scholarly journals Finite Element Model for Free Vibration Analyses of FG-CNT Reinforced Composite Beams using Refined Shear Deformation Theories

2021 ◽  
Vol 1206 (1) ◽  
pp. 012019
Author(s):  
Surojit Biswas ◽  
Priyankar Datta
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Distribution Type

Abstract The present article deals with the free vibration of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams employing various refined deformation theories and validates the accuracy and feasibility of these proposed theories. The theories involved are the first order shear deformation theory (FSDT) and other refined theories involving additional higher order terms. Carbon nanotubes (CNTs) are assumed to be oriented along the axis of the beam. Uniform and three types of different functionally graded (FG) distributions of CNTs through the thickness of the beam are considered. The rule of mixture is used to describe the effective material properties of the beams. The governing equations are derived using Hamilton’s principle and solved using the finite element method (FEM). A FEM code is compiled in MATLAB considering a C 0 finite element. The influences of different key parameters such as CNT volume fraction, distribution type of CNTs, boundary conditions and slenderness ratio on the natural frequencies of FG-CNTRC beams are investigated. It can be concluded that the above-mentioned parameters have significant influence on the free vibration of the beam and the accuracy of the proposed refined theories is good.

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.

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.

Free Vibration and Buckling Analysis of Sandwich Beams with Functionally Graded Carbon Nanotube-Reinforced Composite Face Sheets

2015 ◽  
Vol 15 (07) ◽  
pp. 1540011 ◽  
Author(s):  
Helong Wu ◽  
Sritawat Kitipornchai ◽  
Jie Yang
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Micromechanical Model ◽  
Sandwich Beam ◽  
Sheet Thickness ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Reinforced Composite

This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison.

scholarly journals STATIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED SANDWICH PLATES USING A THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT MODEL

2020 ◽  
Vol 57 (6A) ◽  
pp. 77
Author(s):  
Nguyen Van Chinh
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Functionally Graded ◽  
Third Order ◽  
Layer Thickness Ratio ◽  
Classical Boundary ◽  
Bending Behavior

In this paper, static bending of two-direction functionally graded sandwich (2D-FGSW) plates is studied by using a finite element model. The plates consist of a homogeneous core and two functionally graded skin layers with material properties being graded in both the thickness and length directions by power gradation laws. Based on a third-order shear deformation theory, a finite element model is derived and employed in the analysis. Bending characteristics, including deflections and stresses are evaluated for the plates with classical boundary conditions under various types of distributed load. The effects of material distribution and layer thickness ratio on the static bending behavior of the plates are examined and highlighted.

scholarly journals Finite Element Analysis of Functionally Graded Beams using Different Beam Theories

2020 ◽  
Vol 6 (11) ◽  
pp. 2086-2102
Author(s):  
Farshad Rahmani ◽  
Reza Kamgar ◽  
Reza Rahgozar
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Power Law ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Material Distribution ◽  
Beam Theories

The present study deals with buckling, free vibration, and bending analysis of Functionally Graded (FG) and porous FG beams based on various beam theories. Equation of motion and boundary conditions are derived from Hamilton’s principle, and the finite element method is adopted to solve problems numerically. The FG beams are graded through the thickness direction, and the material distribution is controlled by power-law volume fraction. The effects of the different values of the power-law index, porosity exponent, and different boundary conditions on bending, natural frequencies and buckling characteristics are also studied. A new function is introduced to approximate the transverse shear strain in higher-order shear deformation theory. Furthermore, shifting the position of the neutral axis is taken into account. The results obtained numerically are validated with results obtained from ANSYS and those available in the previous work. The results of this study specify the crucial role of slenderness ratio, material distribution, and porosity condition on the characteristic of FG beams. The deflection results obtained by the proposed function have a maximum of six percent difference when the results are compared with ANSYS. It also has better results in comparison with the Reddy formulae, especially when the beam becomes slender. Doi: 10.28991/cej-2020-03091604 Full Text: PDF

Nonlinear transient and thermal analysis of functionally graded shells using a seven-parameter shell finite element

2017 ◽  
Vol 1 (2) ◽  
Author(s):  
Miguel Gutierrez Rivera ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Mechanical Response ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Shell Element ◽  
Element Model ◽  
Functionally Graded ◽  
Plates And Shells ◽  
Shell Finite Element ◽  
Transient Thermal

AbstractIn this paper the thermo-mechanical response of functionally graded plates and shells is studied using a continuum shell finite element model with high-order spectral/hp basis functions. The shell element is based on the seven-parameter first-order shear deformation theory, and it does not utilize reduced integration or stabilization ideas and yet exhibits no locking. The static and dynamic response of functionally graded shells, with power-law variation of the constituents, under mechanical and thermal loads is investigated by varying the volume fraction of the constituents. Numerical results for deflections and stresses are presented and compared with available analytical and finite element results from the literature. The performance of the shell element for transient thermal problems is found to be excellent.

scholarly journals STATIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED SANDWICH PLATES USING A THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT MODEL

2020 ◽  
Vol 57 (6A) ◽  
pp. 77
Author(s):  
Nguyen Van Chinh
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Functionally Graded ◽  
Third Order ◽  
Layer Thickness Ratio ◽  
Classical Boundary ◽  
Bending Behavior

In this paper, static bending of two-direction functionally graded sandwich (2D-FGSW) plates is studied by using a finite element model. The plates consist of a homogeneous core and two functionally graded skin layers with material properties being graded in both the thickness and length directions by power gradation laws. Based on a third-order shear deformation theory, a finite element model is derived and employed in the analysis. Bending characteristics, including deflections and stresses are evaluated for the plates with classical boundary conditions under various types of distributed load. The effects of material distribution and layer thickness ratio on the static bending behavior of the plates are examined and highlighted.

Sign in / Sign up

Export Citation Format

Share Document