scholarly journals Analysis of Functionally Graded Timoshenko Beams by Using Peridynamics

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Boundary Conditions ◽  
Lagrange Equation ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Governing Equations ◽  
Element Analysis ◽  
Free Boundary Conditions ◽  
Support Roller ◽  
Roller Support ◽  
Good Agreement

Abstract In this study, a new peridynamic formulation is presented for functionally graded Timoshenko beams. The governing equations of the peridynamic formulation are obtained by utilising Euler-Lagrange equation and Taylor’s expansion. The proposed formulation is validated by considering a Timoshenko beam subjected to different boundary conditions including pinned support-roller support, clamped-roller support and clamped-free boundary conditions. Results from peridynamics are compared against finite element analysis results. A very good agreement is obtained for transverse displacements, rotations and axial displacements along the beam.

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

scholarly journals A state-based peridynamic formulation for functionally graded Kirchhoff plates

2020 ◽  
pp. 108128652096338
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Material Properties ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Benchmark Problems ◽  
Transverse Loading ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Kirchhoff Plates ◽  
Peridynamic Model

Functionally graded materials are a potential alternative to traditional fibre-reinforced composite materials as they have continuously varying material properties which do not cause stress concentrations. In this study, a state-based peridynamic model is presented for functionally graded Kirchhoff plates. Equations of motion of the new formulation are obtained using the Euler–Lagrange equation and Taylor’s expansion. The formulation is verified by considering several benchmark problems including a clamped plate subjected to transverse loading and a simply supported plate subjected to transverse loading and inclined loading. The material properties are chosen such that Young’s modulus is assumed to be varied linearly through the thickness direction and Poisson’s ratio is constant. Peridynamic results are compared against finite element analysis results, and a very good agreement is obtained between the two approaches.

scholarly journals Modeling the Size Effect on the Mechanical Behavior of Functionally Graded Curved Micro/Nanobeam

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Seyyed Amirhosein Hosseini1 ◽  
O. Rahmani2
Keyword(s):  
Size Effect ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Power Index ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Opening Angle ◽  
Simply Supported ◽  
Fg Nanobeam ◽  
Good Agreement

The size effect on the free vibration and bending of a curved FG micro/nanobeam is studied in this paper. Using the Hamilton principle the differential equations and boundary conditions is derived for a nonlocal Euler-Bernoulli curved micro/nanobeam.  The material properties vary through radius direction. Using the Navier approach an analytical solution for simply supported boundary conditions is obtained where the power index law of FGM, the curved micro/nanobeam opening angle, the effect of aspect ratio and nonlocal parameter on natural frequencies and the radial and tangential displacements were analyzed. It is concluded that increasing the curved micro/nanobeam opening angle results in decreasing and increasing the frequencies and displacements, respectively. To validate the natural frequencies of curved nanobeam, when the radius of it approaches to infinity, is compared with a straight FG nanobeam and showed a good agreement.

An Improved Unified Solution for a Vibration Equation of Tension-Stiffening Beam Using Extended Rayleigh Energy Method

2019 ◽  
Author(s):  
Zhijun Yang ◽  
Ruiqi Li ◽  
Youdun Bai
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Energy Method ◽  
Physical Science ◽  
Element Analysis ◽  
Tension Stiffening ◽  
Design And Optimization ◽  
Micro Motion ◽  
Stiffening Effect ◽  
Good Agreement

Abstract The tension-stiffening effect is very important for physical science, which has been widely used in MEMS, sensors and micro-motion stages. The analytical solutions of the tension-stiffening beam are extremely significant, in consideration of the inefficiency of finite element analysis (FEA) for the design and optimization. Commonly, there are three typical types of boundary conditions for tension-stiffening (or stress-induced) beams, i.e., clamped-clamped, clamped-hinged, and hinged-hinged. But only the hinged-hinged beam has an analytical solution. Therefore, a method based on extended Rayleigh energy method is proposed in this paper to deduce the analytical solutions of three boundary conditions. The predictions are verified to be in good agreement with FEA and experiment results.

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

2018 ◽  
Vol 29 (11) ◽  
pp. 2344-2361 ◽  
Author(s):  
Mohammad Hassan Shojaeefard ◽  
Hamed Saeidi Googarchin ◽  
Mohammad Mahinzare ◽  
Morteza Adibi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Piezoelectric Properties ◽  
Scale Parameter ◽  
Differential Quadrature Method ◽  
Nonlocal Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Viscoelastic Media ◽  
Generalized Differential

This article investigates free vibration of a functionally graded piezomagnetic material cylindrical nanoshell embedded in viscoelastic media under rotational, external electric and magnetic loadings. The governing equations of the nanoshell are derived based on Eringen’s nonlocal theory. It is found that, magnetic and piezoelectric properties of the structure change exponentially along the thickness. The rotational loading is calculated considering initial hoop tension. The results are obtained by applying generalized differential quadrature method to the governing equations and associated boundary conditions. Results also include those achieved for clamped-clamped and simply hinged-hinged boundary conditions. It is found that free vibration characteristics of functionally graded piezomagnetic material cylindrical nanoshell are influenced by several factors including angular velocity, length scale parameter, external voltage, external amperage, functionally graded power index, and viscoelastic media parameters.

