Functionally Graded Circular Plates Research Articles

An extension of Carrera unified formulation in polar coordinates for mechanical and thermal buckling analysis of axisymmetric FG circular plate using FEM

The main goal of this article is to extend the Carrera unified formulation (CUF) in polar coordinates to analyze the mechanical and thermal buckling of functionally graded (FG) circular plates with axisymmetry. The governing equations are derived using CUF in polar coordinates for FEM. The fundamental nuclei, and accordingly, the elemental matrices for a 3-node line axisymmetric element are proposed. Mechanical and thermal buckling under uniform, nonlinear temperature rise with and without the effect of convection has been investigated. The results have been verified with several plate theories and the finite element method using the second-order axisymmetric 2D elements.

Nonlinear vibration analysis of functionally graded porous circular plates under hygro-thermal loading

In this work, the nonlinear vibrations of functionally graded (FG) porous circular plates under hygro-thermal loading is studied utilizing a numerical approach. Hygroscopic stresses generated due to the nonlinear rise in moisture concentration, even and uneven porosity distributions, and temperature dependency of material properties are all taken into account. Modified Voigt’s rule of mixture is applied to obtain the hygro-thermo-mechanical properties of the FG circular plate. All material properties are assumed to be temperature-dependent using the Touloukian formula. In order to obtain the equations of motion, the first-order shear deformation theory, von-Kármán geometrical non-linearity assumption, and hygro-thermal strains are considered concurrently. After deriving the equations of motion using Hamilton’s principle, the differential quadrature method and the Newmark-beta time integration scheme are employed in conjunction with an iterative approach to solve the set of nonlinear governing differential equations of motion. The effects of various parameters including temperature distribution, plate’s thickness, porosity volume fraction, moisture concentration, and FG index are studied on plate’s maximum non-dimensional lateral deflection.

Effect of uniform and nonuniform porosity on free vibration of functionally graded circular plate

The purpose of this study is to determine the natural frequencies of functionally graded (FG) porous circular plates while taking into account the uniform and nonuniform porosity distribution in the thickness direction. The material properties of FG plates are assumed to be varying continuously in the thickness direction. The material properties are calculated based on Voigt’s micro-mechanical model taking power law distribution method with arbitrary power index. The mathematical model of the FG circular porous plate is based on the first-order shear deformation theory (FSDT). The motion of equations is derived using Hamilton’s energy principle and the Differential Quadrature Method (DQM) is applied to solve this equation. Convergence studies with respect to the number of nodes are used to validate the established solution methodology for nondimensional frequencies of FG circular plates. The nondimensional frequency for the FG circular plate is calculated and compared to the existing literature results. The effects of the thickness to radius ratio, material parameters, porosity distribution, and boundary conditions on the fundamental frequency for FG porous circular plates are also discussed in detail.

Quasi-3D static analysis of two-directional functionally graded circular plates

weak-form formulation of finite annular prism methods (FAPM) based on Reissner's mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates with various boundary conditions and under mechanical loads. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of the loaded FG circular plates with both simply-supported and clamped edges are in excellent agreement with the solutions obtained using the 3D analytical approach and two-dimensional advanced plate theories available in the literature.

Nonlinear thermal buckling analyses of functionally graded circular plates using higher-order shear deformation theory with a new transverse shear function and an enhanced mesh-free method

This study presents nonlinear buckling analyses of functionally graded (FG) circular plates in thermal environments using a mesh-free method. The thermal buckling response is formulated based on higher-order shear deformation plate theory in which a new transverse shear function is incorporated to better represent the displacement fields. An enhanced mesh-free radial point interpolation method (RPIM) in which the shape functions are constructed without any fitting parameters by virtue of the radial basis function in a compactly supported form is developed and utilized to explore the thermal buckling behavior. A radial basis function in a compactly supported form is proposed and included in the RPIM. Two types of FG circular plates with different FGM orientation, i.e., metal–ceramic FG circular plates and ceramic–metal FG circular plates, are considered in the analyses. The effectiveness and accuracy of the enhanced RPIM based on the higher-order shear deformation theory is first confirmed by simulating a numerical example found in the literature and comparing the results with the analytical solutions. Detailed parametric studies are then performed to investigate the effects of the volume fraction, plate thickness-to-radius ratio and metallic surface temperature on the critical buckling temperatures of FG circular plates subjected to various through-thickness temperature distributions. Results demonstrate that the enhanced mesh-free RPIM based on the higher-order shear deformation plate theory with the proposed transverse shear function can effectively predict the thermal buckling responses of FG circular plates, and that the volume fraction, plate thickness-to-radius ratio, bottom surface temperature and FGM orientation have considerable effects on the critical buckling temperatures.

