Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

2015 ◽  
Vol 268 ◽  
pp. 1240-1258 ◽  
Author(s):  
Karan K. Pradhan ◽  
S. Chakraverty
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Power Law ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Power Law Exponent

scholarly journals Free Vibration Response of Four-Parameter Functionally Graded Thick Spherical Shell Formulation on Higher-Order Shear Deformation Theory

2020 ◽  
Vol 9 (3) ◽  
pp. 464-473
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Power Law ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Skew Angle

This paper emphasizes on the free vibration (FV) responses of functionally graded thick spherical shell in rectangular form using traditional mathematical formulation on finite element method and governed by Higher order shear deformation theory (HOSDT). A functionally graded spherical shell made up of metal-rich on the top surface and in contrast, base surface of the model is ceramic-rich. The FG volume fraction of four-parameter power-law material constituents assumed in the thickness direction. To highlight the potential for the current method, convergence studies, and validation tests performed to establish the stability and accuracy attained by the current approach. The parametric studies presented to scrutinize the influence of choice of four parameters employed through power-law distribution. The eminence effect of spherical shell geometrical properties, and different types of support conditions, skew angle on the FV behavior of non-dimensional frequency responses examined in detail.

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

On the buckling of advanced composite sandwich rectangular plates

2020 ◽  
pp. 109963622092508 ◽  
Author(s):  
Atteshamuddin S Sayyad ◽  
Yuwaraj M Ghugal
Keyword(s):  
Shear Deformation ◽  
Power Law ◽  
Analytical Solutions ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Skin Thickness ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Aspect Ratios

In this paper, higher order closed-formed analytical solutions for the buckling analysis of functionally graded sandwich rectangular plates are obtained using a unified shear deformation theory. Three-layered sandwich plates with functionally graded skins on top and bottom; and isotropic core in the middle are considered for the study. The material properties of skins are varied through the thickness according to the power-law distribution. Two types of sandwich plates (hardcore and softcore) are considered for the detail numerical study. A unified shear deformation theory developed in the present study uses polynomial and non-polynomial-type shape functions in terms of thickness coordinate to account for the effect of shear deformation. In the present theory, the in-plane displacements consider the combined effect of bending rotation and shear rotation. The parabolic shear deformation theory of Reddy and the first-order shear deformation theory of Mindlin are the particular cases of the present unified formulation. The governing differential equations are evaluated from the principle of virtual work. Closed-formed analytical solutions are obtained by using the Navier’s technique. The non-dimensional critical buckling load factors are obtained for various power-law coefficients, aspect ratios and skin-core-skin thickness ratios.

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