Buckling Analysis of FGM Thick Beam under Different Boundary Conditions Using GDQM

2012 ◽  
Vol 433-440 ◽  
pp. 4920-4924 ◽  
Author(s):  
Fatemeh Farhatnia ◽  
Mohammad Ali Bagheri ◽  
Amin Ghobadi
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Graded Materials ◽  
Generalized Differential ◽  
Thick Beam

In this paper, buckling analysis of functionally graded (FG) thick beam under different conditions is presented. Based on the first order shear deformation theory, governing equations are obtained for Thimoshenko beam which is subjected to mechanical loads. In functionally graded materials (FGMs) the material properties obeying a simple power law is assumed to vary through thickness. In order to solve the buckling differential equations, Generalized Differential Quadrature Method (GDQM) is employed and thus a set of eigenvalue equations resulted. For solving this eigenvalue problem, a computer program was developed in a way that the influence of different parameters such as height to length ratio, various volume fraction functions and boundary conditions were included. Non-dimensional critical stress was calculated for simply-simply, clamped-simply and clamped-clamped supported beams. The results of GDQ method were compared with reported results from solving the Finite element too. The comparison showed the accuracy of obtained results clearly in this work.

Polynomial Based Elasticity Solutions of Beams and their Numerical Validation: A Review

2011 ◽  
Vol 311-313 ◽  
pp. 2315-2321
Author(s):  
Sebin Jose ◽  
Sunil Bhat
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Stress Problem ◽  
Elasticity Solutions ◽  
Harmonic Equation ◽  
Complex Cases ◽  
Good Agreement

Solution of two-dimensional stress problem is reduced to integration of bi-harmonic equation[1].A polynomial is chosen as Airy’s stress function.Constants of the polynomial[2] are found by fulfilling the boundary conditions. Stress solutions are obtained from.The paper presents polynomial based stress solutions of beams for complex cases involving offset loads and other combinations with offset loads.The results are compared with those obtained from finite element analysis[3] and conventional methods.The results are in good agreement with each other.

A NOVEL HIGHER ORDER SHEAR AND NORMAL DEFORMATION THEORY BASED ON NEUTRAL SURFACE POSITION FOR BENDING ANALYSIS OF ADVANCED COMPOSITE PLATES

2014 ◽  
Vol 11 (06) ◽  
pp. 1350082 ◽  
Author(s):  
ABDELMOUMEN ANIS BOUSAHLA ◽  
MOHAMMED SID AHMED HOUARI ◽  
ABDELOUAHED TOUNSI ◽  
EL ABBAS ADDA BEDIA
Keyword(s):  
Boundary Conditions ◽  
Composite Plates ◽  
Present Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plates ◽  
Governing Equations ◽  
Normal Deformation ◽  
Advanced Composite

In this paper, a new trigonometric higher-order theory including the stretching effect is developed for the static analysis of advanced composite plates such as functionally graded plates. The number of unknown functions involved in the present theory is only five as against six or more in case of other shear and normal deformation theories. The governing equations are derived by employing the principle of virtual work and the physical neutral surface concept. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory.

In-plane free vibrations of functionally graded sandwich arches using shear and quasi-3D deformation theories

2021 ◽  
pp. 109963622110219
Author(s):  
Ke Xie ◽  
Yuewu Wang ◽  
Hongpan Niu ◽  
Hongyong Chen
Keyword(s):  
Boundary Conditions ◽  
Lagrange Equation ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Displacement Fields ◽  
Various Boundary Conditions ◽  
Shear Deformation Theories ◽  
3D Deformation ◽  
First Time ◽  
Stress Free Boundary

The in-plane vibration problem of functionally graded (FG) sandwich circular arch made up of two layers of power law FGM face sheet and one layer of homogeneous core is investigated. A framework for the vibration analysis of FG sandwich circular arches is presented, and the quasi-3D theories for the arch structures compatible with this framework are established for the first time. The quasi-3D theories take into account the changes of displacement through the thickness of the arch, and satisfy the stress-free boundary conditions naturally. The Lagrange equation is employed to derive the equation of motion, and various boundary conditions are implemented by applying simple algebraic polynomials as admissible functions to discrete the displacement fields of the FG sandwich arches. The comparison study of various high-order shear deformation theories and quasi-3D deformation theories for the FG sandwich circular arches is carried out via different numerical examples. The influences of material distributions and geometric parameters on the vibration characteristics of the FG sandwich circular arches are also presented and discussed for the first time.

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