Effects of Material Properties Estimations on the Thermo-Elastic Analysis for Functionally Graded Thick Spheres and Cylinders

2007 ◽  
Author(s):  
P. Ghaderi ◽  
M. Bankehsaz
Keyword(s):  
Material Properties ◽  
Mechanical Response ◽  
Functionally Graded ◽  
Elastic Response ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Constant Coefficients ◽  
Elastic Responses ◽  
Particulate Reinforced Composites ◽  
Material Gradation

In this paper effects of material properties estimations, used for particulate reinforced composites, on the thermo-mechanical response of functionally graded sphere and cylinder are presented. A numerical solution for an arbitrary material gradation is obtained for each geometry independently. With this assumption, the governing partial differential equations are reduced to an ordinary differential equation in each geometry. The thermo-elastic solution for hollow sphere is derived using spherical symmetry. However, plane strain and axial symmetry are assumed for solving hollow cylinder. In the numerical method, radial domain is divided into some finite sub-domains and material properties are assumed to be constant in each sub-domain. With this assumption, the governing thermal and mechanical equations in each sub-domain are an ODE with constant coefficients. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the thermo-elastic responses for the thick-walled FG sphere and cylinder are obtained. Three methods of gradation are used for comparing the effects of different material properties estimations on the results; Rule of Mixtures as a conventional method, Mori-Tanaka estimation and self-consistent scheme. The results show that estimations for material properties could be influential to the thermo-elastic response for some profiles of volume fractions of constituents. However, the effect on elastic response is negligible.

Analysis of Functionally Graded Cylindrical Panel Under Mechanical Loading

2007 ◽  
Author(s):  
P. Ghaderi ◽  
A. Fathizadeh ◽  
M. Bankehsaz
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Cylindrical Panel ◽  
Functionally Graded ◽  
Algebraic Equations ◽  
Aspect Ratios ◽  
Linear Algebraic Equations ◽  
Cylindrical Panels

In this paper a semi-analytical method is developed to analyze functionally graded cylindrical panels. In this method, the radial domain is divided into some finite sub-domains and the material properties are assumed to be constant in each subdomain. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the elastic response for the thick-walled FG cylindrical panel is obtained. The method can be used for all material properties variations but in present study, material properties are assumed vary with Mori-Tanaka estimation. Results are compared with the first order shear deformation theory and third order shear deformation theory of Reddy and accuracy of these theories in assessed for FG cylindrical panels with different aspect ratios.

Amplitude Incremental Method: A Novel Approach to Capture Stable and Unstable Solutions of Harmonically Excited Vibration Response of Functionally Graded Beams under Large Amplitude Motion

2019 ◽  
Vol 20 (5) ◽  
pp. 581-594 ◽  
Author(s):  
B. Panigrahi ◽  
G. Pohit
Keyword(s):  
Large Amplitude ◽  
Harmonic Balance Method ◽  
Functionally Graded ◽  
Vibration Response ◽  
Algebraic Equations ◽  
Unstable Solution ◽  
Linear Algebraic Equations ◽  
Excited Vibration ◽  
Non Linear ◽  
Large Amplitude Motion

AbstractAn interesting phenomenon is observed while conducting numerical simulation of non-linear dynamic response of FGM (functionally graded material) beam having large amplitude motion under harmonic excitation. Instead of providing a frequency sweep (forward or backward), if amplitude is incremented and response frequency is searched for a particular amplitude of vibration, solution domain can be enhanced and stable as well as unstable solution can be obtained. In the present work, first non-linear differential equations of motion for large amplitude vibration of a beam, which are obtained using Timoshenko beam theory, are converted into a set of non-linear algebraic equations using harmonic balance method. Subsequently an amplitude incremental iterative technique is imposed in order to obtain steady-state solution in frequency amplitude plane. It is observed that the method not only shows very good agreement with the available research but the domain of applicability of the method is enhanced up to a considerable extent as the stable and unstable solution can be captured. Subsequently forced vibration response of FGM beams are analysed.

Quasi-Analytic Sensitivity Analysis of a Unified Viscoplastic Constitutive Model for a Solder Alloy

1997 ◽  
Vol 50 (11S) ◽  
pp. S44-S49 ◽  
Author(s):  
Martin A. Eisenberg ◽  
Erhard Krempl ◽  
Luca Maciucescu
Keyword(s):  
Sensitivity Analysis ◽  
Solder Alloy ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Professional Judgment ◽  
Multidisciplinary Teams ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Engineering Alloys ◽  
High Homologous Temperature

Unified constitutive models for the consistent description of inelastic thermomechanical response of engineering alloys to widely varying control conditions are strongly nonlinear; there are numerous constants to be determined; and successful use depends critically on expert professional judgment. These circumstances are not unlike those associated with the design of complex systems dependent on successful interaction of multidisciplinary teams. Introduced in this paper is a paradigm for design of constitutive models motivated by modern system design methodologies. Specifically, a quasi-analytic sensitivity analysis is applied to a special form of a viscoplasticity-based overstress model (VBO) for the uniaxial, isothermal, high-homologous temperature mechanical response of a solder alloy. Parameter sensitivity is demonstrated via linear algebraic equations. The technique is a critical first step to application of sophisticated techniques of multidisciplinary design optimization (MDO) to constitutive modeling.

