scholarly journals Large displacements of FGSW beams in thermal environment using a finite element formulation

2020 ◽  
Author(s):  
Bui Thi Thu Hoai ◽  
Nguyen Dinh Kien ◽  
Tran Thi Thu Huong ◽  
Le Thi Ngoc Anh
Keyword(s):  
Finite Element ◽  
Temperature Rise ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Effect Of Temperature ◽  
Element Formulation ◽  
Beam Model ◽  
Large Displacements

The large displacements of functionally graded sandwich (FGSW) beams in thermal environment  are studied using a finite element formulation. The beams are composed of three layers, a homogeneous core and two functionally graded face sheets with volume fraction of constituents following a power gradation law. The material properties of the beams are considered to be temperature-dependent.  Based on Antman beam model and the total Lagrange formulation, a two-node nonlinear beam element taking the effect of temperature rise into account  is formulated and employed in the study. The element with explicit expressions for the internal force vector and tangent stiffness matrix is derived using linear interpolations and reduced integration technique to avoid the shear locking. Newton-Raphson based iterative algorithm is employed in combination with the arc-length control method to compute the large displacement response of a cantilever FGSW beam subjected to end forces.  The accuracy of the formulated element is confirmed through a comparison study. The effects of the material inhomogeneity, temperature rise and layer thickness ratio on the large deflection response of the beam are examined and highlighted.

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.

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.

A Simple Total-Lagrangian Finite-Element Formulation for Nonlinear Behavior of Planar Beams

2018 ◽  
Author(s):  
Enrico Babilio ◽  
Stefano Lenci
Keyword(s):  
Finite Element ◽  
Theoretical Model ◽  
Finite Difference ◽  
Shear Angle ◽  
Difference Schemes ◽  
Finite Element Formulation ◽  
Finite Difference Schemes ◽  
Element Formulation ◽  
Beam Model ◽  
Lagrangian Finite Element

The present contribution reports some preliminary results obtained applying a simple finite element formulation, developed for discretizing the partial differential equations of motion of a novel beam model. The theoretical model we are dealing with is geometrically exact, with some peculiarities in comparison with other existing models. In order to study its behavior, some numerical investigations have already been performed through finite difference schemes and other methods and are reported in previous contributions. Those computations have enlightened that the model under analysis turns out to be quite hard to handle numerically, especially in dynamics. Hence, we developed ad hoc the total-lagrangian finite-element formulation we report here. The main differences between the theoretical model and its numerical formulation rely on the fact that in the latter the absolute value of the shear angle is assumed to remain much smaller than unity, and strains are piecewise constant along the beam. The first assumption, which actually simplifies equations, has been taken on the basis of results from previous integrations, mainly through finite difference schemes, which clearly showed that, while other strains can achieve large values in their range of admissibility, shear angle actually remains small. The second assumption led us to define a two-nodes constant-strain finite element, with a fast convergence, in terms of number of elements versus solution accuracy. Although, at the present stage of this ongoing research, we have only early results from finite elements, they appear encouraging and start to shed new light on the behavior of the beam model under analysis.

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.

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