Free vibration characteristics of functionally graded structures by an isogeometrical analysis approach

2013 ◽  
Vol 228 (9) ◽  
pp. 1512-1530 ◽  
Author(s):  
Alireza Hassanzadeh Taheri ◽  
Mohammad Hossein Abolbashari ◽  
Behrooz Hassani
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Material Properties ◽  
Isogeometric Analysis ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Analysis Method ◽  
Graded Structures ◽  
Functionally Graded Structures

An improved methodology based on isogeometric analysis (IGA) approach is suggested to investigate the free vibration characteristics of functionally graded structures. The proposed method, which can be considered as an extension of the isogeometric analysis method to inhomogeneous elasticity, employs a fully isogeometric formulation for construction of the geometry, approximation of the solution as well as modelling the variations of material properties. The gradations of material properties are captured using the same NURBS basis functions employed for geometric and computational modelling by utilization of an interpolation technique. It will be seen that the proposed NURBS-based analysis method constitutes an efficient tool for studying integrated modelling and vibration analysis of functionally graded structures. Some numerical examples of 2D plane elasticity problems are presented and the effects of different types of unidirectional and bidirectional material profiles on dynamic characteristics of functionally graded structures are investigated. The obtained numerical results are verified with available exact elasticity solutions or the results of commercial finite element method software. It is shown that the difficulties encountered in free vibration analysis of functionally graded structures using the conventional finite element method are considerably circumvented by adopting the proposed procedure.

scholarly journals Free Vibration Analysis of Functionally Graded Shells Using an Edge-Based Smoothed Finite Element Method

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 684 ◽  
Author(s):  
Tien Dat Pham ◽  
Quoc Hoa Pham ◽  
Van Duc Phan ◽  
Hoang Nam Nguyen ◽  
Van Thom Do
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Smoothing Technique ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the stiffness matrices are obtained by using the strain-smoothing technique over the smoothing domains that are formed by two adjacent MITC3 triangular shell elements sharing an edge. The strain-smoothing technique can improve significantly the accuracy and convergence of the original MITC3. The material properties of functionally graded shells are assumed to vary through the thickness direction by a power–rule distribution of volume fractions of the constituents. The numerical examples demonstrated that the present ES-MITC3method is free of shear locking and achieves the high accuracy compared to the reference solutions in the literature.

scholarly journals Parametric Study on Vibration and Harmonic Analysis of Moderately Thick Functionally Graded Plates Using FEM

2018 ◽  
Vol 237 ◽  
pp. 01007
Author(s):  
Avadesh K. Sharma ◽  
M K Gaur ◽  
R K Dwivedi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Harmonic Analysis ◽  
Material Properties ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Finite Element Package

Finite element method is used to investigate the free vibration and harmonic analysis of functionally graded plates. The material properties of the plates are assumed to vary continuously through their thickness direction according to a power-law distribution of the volume fractions of the plate constituents. The four noded shell 181 elements are used to analyse the functionally graded plates. The aim is to fill the void in the available literature with respect to the free vibration results of Functionally Graded plates. Convergence and Comparison studies with respect to the number of nodes has been carried out using FEM. The natural frequency, mode shape and harmonic analysis of FG plate has been determined using finite element package ANSYS.

scholarly journals Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite element method

2016 ◽  
Vol 54 (3) ◽  
pp. 402 ◽  
Author(s):  
Tran Huu Quoc ◽  
Tran Minh Tu ◽  
Nguyen Van Long
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates

In this paper, a new eight-unknown shear deformation theory is developed for bending and free vibration analysis of functionally graded plates by finite element method. The theory based on full twelve-unknown higher order shear deformation theory, simultaneously satisfy zeros transverse stresses at top and bottom surface of FG plates. A four-node rectangular element with sixteen degrees of freedom per node is used. Poisson’s ratios, Young’s moduli and material densities vary continuously in thickness direction according to the volume fraction of constituents which is modeled as power law functions. Results are verified with available results in the literature. Parametric studies are performed for different power law index, side-to-thickness ratios.

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