A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams

2021 ◽  
pp. 115095
Author(s):  
Ngoc-Duong Nguyen ◽  
Thien-Nhan Nguyen ◽  
Trung-Kien Nguyen ◽  
Thuc P. Vo
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Variable Shear

Free vibration and buckling analysis of FGM plates using inverse trigonometric shear deformation theory

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Supen Kumar Sah ◽  
Anup Ghosh
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Rectangular Plate ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Content Type

Purpose The purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate. Design/methodology/approach Equilibrium and stability equations of FGM rectangular plate under different boundary conditions are derived using finite element method-based inverse trigonometric shear deformation theory (ITSDT). Eight-noded rectangular plate element with seven degrees of freedom at each node is used for the present analysis. The power-law distribution method has been considered for the continuously graded variation in composition of the ceramic and metal phases across the thickness of a functionally graded plate. Findings The finite element formulation incorporated with ITSDT and provisions of the constitutive model of FGM plate has been implemented in a numerical code to obtain the natural frequency and critical buckling load under uniaxial and biaxial compressive load. The influence of material gradation, volume fraction index, span to thickness ratio and boundary constraints over free vibration and buckling response has been studied. Originality/value Development and validation of finite element methodology using ITSDT to predict the structural response of the FGM plates under different loading, geometric and boundary conditions.

Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory

2021 ◽  
Vol 264 ◽  
pp. 113712 ◽  
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Mohammed-Sid-Ahmed Houari ◽  
Ahmed Amine Daikh ◽  
Aman Garg ◽  
Tarek Merzouki ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Buckling Analysis ◽  
Functionally Graded

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.

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