Geometrically Nonlinear Free Axisymmetric Vibrations Analysis of Thin Circular Functionally Graded Plates

2014 ◽  
Vol 971-973 ◽  
pp. 489-506
Author(s):  
El Kaak Rachid ◽  
El Bikri Khalid ◽  
Benamar Rhali
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Mass Density ◽  
Functionally Graded ◽  
Algebraic Equations ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Linear Mode ◽  
Linear Algebraic Equations ◽  
Non Linear

This paper deals with nonlinear free axisymmetric vibrations of functionally graded thin circular plates whose properties vary through its thickness. The inhomogeneity of the plate is characterized by a power law variation of the Young’s modulus and mass density of the material along the thickness direction, whereas Poisson’s ratio is assumed to be constant. The theoretical model is based on Hamilton’s principle and spectral analysis using a basis of admissible Bessel’s functions to yield the frequencies of the circular plates under clamped boundary conditions on the basis of the classical plate theory. The large vibration amplitudes problem, reduced to a set of non-linear algebraic equations, is solved numerically. The non-linear to linear frequency ratios are presented for various values of the volume fraction index n showing hardening type non-linearity. The distribution of the radial bending stress associated to the non-linear mode shape is also given for various vibration amplitudes, and is compared with those predicted by the linear theory.

Time-harmonic elastic singularities and oscillating indentation of layered solids

2020 ◽  
Vol 85 (4) ◽  
pp. 542-563
Author(s):  
H Y Yu ◽  
Sanboh Lee
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Point Force ◽  
Elastic Response ◽  
Surface Traction ◽  
Algebraic Equations ◽  
Dual Integral Equations ◽  
Time Harmonic ◽  
Linear Algebraic Equations

Abstract A new approach is proposed for obtaining the dynamic elastic response of a multilayered elastic solid caused by axisymmetric, time-harmonic elastic singularities. The method for obtaining the elastodynamic Green’s functions of the point force, double forces and center of dilatation is presented. For this purpose, the boundary conditions in an infinite solid at the plane passing through the singularity are derived first by using Helmholtz potentials. Then the Green’s function solution for layered solids is obtained by solving a set of simultaneous linear algebraic equations using the boundary conditions for both the singularities and for the layer interfaces. The application of the point force solution for the oscillating normal indentation problem is also given. The solution of the forced normal oscillation is formulated by integrating the point force Green’s function over the contact area with unknown surface traction. The dual integral equations of the unknown surface traction are established by considering the boundary conditions on the contact surface of the multilayered solid, which can be converted into a Fredholm integral equation of the second kind and solved numerically.

A Semi-Analytical Study of Geometrically Nonlinear Free Axisymmetric Vibrations of Thin Circular Functionally Graded Plates Using Iterative and Explicit Analytical Solution

2014 ◽  
Vol 704 ◽  
pp. 131-136
Author(s):  
El Kaak Rachid ◽  
Khalid El Bikri ◽  
Benamar Rhali
Keyword(s):  
Plate Theory ◽  
Mass Density ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Algebraic Equations ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Explicit Analytical Solution ◽  
Linear Algebraic Equations ◽  
Non Linear

. This paper deals with nonlinear free axisymmetric vibrations of functionally graded thin circular plates (FGCP) whose properties vary through its thickness. The inhomogeneity of the plate is characterized by a power law variation of the Young’s modulus and mass density of the material along the thickness direction, whereas Poisson’s ratio is assumed to be constant. The theoretical model is based on Hamilton’s principle and spectral analysis using a basis of admissible Bessel’s functions to yield the frequencies of the circular plates under clamped boundary conditions on the basis of the classical plate theory. The large vibration amplitudes problem, reduced to a set of non-linear algebraic equations, is solved numerically. The non-linear to linear frequency ratios are presented. Then, explicit analytical solutions are presented, based on the semi-analytical model previously developed by EL Kadiri et al. [1-2] for beams and rectangular plates, which allow direct and easy calculation for the first non-linear axisymmetric mode shape, with their associated non-linear frequencies of FG circular plates and which are expected to be very useful in engineering applications and in further analytical developments. An excellent agreement is found with the results obtained by the iterative method.

scholarly journals Stress Analysis of Functionally Graded Disk with Exponentially Varying Thickness using Iterative Method

2021 ◽  
Vol 16 ◽  
pp. 232-244
Author(s):  
Sandeep Kumar Paul ◽  
Manoj Sahni
Keyword(s):  
Functionally Graded Material ◽  
Variable Thickness ◽  
Mechanical Response ◽  
External Pressure ◽  
Functionally Graded ◽  
Plane Stress Condition ◽  
Graded Material ◽  
Navier Equation ◽  
Material Gradation ◽  
Iteration Technique

In this paper, variable thickness disk made up of functionally graded material (FGM) under internal and external pressure is analyzed using a simple iteration technique. Thickness of FGM disk and the material property, namely, Young’s modulus are varying exponentially in radial direction. Poisson’s ratio is considered invariant for the material. Navier equation is used to formulate the problem in the differential equation form under plane stress condition. Displacement, stresses, and strains are obtained under the influence of material gradation and variable thickness. Three different material combinations are considered for the FGM disk. The mechanical response of disk obtained for different functionally graded material combinations are compared with the homogenous disk, and results are plotted graphically

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

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