scholarly journals Material-Oriented Shape Functions for FGM Plate Finite Element Formulation

Materials ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 803
Author(s):  
Wojciech Gilewski ◽  
Jan Pełczyński
Keyword(s):  
Finite Element ◽  
Analytical Form ◽  
Functionally Graded ◽  
Element Formulation ◽  
Shape Functions ◽  
Good Convergence ◽  
Moderately Thick Plate ◽  
Graded Material ◽  
Load Vector ◽  
Plate Strip

A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM’s material parameters and are called material-oriented. The shape function matrix is based on a superposition displacement field of two plate strips with 1D exact shape functions. A characteristic feature of the proposed formulation is full coupling of the membrane and bending states in the plate. The analytical form of the stiffness matrix and the nodal load vector was obtained, which leads to the numerical efficiency of the formulation. The element has been incorporated into Abaqus software with the use of Maple program. The finite element shows good convergence properties for different FGM models in the transverse direction to the middle plane of the plate. During derivation of the 2D plate element the formally exact 1D finite element for transverse nonhomogeneous FGM plate strip was developed.

BUCKLING ANALYSIS OF FUNCTIONALLY GRADED SKEW PLATES: AN EFFICIENT FINITE ELEMENT APPROACH

2013 ◽  
Vol 05 (04) ◽  
pp. 1350041 ◽  
Author(s):  
M.N.A. GULSHAN TAJ ◽  
ANUPAM CHAKRABARTI
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Element Formulation ◽  
Skew Angle ◽  
Buckling Behavior ◽  
Metal Plates ◽  
Graded Material

In the present study, an attempt has been made to present the Co finite element formulation based on third order shear deformation theory for buckling analysis of functionally graded material skew plate under thermo-mechanical environment. Here, prime emphasis has been given to study the influence of skew angle on the buckling behavior of functionally graded plate. Two dissimilar homogenization schemes, namely Mori–Tanaka scheme and Voigt rule of mixture are employed to sketch their influence for the interpretation of data. Temperature-dependent material properties of the constituents of the plate are considered to perform thermal analysis. Numerical examples are solved using different mixture of ceramic and metal plates to generate the new results and relative imperative conclusions are highlighted. The roles played by the different factors like loading condition, volume fraction index, skew angle, boundary condition, aspect ratio, thickness ratio and homogenization schemes on buckling behavior of the FGM skew plates are presented in the form of tables and figures.

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.

scholarly journals A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2021 ◽  
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MAT LAB software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

scholarly journals An edge-based smoothed finite element for buckling analysis of functionally graded material variable-thickness plates

2021 ◽  
Author(s):  
Tran Trung Thanh ◽  
Tran Van Ke ◽  
Pham Quoc Hoa ◽  
Tran The Van ◽  
Nguyen Thoi Trung
Keyword(s):  
Finite Element ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Triangular Element ◽  
Stiffness Matrices ◽  
Strain Smoothing ◽  
Graded Material ◽  
Smoothed Finite Element Method ◽  
Edge Based

The paper aims to extend the ES-MITC3 element, which is an integration of the edge-based smoothed finite element method (ES-FEM) with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3 element), for the buckling analysis of the FGM variable-thickness plates subjected to mechanical loads. The proposed ES-MITC3 element is performed to eliminate the shear locking phenomenon and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing the same edge. The numerical results demonstrated that the proposed method is reliable and more accurate than some other published solutions in the literature. The influences of some geometric parameters, material properties on the stability of FGM variable-thickness plates are examined in detail.

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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