Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support

2020 ◽  
pp. 107754632094730
Author(s):  
Şeref D Akbaş ◽  
Abdullateef H Bashiri ◽  
Amr E Assie ◽  
Mohamed A Eltaher
Keyword(s):  
Time Integration ◽  
Solution Process ◽  
Layered Composite ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Pulse Load ◽  
Graded Materials ◽  
Numerical Time Integration ◽  
Thick Beam ◽  
Material Gradation

This study presents dynamic responses of a composite thick beam with a functionally graded porous layer under dynamic sine pulse load. The boundary conditions of the composite beam are considered as viscoelastic supports. Three layers are considered, and face sheet layers have porous functionally graded materials in which the distribution of material gradation through the graded layer is described by the power law function, and the porosity is depicted by three different distributions (i.e., symmetric distribution, X distribution, and ◊ distribution). The layered composite thick beam is modeled as a two-dimensional plane stress problem. The equation of motion is obtained by Lagrange’s equations. In formation of the problem, the finite element method is used with a 12-node 2D plane element. In the solution process of the dynamic problem, a numerical time integration method of the Newmark method is used. In numerical analyses, influences of stiffness and damping coefficients of viscoelastic supports, material gradation index, porosity parameter, and porosity models on the dynamic response of thick functionally graded porous beam are investigated under the pulse load.

Bi-Directional Functionally Graded Nanotubes: Fluid Conveying Dynamics

2018 ◽  
Vol 10 (04) ◽  
pp. 1850041 ◽  
Author(s):  
Ye Tang ◽  
Tianzhi Yang
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Graded Materials ◽  
Critical Flow Velocity ◽  
Dynamic Behaviors ◽  
Fundamental Frequencies ◽  
Material Gradation

In the paper, a novel model of fluid-conveying nanotubes made of bi-directional functionally graded materials is presented for investigating the dynamic behaviors and stability. For the first time, the material properties of the nanotubes along both radical and axial directions are under consideration. Based on Euler–Bernoulli beam and Eringen’s nonlocal elasticity theories, the governing equation of the nanotubes and associated boundary conditions are developed using Hamilton’s principle. Differential quadrature method (DQM) is applied for discretizing the equation to determine the numerical solutions of the nanotubes with different boundary conditions. Numerical examples are presented to examine the effects of the material gradation, nonlocal parameter, and mode order on the dynamics and stability. It is shown that the two-directional materials distribution can significantly change the critical flow velocity, fundamental frequencies and stability. Comparing with traditional one-directional distribution, such 2D is more flexible to tune overall dynamic behaviors, this may provide new avenues for smart pipes.

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.

A Generalized Interaction Integral Method for the Evaluation of the T-Stress in Orthotropic Functionally Graded Materials Under Thermal Loading

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Jeong-Ho Kim ◽  
Amit KC
Keyword(s):  
Orthotropic Material ◽  
Integral Method ◽  
Mixed Mode ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Interaction Integral ◽  
T Stress ◽  
Mode Stress ◽  
Material Gradation

The interaction integral method that is equipped with the nonequilibrium formulation is generalized to evaluate the nonsingular T-stress as well as mixed-mode stress intensity factors in orthotropic functionally graded materials under thermomechanical loads. This paper addresses both Mode-I and mixed-mode fracture problems and considers various types of orthotropic material gradation. The orthotropic thermomechanical material properties are graded spatially and integrated into the element stiffness matrix using the direct Gaussian formulation. The types of orthotropic material gradation considered include exponential, power-law, and hyperbolic-tangent functions, and the numerical formulation is generalized for any type of smooth material gradation. The T-stress and mixed-mode stress intensity factors are evaluated by means of the interaction integral method developed in conjunction with the finite element method. The accuracy of numerical results is assessed by means of thermomechanically equivalent problems.

scholarly journals Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects

2021 ◽  
Author(s):  
Paulina Stempin ◽  
Wojciech Sumelka
Keyword(s):  
Functionally Graded Materials ◽  
Timoshenko Beam ◽  
Functionally Graded ◽  
Beam Model ◽  
Material Parameter Identification ◽  
Graded Materials ◽  
Size Dependent ◽  
Non Local ◽  
Thick Beam ◽  
Euler Bernoulli Beam

AbstractIn this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory is a further development and extension of the space-fractional (non-local) Euler–Bernoulli beam model (s-FEBB) to space-fractional Timoshenko beam (s-FTB) one by proper taking into account shear deformation. Furthermore, a detailed parametric study on the influence of length scale and order of fractional continua for different boundary conditions demonstrates, how the non-locality affects the static bending response of the s-FTB model. The differences in results between s-FTB and s-FEBB models are shown as well to indicate when shear deformations need to be considered. Finally, material parameter identification and validation based on the bending of SU-8 polymer microbeams confirm the effectiveness of the presented model.

