scholarly journals Finite Element Analysis of Functionally Graded Piezoelectric Spheres

10.5772/52932 ◽  
2012 ◽  
Author(s):  
A. Ghorbanpour ◽  
R. Kolahchi ◽  
A. A. Mosalaei Barzoki ◽  
A. Loghman ◽  
F. Ebrahimi
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Functionally Graded ◽  
Element Analysis ◽  
Functionally Graded Piezoelectric

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

2016 ◽  
Vol 33 (8) ◽  
pp. 2421-2447 ◽  
Author(s):  
João Paulo Pascon
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Scientific Literature ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Transverse Strain ◽  
Thickness Direction ◽  
Element Analysis ◽  
Content Type

Purpose The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio. Design/methodology/approach The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated. Findings In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution. Originality/value In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.

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