculation and blasting funnel tests we can see that the frozen soil is suffered to much smaller force along horizontal direction than normal direction. Along with the time and expansion of blasting chamber, pressure of frozen soil is quickly reduced. And it is discovered that regardless of any stage of explosive, there appears the critical point of changes from tension to compression along the direction from explosive center to the all-around within a radius of about 0.9 m. This model can provide a theoretical guidance for the analysis of dynamic stress and the selection of blasting parameters for frozen soil blasting.

Finite element analysis of sandwich panels subjected to shock tube blast loadings

Sandwich panels with a cellular core are being widely considered for blast mitigation applications, including armor systems, because of their capability to carry transverse loads with minimal weight penalty and absorb plastic energy. In this study, several finite element models are generated and used in simulating the performance of sandwich circular panels against shock tube blast loadings. A comparison of the numerical results for aluminum and Kevlar sandwich circular panels and their corresponding monolithic solid circular plates having similar mass shows that under the shock tube blast loadings considered in this study, the peak values of the transmitted overpressure, particle acceleration, and deflection of the back face measured from gauges are less for the sandwich circular panels than for the monolithic solid circular plates. The findings are consistent with those reported by other researchers. A parametric study is conducted in investigating the influence of sandwich panel material property, configuration and mass distribution, on the sandwich performance against shock tube blast loadings. It is revealed that the peak values of transmitted overpressure, particle acceleration, and deflection of the back face are dependent on these parameters.

Basic equations of the theory of thermoviscoelastic plates with distributed sensors and actuators

The basic equations of the theory of thermoviscoelastic thin-walled plates with piezoelectric sensors and actuators under monoharmonic mechanical and electric loading are derived using the Kirchhoff-Love hypotheses. The thermomechanical behavior of passive and piezoactive materials is described using the concept of complex characteristics. Methods of solving nonlinear problems of active damping of thermomechanical vibrations of plates with sensors and actuators are considered. The effect of dissipative heating on the damping of axisymmetric vibrations of a thermoviscoelastic solid circular plate is analyzed as an example

Solid Circular Plate Clamped along Two Antipodal Edge Arcs and Deflected by a Central Transverse Concentrated Force

A static, purely flexural mechanical analysis is presented for a Kirchhoff solid circular plate, deflected by a transverse central force, and clamped along two antipodal arcs, the remaining part of the boundary being free. By adopting an integral formulation, the contact reaction is assumed to be formed by four equal concentrated forces acting at the support extremities, accompanied by two distributed moments with radial and circumferential axis, respectively. This plate problem is rephrased in terms of a complex-valued Hilbert singular integral equation of the second kind, whose solution is obtained in analytical, integral form. A design chart is presented that reports the plate central deflection as a function of the angular width of the plate supports.

Non-linear analysis of functionally graded circular plates under asymmetric transverse loading

Based on the first-order shear deformation plate theory with von Karman non-linearity, the non-linear axisymmetric and asymmetric behavior of functionally graded circular plates under transverse mechanical loading are investigated. Introducing a stress function and a potential function, the governing equations are uncoupled to form equations describing the interior and edge-zone problems of FG plates. This uncoupling is then used to conveniently present an analytical solution for the non-linear asymmetric deformation of an FG circular plate. A perturbation technique, in conjunction with Fourier series method to model the problem asymmetries, is used to obtain the solution for various clamped and simply supported boundary conditions. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified by comparison with the existing results in the literature. The effects of non-linearity, material properties, boundary conditions, and boundary-layer phenomena on various response quantities in a solid circular plate are studied and discussed. It is found that linear analysis is inadequate for analysis of simply supported FG plates which are immovable in radial direction even in the small deflection range. Furthermore, the responses of FG materials under a positive load and a negative load of identical magnitude are not the same. It is observed that the boundary-layer width is approximately equal to the plate thickness with the boundary-layer effect in clamped FG plates being stronger than that in simply supported plates.