Numerical Solution of Thermal Residual Stress Analysis with Finite Difference Method of Functionally Graded Circular Plates

In this study, thermal residual stress analysis of functionally graded circular plates (FGCP) carried out. Finite difference equations are used in solving Navier's equations of elasticity and Fourier's heat conduction equation. The grading along the plate was made along the surface of plate and it was assumed that the material properties changed according to the Mori-Tanaka approach. Grading along the plate was made in both radial and tangential directions. In this study, the effect of the coordinate derivatives of material properties was taken into consideration in both Fourier's heat conduction equation and Navier's equations of elasticity, unlike the other studies. As a result, when the materials compositions of FGCP were changed from ceramic-rich to metal-rich compositions, the stress levels were not affected considerably. The strain levels increased significantly when the metal compound in the material composition of FGCP was increased. FGCP are emphasized that the change of material properties due to two-dimensional significantly affect distributions of thermal strain and stress. In this study, it was emphasized that changing the radial and tangential direction of the compositional gradient exponents of FGCP subjected to heat flux along the outer edge significantly influences the strain and stress distributions.

Buckling analysis of circular functionally graded plate under uniform radial compression including shear deformation with linear and quadratic thickness variation on the Pasternak elastic foundation

A numerical scheme for buckling analysis of functionally graded circular plate (FGCP) subjected to uniform radial compression including shear deformation rested on Pasternak elastic foundation is presented. The linear and quadratic thickness variation patterns with various boundary conditions are considered. A modified Euler–Lagrange equation is achieved and then solved by converting differential equation to a nonlinear algebraic system of equations. Also, based on traction–free surface without using shear correction factor, a new approach by considering shear deformation for buckling analysis of FGCP rested on elastic foundation is carried out. The stability equation based on shear stress-free surface is solved by the spectral Ritz method. The spectral Ritz method has good flexibility in the sense of satisfying the boundary conditions. The effects of both linear and quadratic thickness variations and Poisson’s ratio are investigated. By taking small numbers of the basis, the outcomes in literature are improved.

Static response of 2-D functionally graded circular plate with gradient thickness and elastic foundations to compound loads

In this paper, the static behavior of bi-directional functionally graded (FG) non-uniform thickness circular plate resting on quadratically gradient elastic foundations (Winkler-Pasternak type) subjected to axisymmetric transverse and in-plane shear loads is carried out by using state-space and differential quadrature methods. The governing state equations are derived based on 3D theory of elasticity, and assuming the material properties of the plate except the Poisson's ratio varies continuously throughout the thickness and radius directions in accordance with the exponential and power law distributions. The stresses and displacements distribution are obtained by solving state equations. The effects of foundation stiffnesses, material heterogeneity indices, geometric parameters and loads ratio on the deformation and stress distributions of the FG circular plate are investigated in numerical examples. The results are reported for the first time and the new results can be used as a benchmark solution for future researches.

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.

Impact performance of Al/SiC functionally graded circular plates

This experimental study addresses the effect of ceramic reinforcement on the impact performance of functionally graded (FG) circular plates. The FG circular plates were produced from two different ceramic (SiC or Al 2 O 3 ) and metal (Al) combinations using powder stacking-hot pressing technique. The Al/SiC FG circular plates exhibited better impact resistance than Al/Al 2 O 3 FG circular plates. The effect of ceramic particle size was also investigated on the impact performance of specimens with different composition variations. A ceramic particle size of 50 μm improved the impact performance. In addition, the material composition and impactor velocity also affected the impact performance. Thus, the contact force increases as the composition changes from metal-rich to ceramic-rich. The peak contact force increases with increasing the velocity of impactor.

Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment

Free vibration analysis of functionally graded (FG) thin-to-moderately thick annular plates subjected to thermal environment and supported on two-parameter elastic foundation is investigated. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The equations of motion and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the Hamilton’s principle based on the first order shear deformation theory (FSDT). The initial thermal stresses are obtained by solving the thermoelastic equilibrium equations. Differential quadrature method (DQM) as an efficient and accurate numerical tool is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The formulations are validated by comparing the results in the limit cases with the available solutions in the literature for isotropic and FG circular and annular plates. The effects of the temperature rise, elastic foundation coefficients, the material graded index and different geometrical parameters on the frequency parameters of the FG annular plates are investigated. The new results can be used as benchmark solutions for future researches.

