A Comparison of Finite Element Beam Formulations for Thermoelastic Behavior of Functionally Graded Structures

Aerospace ◽  
2005 ◽  
Author(s):  
Thomas G. Eason ◽  
Simo´n A. Caraballo
Keyword(s):  
Finite Element ◽  
Shear Deformation Theory ◽  
Axial Direction ◽  
Beam Element ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Shell Elements ◽  
Static Condensation ◽  
Graded Structures ◽  
Structural Scale

Modeling at the structural scale most often requires the use of beam and shell elements. This paper compares two finite element formulations based on first-order shear deformation theory undergoing thermo-mechanical loading. One formulation is a two node beam element employing static condensation based on the work of Chakraborty et al. The second formulation follows a more traditional route using FSOD theory for a three node beam element. Both formulations are used to investigate the behavior of a functionally graded beam under axial and through-the-thickness temperature gradients. Both formulations work well for a constant uniform mechanical or temperature loading. However, for beam structures containing a thermal gradient in the axial direction, the two node beam element performs poorly as compared to the three node element in terms of transverse shearing stress calculated from the equilibrium equation.

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

2021 ◽  
pp. 146442072110050
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Abdelhak Khechai ◽  
Aicha Bessaim ◽  
Mohammed-Sid-Ahmed Houari ◽  
Aman Garg ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams

In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

scholarly journals A COMBINED STRAIN ELEMENT TO FUNCTIONALLY GRADED STRUCTURES IN THERMAL ENVIRONMENT

2020 ◽  
Vol 60 (6) ◽  
Author(s):  
Hoang Lan Ton-That
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Element Analysis ◽  
First Order ◽  
Graded Structures

Functionally graded materials are commonly used in a thermal environment to change the properties of constituent materials. They inherently withstand high temperature gradients due to a low thermal conductivity, core ductility, low thermal expansion coefficient, and many others. It is essential to thoroughly study mechanical responses of them and to develop new effective approaches for an accurate prediction of solutions. In this paper, a new four-node quadrilateral element based on a combined strain strategy and first-order shear deformation theory is presented to achieve the behaviour of functionally graded plate/shell structures in a thermal environment. The main notion of the combined strain strategy is based on the combination of the membrane strain and the shear strain related to tying points as well as bending strain with respect to a cell-based smoothed finite element method. Due to the finite element analysis, the first-order shear deformation theory (FSDT) is simple to implement and apply for structures, but the shear correction factors are used to achieve the accuracy of solutions. The author assumes that the temperature distribution is uniform throughout the structure. The rule of mixtures is also considered to describe the variation of material compositions across the thickness. Many desirable characteristics and the enforcement of this element are verified and proved through various numerical examples. Numerical solutions and a comparison with other available solutions suggest that the procedure based on this new combined strain element is accurate and efficient.

scholarly journals Extension of Boley’s method to functionally graded beams

2020 ◽  
Author(s):  
J. Gahleitner ◽  
J. Schoeftner
Keyword(s):  
Finite Element ◽  
Stress Function ◽  
Poisson Ratio ◽  
Axial Direction ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Functionally Graded Beam ◽  
Element Analysis ◽  
Perfect Agreement ◽  
Graded Material

AbstractThe objective of this contribution is the computation of the Airy stress function for functionally graded beam-type structures subjected to transverse and shear loads. For simplification, the material parameters are kept constant in the axial direction and vary only in the thickness direction. The proposed method can be easily extended to material varying in the axial and thickness direction. In the first part an iterative procedure is applied for the determination of the stress function by means of Boley’s method. This method was successfully applied by Boley for two-dimensional (2D) isotropic plates under plane stress conditions in order to compute the stress distribution and the displacement field. In the second part, a shear loaded cantilever made of isotropic, functionally graded material is studied in order to verify our theory with finite element results. It is assumed that the Young’s modulus varies exponentially in the transverse direction and the Poisson ratio is constant. Stresses and displacements are analytically determined by applying our derived theory. Results are compared to a 2D finite element analysis performed with the commercial software ABAQUS. It is found that the analytical and numerical results are in perfect agreement.

Finite Element Analysis of Non-Uniform Beam Made of Axially FGM Subjected to Multiple Loads

2015 ◽  
Vol 764-765 ◽  
pp. 1170-1174
Author(s):  
Thanh Huong Trinh ◽  
Buntara Sthenly Gan ◽  
Dinh Kien Nguyen
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Axial Direction ◽  
Beam Element ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Moving Loads ◽  
Element Analysis ◽  
Cross Sectional ◽  
Graded Materials

The dynamic response of non-uniform Timoshenko beams made of axially functionally graded materials subjected to multiple moving point loads is studied by using the finite element method. The material properties are assumed to vary continuously in the axial direction according to a power law. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials obtained from the governing differential equations of a homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving loads. The effects of the distance between the moving loads, material non-homogeneity, section profile as well as aspect ratio on the dynamic response of the beams are investigated in detail and highlighted.

Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory

2021 ◽  
Vol 264 ◽  
pp. 113712 ◽  
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Mohammed-Sid-Ahmed Houari ◽  
Ahmed Amine Daikh ◽  
Aman Garg ◽  
Tarek Merzouki ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Buckling Analysis ◽  
Functionally Graded

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

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.

Vibrational Characteristics of Composite Shafts

1999 ◽  
Author(s):  
A. S. Sekhar ◽  
N. Ravi Kumar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Deformation Theory ◽  
Great Influence ◽  
Shear Deformation Theory ◽  
Stacking Sequence ◽  
Shell Elements ◽  
First Order ◽  
Composite Shaft ◽  
Vibrational Characteristics

Abstract The present study aims in performing eigenvalue analysis and unbalance response for a rotor system having a composite shaft, modelled based on first order shear deformation theory using finite element method with shell elements. Different materials such as boron epoxy, carbon epoxy and graphite epoxy have been tried for various stacking sequences. From the study it is clear that the stacking sequence and material have great influence on the vibrational characteristics of composite shafts.

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