A finite element formulation for thermally induced vibrations of functionally graded material sandwich plates and shell panels

2017 ◽  
Vol 160 ◽  
pp. 877-886 ◽  
Author(s):  
Shashank Pandey ◽  
S. Pradyumna
Keyword(s):  
Finite Element ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Thermally Induced ◽  
Graded Material ◽  
Thermally Induced Vibrations

Effect of porosity and skew edges on transient response of functionally graded sandwich plates

2021 ◽  
pp. 030932472110626
Author(s):  
Abhilash Karakoti ◽  
Mahesh Podishetty ◽  
Shashank Pandey ◽  
Vishesh Ranjan Kar
Keyword(s):  
Finite Element ◽  
Transient Response ◽  
Volume Fraction ◽  
Pure Metal ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Skew Angle ◽  
Wide Range

This work for the first time presents the effect of porosity and skew edges on the transient response of functionally graded material (FGM) sandwich plates using a layerwise finite element formulation. Two configurations of FGM sandwich plates are considered. In the first configuration, the top and the bottom layers are made of the FGM and the core is made of pure metal, whereas in the second configuration, the bottom, core and the top layers are made of pure metal, FGM and pure ceramic, respectively. Four micromechanics models based on the rule of mixture are used to model porosity for these two configurations of FGM sandwich plates. A layerwise theory based on a first-order shear deformation theory for each layer that maintains the displacement continuity at the layer interface is used for the present investigation. An eight-noded isoparametric element with nine degrees of freedom per node is used to develop the finite element model (FEM). The governing equations for the present investigation are derived using Hamilton’s principle. A wide range of comparison studies are presented to establish the accuracy of the present FEM formulation. It has been shown here that the parameters like skew angle, porosity coefficient, volume fraction index, core to facesheet thickness ratio and boundary conditions have a significant effect on the transient response of FGM sandwich plates. Also, the present finite element formulation is simple and accurate.

scholarly journals Free vibration of FG sandwich plates partially supported by elastic foundation using a quasi-3D finite element formulation

2020 ◽  
Author(s):  
Le Cong Ich ◽  
Pham Vu Nam ◽  
Nguyen Dinh Kien
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Layer Thickness ◽  
Elastic Foundation ◽  
Functionally Graded ◽  
Thickness Ratio ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Layer Thickness Ratio

Free vibration of functionally graded (FG) sandwich plates partially supported by a Pasternak elastic foundation is studied. The plates consist of three layers, namely a pure ceramic hardcore and two functionally graded skin layers. The effective material properties of the skin layers are considered to vary in the plate thickness by a power gradation law, and they are estimated by Mori--Tanaka scheme. The quasi-3D shear deformation theory, which takes the thickness stretching effect into account, is adopted to formulate a finite element formulation for computing vibration characteristics.  The accuracy of the derived formulation is confirmed through a comparison study. The numerical result reveals that the foundation supporting area plays an important role on the vibration behavior of the plates, and the effect of the layer thickness ratio on the frequencies is governed by the supporting area. A parametric study is carried out to highlight the effects of material distribution, layer thickness ratio, foundation stiffness and area of the foundation support on the frequencies and mode shapes of the plates. The influence of the side-to-thickness ratio on the frequencies of the plates is also examined and discussed.

Vibration of Initially Stressed Functionally Graded Material Plates and Shells

2014 ◽  
Vol 684 ◽  
pp. 158-164 ◽  
Author(s):  
Sugirtha Singh J. Monslin ◽  
Thangaratnam R. Kari
Keyword(s):  
Finite Element ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Shell Element ◽  
Functionally Graded ◽  
Element Formulation ◽  
Vibration Frequencies ◽  
Functionally Graded Plates ◽  
Graded Material ◽  
Plates And Shells

Finite element formulation using semiloof shell element for initially stressed vibration of Functionally Graded Material (FGM) plates and shells are presented. The influence of volume fraction index on the vibration frequencies of thin functionally graded plates and shells and variation of temperature on frequency are studied. New results are presented for initially stressed vibration of FGM plates and shells.

