Magnetoelastic Field of a Multilayered and Functionally Graded Cylinder With a Dynamic Polynomial Eigenstrain

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Magnetic Field ◽  
Analytical Solution ◽  
Functionally Graded ◽  
Composite Cylinder ◽  
Power Law Distribution ◽  
Lommel Functions ◽  
Stress Components ◽  
Internal Core ◽  
Cubic Polynomial ◽  
Polynomial Distribution

In this paper, an analytical solution is obtained for the magnetoelastic response of a multilayered and functionally graded cylinder with an embedded dynamic polynomial eigenstrain. The internal core of the cylinder endures a harmonic eigenstrain of cubic polynomial distribution along the radial direction. Both plane strain and plane stress conditions are assumed for the axisymmetric cylinder. The composite cylinder is placed in a constant magnetic field parallel to its axis. The magnetoelastic governing equations are solved exactly and the displacement and stress components are obtained in terms of Bessel, Struve, and Lommel functions. Using the analytical solution for the multilayered, composite cylinder, the magnetoelastic response of a functionally graded cylinder with exponential and power law distribution of material properties is investigated. Finally, the numerical results reveal the effects of external magnetic field, eigenstrain, and nonhomogeneity indices on the magnetoelastic response of the heterogeneous cylinders.

Magnetoelastic Analysis of Sandwich Cellular Cylinders

2014 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
J. W. Fu ◽  
Z. T. Chen ◽  
D. Pasini
Keyword(s):  
Magnetic Field ◽  
Relative Density ◽  
Solid Material ◽  
Analytic Solutions ◽  
Cellular Material ◽  
Stress Regime ◽  
Lommel Functions ◽  
Time Harmonic ◽  
Cell Topology ◽  
Cubic Polynomial

This paper examines the time-harmonic eigenstrain behavior of a magnetoelastic sandwich cylinder with solid and cellular material layers. A sandwich panel subjected to an external magnetic field is assumed to endure an eigenstrain with a cubic polynomial radial distribution in the sandwich core. Using asymptotic homogenization, the effective material properties of the cellular material are determined as a function of relative density for various cell topologies, that are used in the cellular layers of a cylinder under given magnetic field. Bessel, Struve, and Lommel functions are used to obtain semi-analytic solutions for a sandwich cylinder with perfectly and imperfectly bonded interfaces. The results are first verified with those available in the literature of composite cylinders with solid material layers. Then the paper studies the role that cell topology, relative density, and bonding type at the layer interfaces play on the time-harmonic magnetoelastic responses. The numerical results reveal that the proper choice of relative density, cell topology, and cellular layer configuration can reduce the weight and stress regime, as well as improve the dynamic response of a sandwich cylinder subjected to a given magnetic field.

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

Forces on a Circular Hole Located in Functionally Graded Material

2011 ◽  
Vol 704-705 ◽  
pp. 631-635
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Circular Hole ◽  
Constant Term ◽  
Complex Stress ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Dimensional Problem ◽  
Stress Components ◽  
Graded Material ◽  
Stress Functions ◽  
Stress Function Method

The complex stress function method is used in this study to formulate the 2-dimensional problem for nonhomogeneous materials. The Young’s modulus E varies linearly with the coordinate x and the Poisson’s ratio of the material is assumed constant and. The stress components and the boundary conditions are expressed in terms of two complex stress functions in explicit forms. It is noted that the constant term in stress functions has an influence on the stress components, which is different from the homogeneous material case. Subsequently, the problem of a nonhomogeneous plane containing a circular hole subjected to a uniform internal pressure is studied.

Effect of Temperature Gradient on the Mechanical Buckling Resistance of FGM Shallow Arches

2014 ◽  
Author(s):  
M. Bateni ◽  
M. R. Eslami
Keyword(s):  
Temperature Gradient ◽  
Thermal Environment ◽  
Mechanical Load ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Power Law Distribution ◽  
Concentrated Load ◽  
Shallow Arches ◽  
Buckling Resistance ◽  
Graded Material

This work presents a closed form investigation on the effect of temperature gradient on the buckling resistance of functionally graded material (FGM) shallow arches. The constituents are assumed to vary smoothly through the thickness of the arch according to the power law distribution and they are assumed to be temperature dependent. The arches subjected to the both uniform distributed radial load and central concentrated load and both boundary supports are supposed to be pinned. The temperature field is approximated by one-dimensional linear gradient through the thickness of the arch and the displacement field approximated by classical arches model. Also, Donnell type kinematics is utilized to extract the suitable strain-displacement relations for shallow arches. Adjacent equilibrium criterion is used to buckling analysis, and, critical bifurcation load is obtain in the complete presence of pre-buckling deformations. Results discloses the usefulness of using the FGM shallow arches in thermal environment because the temperature gradient enhances the buckling resistance of these structures when they are subjected to a lateral mechanical load.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Dao Huy Bich
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Linear Buckling ◽  
Non Linear ◽  
Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

scholarly journals Weight optimisation of functionally graded beams using modified differential evolution

2019 ◽  
Vol 13 (2) ◽  
pp. 48-63 ◽  
Author(s):  
Pham Hoang Anh ◽  
Tran Thuy Duong
Keyword(s):  
Differential Evolution ◽  
Volume Fraction ◽  
Lightweight Design ◽  
Shear Deformation Theory ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Parameter Distribution ◽  
Power Law Distribution ◽  
De Algorithm ◽  
Fgm Beam

In this article, an efficient numerical approach for weight optimisation of functionally graded (FG) beams in the presence of frequency constraints is presented. For the analysis purpose, a finite element (FE) solution based on the first order shear deformation theory (FSDT) is established to analyse the free vibration behaviour of FG beams. A four-parameter power law distribution and a five-parameter trigonometric distribution are used to describe the volume fraction of material constituents in the thickness direction. The goal is to tailor the thickness and material distribution for minimising the weight of FG beams while constraining the fundamental frequency to be greater than a prescribed value. The constrained optimisation problem is effectively solved by a novel differential evolution (DE) algorithm. The validity and efficiency of the proposed approach is demonstrated through two numerical examples corresponding to the four-parameter distribution and the five-parameter distribution.Keywords: FGM beam; lightweight design; frequency constraint; differential evolution.

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