The elasto-plastic impact analysis of functionally graded circular plates under low-velocities

Abstract In this study, three-dimensional elasto-plastic analysis of functionally graded (FG) circular plates under low-velocity impact loads is presented. The FG circular plate is composed of ceramic (SiC) and metal (Al) phases, varying in a predetermined fashion through the plate thickness. The elasto-plastic behaviour of the FG circular plate is described by the TTO model. In the analyses, the ceramic phase is taken to be an isotropic elastic material whereas the metal phase is taken to be elasto-plastic material in accordance with the TTO model. The locally effective material properties were evaluated using homogenization method which is based on the Mori–Tanaka scheme. The effects of compositional gradient exponent and impactor velocity on the elasto-plastic impact response of the FG circular plates are investigated, and results are presented graphical form. The compositional gradient exponent and impactor velocity have significant effects on the elasto-plastic impact response of the FG circular plates. The elasto-plastic impact response of FG circular plates is similar to those of homogeneous plates. Therefore, the TTO model can be used to describe the mechanical behaviour of FG plates beyond the elastic range, assuming that the material response is essentially governed by the spreading of plasticity in the metal phase.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Elastic response of functionally graded circular plates under a drop-weight

Abstract The three-dimensional impact behaviours of functionally graded (FG) circular plates were studied under a drop-weight. The functionally graded circular plate was composed of ceramic (SiC) and metal (Al) phases and the through-thickness mechanical properties through the region between the metal and ceramic layers vary continuously according to a power-law distribution of the volume fraction of the ceramic. The through-thickness material properties of the FG circular plate were determined using the Mori–Tanaka scheme. The effects of layer number and compositional gradient exponent as well as impactor velocity and plate radius on the elastic impact response of the FG circular plates were investigated. The compositional gradient exponent, impactor velocity and plate radius played an important role on the impact response of the FG circular plates, whereas the layer number through the plate thickness had a minor effect. In addition, the failure strains in all layers were determined using Tamura–Tomota–Ozowa (TTO) model in order to predict the damage regions in each layer through the thickness of FG circular plates.

Axisymmetric bending analysis of thick functionally graded circular plates using fourth-order shear deformation theory

In the present article, axisymmetric bending and stretching of functionally graded (FG) circular plates subjected to uniform transverse loading based on fourth-order shear deformation plate theory (FOST) have been studied. Using a fourth-order shear deformation theory, the solutions for deflection and rotation functions of FG plates are presented in terms of the corresponding quantities for a homogeneous plate using the classical plate theory (CPT), from which solutions one can easily obtain the FOST solutions for axisymmetric bending of FG circular plates. It is assumed that the effective mechanical properties of the functionally graded plates through the thickness are continuous functions of the volume fractions of the constituent parts which are themselves defined by a power-law function. Numerical results for maximum deflection and shear stress are presented for various percentages of ceramic–metal volume fractions. These results are also compared with those obtained from the first-order shear deformation plate theory of Mindlin (FST), the third-order shear deformation plate theory of Reddy (TST) as well as the exact three-dimensional elasticity solution. It is found that although the maximum deflections obtained using FOST and TST are close to each other, the through-thickness shear stress is predicted more accurately by the FOST formulation than by the TST.

An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression

In this research, mechanical buckling of circular plates composed of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM circular plate under uniform radial compression are derived, based on the higher order shear deformation plate theory (HSDT). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations are established. A buckling analysis of a functionally graded circular plate (FGCP) under uniform radial compression is carried out and the results are given in closed-form solutions. The results are compared with the buckling loads of plates obtained for FGCP based on the first order shear deformation plate theory (FSDT) and classical plate theory (CPT) given in the literature. The study concludes that HSDT accurately predicts the behavior of FGCP, whereas the FSDT and CPT overestimates buckling loads.

Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory

In this research, thermal buckling of circular plates compose of functionally graded material (FGM) is considered. Equilibrium and stability equations of a FGM circular plate under thermal loads are derived, based on the higher order shear deformation plate theory (3rd order plate theory). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations is established. A buckling analysis of a functionally graded circular plate (FGCP) under various types of thermal loads is carried out and the result are given in closed-form solutions. The results are compared with the critical buckling temperature obtained for FGCP based on first order (1st order plate theory) and classical plate theory (0 order plate theory) given in the literature. The study concludes that higher order shear deformation theory accurately predicts the behavior of FGCP, whereas the first order and classical plate theory overestimates buckling temperature.