scholarly journals Dynamic behavior of nonuniform functionally graded Euler-Bernoulli beams under multiple moving forces

2015 ◽  
Vol 37 (3) ◽  
pp. 151-168
Author(s):  
Le Thi Ha ◽  
Nguyen Dinh Kien ◽  
Vu Tuan Anh
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Dynamic Behavior ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Cross Sectional ◽  
Material Inhomogeneity ◽  
Graded Material ◽  
Sectional Profile

The dynamic behavior of nonuniform Euler-Bernoulli beams made of transversely functionally graded material under multiple moving forces is studied by the finite element method. The beam cross-section is assumed to vary in the width direction by two different types. A simple finite element formulation, accounting for variation of the material properties through the beam thickness  and the shift in the physically neutral surface, is derived and employed in the study. The exact variation of the cross-sectional profile is employed in evaluation of the element stiffness and mass matrices. The dynamic response of the beam is computed with the aid of the implicit Newmark method. The numerical results show that the derived finite element formulation is capable to assess accurately the dynamic characteristics of the beam by using just several elements. The effect of the moving speed, material inhomogeneity and section profile on the dynamic behavior of the beams is investigated. The influence of the distance between the forces as well as the number of forces on the dynamic response is also examined and highlighted.

scholarly journals Extended finite -element method for modeling the mechanical behavior of functionally graded material plates with multiple random inclusions

2017 ◽  
Vol 20 (K3) ◽  
pp. 119-125
Author(s):  
Bang Kim Tran ◽  
Huy The Tran ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Functionally Graded Material ◽  
Extended Finite Element Method ◽  
Functionally Graded ◽  
Extended Finite Element ◽  
Graded Material ◽  
Element Method

Functionally graded material is of great importance in many engineering problems. Here the effect of multiple random inclusions in functionally graded material (FGM) is investigated in this paper. Since the geometry of entire model becomes complicated when many inclusions with different sizes appearing in the body, a methodology to model those inclusions without meshing the internal boundaries is proposed. The numerical method couples the level set method to the extended finite-element method (X-FEM). In the X-FEM, the finite-element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of random inclusions. Numerical examples are presented to demonstrate the accuracy and potential of this technique. The obtained results are compared with available refered results and COMSOL, the finite element method software.

Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate

2017 ◽  
Vol 29 (7) ◽  
pp. 1430-1455 ◽  
Author(s):  
Vinyas Mahesh ◽  
Piyush J Sagar ◽  
Subhaschandra Kattimani
Keyword(s):  
Finite Element ◽  
Electric Fields ◽  
Elastic Plate ◽  
Coupling Effect ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Geometrical Parameters ◽  
Element Formulation ◽  
Elastic Plates

In this article, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has been investigated using finite element methods. The contribution of overall coupling effect as well as individual elastic, piezoelectric, piezomagnetic, and thermal phases toward the stiffness of magneto-electro-thermo-elastic plates is evaluated. A finite element formulation is derived using Hamilton’s principle and coupled constitutive equations of magneto-electro-thermo-elastic material. Based on the first-order shear deformation theory, kinematics relations are established and the corresponding finite element model is developed. Furthermore, the static studies of magneto-electro-elastic plate have been carried out by reducing the fully coupled finite element formulation to partially coupled state. Particular attention has been paid to investigate the influence of thermal fields, electric fields, and magnetic fields on the behavior of magneto-electro-elastic plate. In addition, the effect of pyrocoupling on the magneto-electro-elastic plate has also been studied. Furthermore, the effect of geometrical parameters such as aspect ratio, length-to-thickness ratio, stacking sequence, and boundary conditions is studied in detail. The investigation may contribute significantly in enhancing the performance and applicability of functionally graded magneto-electro-thermo-elastic structures in the field of sensors and actuators.

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