scholarly journals Shape control of hybrid functionally graded plate through smart application of piezoelectric material using simple plate theory

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
K. M. Bajoria ◽  
S. A. Patare
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Piezoelectric Material ◽  
Functionally Graded Material ◽  
Shape Control ◽  
Functionally Graded ◽  
Simple Mathematical Model ◽  
Graded Material ◽  
Flexural Analysis

AbstractThe present study takes its inspiration from notable work in the literature related to the flexural analysis of functionally graded material (FGM) plate along with a smart application of piezoelectric material but maintains its novelty in terms of simple approach, an analytical solution with a wide scope of application. Coupling the plate element with piezoelectric smart material can control deflection, vibration thereby increasing the safety, stability, and life of these elements. Plates made up of functionally graded material further enhances the applicability as two different materials are fused. Analysis of such a system is challenging especially for a closed form mathematical solution along with complex boundary conditions. In the present study, it is proposed to develop a simple analytical model for bending analysis of FGM plate coupled with piezoelectric layers. Polynomial based shear deformation function taken from literature is applied to develop a simple mathematical model. A complete flexural analysis is performed for FGM plate to validate the governing simple mathematical model. Through the smart application of piezoelectric material, the deflection of the FGM plate is controlled in as closed loop feedback system. Analytical solution valid over the entire plate domain is obtained incorporating fixed and simple support types of boundary conditions. The initial part of the study details complete mathematical formulation for the plate under consideration, followed by numerical validation in which results of the present model are compared with notable studies in the literature. Lastly, the smart application through shape control of the FGM plate is demonstrated graphically and numerically. The development and application of the discussed mathematical model presented in this study are complete in all aspects of its mathematical form, solution, and numerical validation.

Bending Analysis of Piezoelectric Functionally Graded Material Plates Using HSDT

2019 ◽  
Vol 969 ◽  
pp. 116-121
Author(s):  
Ch. Naveen Reddy ◽  
M. Bhargav ◽  
T. Revanth
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Analytical Formulation ◽  
Simply Supported ◽  
Graded Material

This work investigates the complete analytical solution for functionally graded material (FGM) plates incorporated with smart material. The odjective of the present work is to determine bending characteristics of piezoelectric FGM plates with different geometrical parameters, voltages and boundary conditions for electro-mechanical loading. In this work an analytical formulation based on higher order shear deformation theory (HSDT) is presented for the piezoelectric FGM plates. The solutions are obtained in closed from using Navier’s technique for piezoelectric FGM plates a specific type of simply supported boundary conditions and pc code have been developed to find out the deflections and stresses for various parameters. All the solutions are plotted against aspect proportion, side to thickness proportion as a function of material variety parameter (n) and thickness coordinate for different voltages. The significant trends from the results are obtained.

scholarly journals Three-dimensional semi-analytical solutions for the transient response of functionally graded material cylindrical panels with various boundary conditions

2019 ◽  
Vol 39 (4) ◽  
pp. 1002-1023
Author(s):  
Xu Liang ◽  
Yu Deng ◽  
Xue Jiang ◽  
Zeng Cao ◽  
Yongdu Ruan ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Transient Response ◽  
Functionally Graded Material ◽  
Analytical Method ◽  
Composite Structures ◽  
Outer Radius ◽  
Functionally Graded ◽  
Cylindrical Panels ◽  
Graded Material

In this paper, a 3D semi-analytical method is proposed by introducing the Durbin’s Laplace transform, as well as its numerical inversion method, state space approach and differential quadrature method to analyse the transient behaviour of functionally graded material cylindrical panels. Moreover, to investigate the effectiveness of the proposed semi-analytical solution, four boundary conditions are used to undertake the analyses. Comparing the proposed approach with other theoretical methods from the literatures, we see better agreements in the natural frequencies. Besides, the semi-analytical solution acquires nearly the same transient response as those obtained by ANSYS. Convergence studies indicate that the proposed method has a quick convergence rate with growing sample point numbers along the length direction, so do layer numbers increase along the radial direction. The effects of thickness/outer radius ratio, length/outer radius ratio and functionally graded indexes are also studied. When carbon nanotube is added to functionally graded material cylindrical panel, the composite structures have been reinforced greatly. The proposed 3D semi-analytical method has high accuracy for the analysis of composite structures. This study can serve as a foundation for solving more complicated environments such as fluid–structure interaction of flexible pipe or thermal effect analysis of functionally graded material in aerospace field.

Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions

2018 ◽  
Vol 233 (8) ◽  
pp. 2636-2662 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Mohammad Sikandar Azam ◽  
Vinayak Ranjan
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Functionally Graded Plate ◽  
Material Inhomogeneity ◽  
Power Law Exponent ◽  
Out Of Plane ◽  
Graded Material

In the present research article, classical plate theory has been adopted to analyze functionally graded material plate, having out of plane material inhomogeneity, resting on Winkler–Pasternak foundation under different combinations of boundary conditions. The material properties of the functionally graded material plate vary according to power law in the thickness direction. Rayleigh–Ritz method in conjugation with polynomial displacement functions has been used to develop a computationally efficient mathematical model to study free vibration characteristics of the plate. Convergence of frequency parameters (nondimensional natural frequencies) has been attained by increasing the number of polynomials of displacement function. The frequency parameters of the functionally graded material plate obtained by proposed method are compared with the open literature to validate the present model. Firstly, the present model is used to calculate first six natural frequencies of the functionally graded plate under all possible combinations of boundary conditions for the constant value of stiffness of Winkler and Pasternak foundation moduli. Further, the effects of density, aspect ratio, power law exponent, Young’s modulus on frequency parameters of the functionally graded plate resting on Winkler–Pasternak foundation under specific boundary conditions viz. CCCC (all edges clamped), SSSS (all edges simply supported), CFFF (cantilever), SCSF (simply supported-clamped-free) are studied extensively. Furthermore, effect of stiffness of elastic foundation moduli (kp and kw) on frequency parameters are analyzed. It has been observed that effects of aspect ratios, boundary conditions, Young’s modulus and density on frequency parameters are significant at lower value of the power law exponent. It has also been noted from present investigation that Pasternak foundation modulus has greater effect on frequency parameters as compared to the Winkler foundation modulus. Most of the results presented in this paper are novel and may be used for the validation purpose by researchers. Three dimensional mode shapes for the functionally graded plate resting on elastic foundation have also been presented in this article.

Response analysis of hybrid functionally graded material plate subjected to thermo-electro-mechanical loading

2020 ◽  
pp. 146442072098003
Author(s):  
Pawan Kumar ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Piezoelectric Material ◽  
Functionally Graded Material ◽  
Axial Stress ◽  
Functionally Graded ◽  
Response Analysis ◽  
Functionally Graded Piezoelectric Material ◽  
Graded Material ◽  
Functionally Graded Piezoelectric

Static and free vibration response analysis of a functionally graded piezoelectric material plate under thermal, electric, and mechanical loads is done in this study. The displacement field is acquired using the first-order shear deformation theory, and the Hamilton principle is applied to deduce the motion equations. Temperature-dependent material properties of the functionally graded material plate are used, and these properties follow the power-law distributions along the thickness direction. However, the properties of piezoelectric material layers are assumed to be independent of the electric field and temperature. Finite element formulation for the functionally graded piezoelectric material plate is done using the combined effect of mechanical and electrical loads. The effects of parameters like electrical loading, volume fraction exponent N, and temperature distribution on the static and free vibration characteristics of the functionally graded piezoelectric material square plate are analyzed and presented. Responses are obtained in terms of the centerline deflection, axial stress and the nondimensional natural frequency with various boundary conditions. It is observed that the centerline deflection and nondimensional natural frequency increases as exponent N increases. At the same time, the axial stress decreases with an increase in exponent N. The findings of the static and the free vibration analysis suggest the potential application of the functionally graded piezoelectric material plate in the piezoelectric actuator as well as for sensing deflection in bimorph.