scholarly journals On Some Thermoelastic Problem of a Nonhomogeneous Long Pipe

2021 ◽  
Vol 39 (5) ◽  
pp. 1430-1442
Author(s):  
Roman Kulchytsky-Zhyhailo ◽  
Stanisław J. Matysiak ◽  
Dariusz M. Perkowski
Keyword(s):  
Axial Stress ◽  
Layered Composite ◽  
Functionally Graded ◽  
Thermoelastic Problem ◽  
Graded Materials ◽  
Varying Thickness ◽  
Representative Cell ◽  
Homogenization Approach ◽  
Homogenized Model ◽  
Pipe Materials

The paper deals with the thermoelastic problem of a multilayered pipe subjected to normal loadings on its inner surface and temperature differences on its internal and external surfaces. Two types of nonhomogeneous pipe materials of pipe are considered: (1) a ring-layered composite composed of two repeated thermoelastic solids with varying thickness and (2) a functionally graded ring layer. The ring-layered pipe with periodic structure is investigated by using the homogenized model with microlocal parameters. A homogenization approach is proposed for the modelling of the FGM pipe. The analysis of obtained circumferential, radial and axial stress is presented in the form of figures and discussed in detail. It was shown that the proposed approach to the homogenization allows us to correctly calculate the averaged characteristics in the representative cell (the macro-characteristics) and also the characteristics dependent on the choice of the component in the representative cell (the micro-characteristics) for both microperiodic composites and functionally graded materials.

Supersonic Flutter of Functionally Graded Plates in a Thermal Environment

2006 ◽  
Author(s):  
H. M. Navazi ◽  
H. Haddadpour
Keyword(s):  
Differential Equations ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Time Integration ◽  
Analytical Investigation ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Numerical Time Integration ◽  
Flutter Margin

In this paper, an analytical investigation intended to determine the flutter margin of supersonic functionally graded panels is carried out. For this purpose, piston theory aerodynamics has been employed to model quasi-steady aerodynamic loading. The material properties of the plate are assumed to be graded continuously across the panel thickness. The variation of temperature-dependent thermoelastic properties follows a simple power-law distribution in terms of the volume fraction of the constituent materials. The effects of compressive in-plane loads and static pressure differential are studied. Both uniform and through the thickness nonlinear temperature distributions are also considered. Hamilton’s principle is used to determine the coupled partial differential equations of motion. Using Galerkin’s method, the derived equations are transformed into a set of coupled ordinary differential equations, and then solved by numerical time integration. Some examples comparing the flutter margin of FG panels with that of plates made of pure metals and pure ceramics are presented. The results of the present study are compared with those of the previous works, where finite element method was used. It is shown that the use of functionally graded materials can yield an increase or decrease of the aeroelastic stability in the supersonic flow for different regions.

Dynamic Fracture of Functionally Graded Composites Using an Intrinsic Cohesive Zone Model

2005 ◽  
Vol 492-493 ◽  
pp. 447-452 ◽  
Author(s):  
Glaucio H. Paulino ◽  
Zheng Yu Zhang
Keyword(s):  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Functionally Graded ◽  
Crack Branching ◽  
Zone Model ◽  
Element Formulation ◽  
Element Level ◽  
Graded Materials ◽  
Functionally Graded Composites ◽  
Material Gradation

This paper presents a Cohesive Zone Model (CZM) approach for investigating dy- namic failure processes in homogeneous and Functionally Graded Materials (FGMs). The failure criterion is incorporated in the CZM using both a ßnite cohesive strength and work to fracture in the material description. A novel CZM for FGMs is explored and incorporated into a ßnite element framework. The material gradation is approximated at the element level using a graded element formulation. A numerical example is provided to demonstrate the eácacy of the CZM approach, in which the inàuence of the material gradation on the crack branching pattern is studied.

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.

scholarly journals Non-linear vibration of functionally graded shallow spherical shells

2010 ◽  
Vol 32 (4) ◽  
pp. 199-210 ◽  
Author(s):  
Dao Huy Bich ◽  
Le Kha Hoa
Keyword(s):  
Functionally Graded ◽  
Dynamic Responses ◽  
Dynamical Analysis ◽  
Linear Vibration ◽  
Power Law Distribution ◽  
Spherical Shells ◽  
Graded Materials ◽  
Runge Kutta Method ◽  
Non Linear ◽  
The Galerkin Method

The present paper deals with the non-linear vibration of functionally graded shallow spherical shells. The properties of shell material are graded in the thickness direction according to the power law distribution in terms of volume fractions of the material constituents. In the derived governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. From the deformation compatibility equation and the motion equation a system of partial differential equations for stress function and deflection of shell is obtained. The Galerkin method and Runge-Kutta method are used for dynamical analysis of shells to give expressions of natural frequencies and non-linear dynamic responses. Numerical results show the essential influence of characteristics of functionally graded materials and dimension ratios on the dynamical behaviors of shells.

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