NONLINEAR MECHANICAL BENDING OF FUNCTIONALLY GRADED MATERIAL PLATES UNDER TRANSVERSE LOADS WITH VARIOUS BOUNDARY CONDITIONS

2011 ◽  
Vol 02 (02) ◽  
pp. 237-258 ◽  
Author(s):  
MOHAMMAD TALHA ◽  
B. N. SINGH
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Nonlinear Strain ◽  
Various Boundary Conditions ◽  
Transverse Loads ◽  
Nonlinear Mechanical ◽  
Graded Material ◽  
Mechanical Bending

Nonlinear mechanical bending of functionally graded material (FGM) plates under transverse loads with various boundary conditions are presented. The material properties of the FGM plates are graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The theoretical nonlinear finite element formulations are based on the higher-order shear deformation theory, with a special modification in the transverse displacement in order to estimate the parabolic distribution of transverse shear strains through the plate thickness. The Green–Lagrange nonlinear strain–displacement relation with all higher-order nonlinear strain terms is included to account for the large deflection response of the plate. The fundamental equations for FGM plates with traction-free boundary conditions on the top and bottom faces of the plate are accomplished using variational approach. Results have been achieved using a C0 continuous isoparametric Lagrangian finite element with 13 degrees of freedom per node. Convergence and comparison studies have been performed to ascertain the effectiveness of the present model. Numerical results are highlighted for different thickness ratios, aspect ratios, and role played by the constituent volume fraction index with different boundary conditions.

FE Analysis of Functionally Graded Material Plate during Debonding Case with Different Boundary Conditions

2014 ◽  
Vol 627 ◽  
pp. 57-60 ◽  
Author(s):  
Wasim M.K. Helal ◽  
Dong Yan Shi
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Maximum Shear Stress ◽  
Functionally Graded ◽  
Von Mises Stress ◽  
Sigmoid Function ◽  
Different Boundary Conditions ◽  
Graded Material ◽  
The Relationship

Functionally graded materials (FGMs) have become helpful in our engineering applications. Analysis of functionally graded material (FGM) plate during debonding case with different boundary conditions is the main purpose of this investigation. Elastic modulus (E) of functionally graded (FG) plate is assumed to vary continuously throughout the height of the plate, according the volume fraction of the constituent materials based on a modified sigmoid function, but the value of Poisson coefficient is constant. In this research, the finite element method (FEM) is used in order to show the shape of a plate made of FGM during debonding case with different boundary conditions. In the present investigation, the displacement value applied to the FGM plate is changed in order to find the relationship between the maximum von Mises stress and the displacement. Also, the relationship between the maximum shear stress and the displacement is carried out in the present work. The material gradient indexes of the FGM plate are changed from 1 to 10. The stress distributions around the debonding zone with all the material gradient indexes of the FGM plate are investigated in this work.

scholarly journals An application of isogeometric analysis for active control the solid functionally graded material plates with actuator patches using piezoelectric material

2020 ◽  
Vol 2 (SI2) ◽  
pp. First
Author(s):  
Khuong Duy Nguyen ◽  
Nguyen Manh Tien ◽  
Nguyen Xuan Hung ◽  
Vu Cong Hoa
Keyword(s):  
Piezoelectric Material ◽  
Active Control ◽  
Functionally Graded Material ◽  
Isogeometric Analysis ◽  
Piezoelectric Materials ◽  
Middle Layer ◽  
Basic Function ◽  
Functionally Graded ◽  
Three Dimensional Model ◽  
Graded Material

This paper applies isogeometric analysis (IGA) to simulate active control of the functionally graded material (FGM) plates by using piezoelectric material patches. This control helps to reduce the deflection of the plate under the effect of static load, which makes the structure more resistant to loading. IGA is built on the non-uniform rational basis spline (NURBS) basic function with many advantages such as: describing geometry exactly by approximating by higher order function and directly using this function to approach procedure. Furthermore, NURBS geometry has mesh flexibility and high continuity between elements, making the problem highly accurate. Three-dimensional model for plate-like structure consists of upper and lower layers made of piezoelectric materials, the middle layer is FGM. The obtained results will be verified with the published results to prove the efficiency of the proposed method for this problem. Through the obtained results, it is shown that IGA is used effectively for the active control problem by piezoelectric patches to reduce the displacement of FGM plates. The efficiency shown when using a small number of degrees of freedom but still ensuring the solution has accurate results when compared with the reference solution.

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