Axisymmetric Thermal Stresses of a Piezoelectric Poroelastic Circular Solid Plate

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Ali Abjadi ◽  
Mohsen Jabbari ◽  
Ahmad Reza Khorshidvand
Keyword(s):  
Cadmium Selenide ◽  
Material Properties ◽  
Thermal Stresses ◽  
Separation Of Variables ◽  
Electrical Potential ◽  
Material Symmetry ◽  
Exponential Functions ◽  
Cylindrical Coordinates ◽  
Solid Plate ◽  
Electrical Loads

Abstract This paper presents the steady-state thermoelasticity solution for a circular solid plate is made of an undrained porous piezoelectric hexagonal material symmetry of class 6 mm. The porosities of the plate vary through the thickness; thus, material properties, except Poisson's ratio, are assumed as exponential functions of axial variable z in cylindrical coordinates. Having axisymmetric general form, external thermal and electrical loads are acted on the plate and the piezothermoelastic behavior of the plate is investigated. Using a full analytical method based on Bessel Fourier's series and separation of variables, the governing partial differential equations are derived. A formulation is given for the displacements, electric potential, thermal stresses, and electric displacements resulting from prescribed the general form of thermal, mechanical, and electric boundary conditions. Finally, the application of the derived formulas is illustrated by an example for a cadmium selenide solid, the results of which are presented graphically. Also, the effects of material property indexes, the porosity, and Skempton coefficients are discussed on the displacements, thermal stresses, electrical potential function, and electric displacements.

Deformation and Stresses Analysis in FG Rotating Hollow Disk and Cylinder Subjected to Thermal and Mechanical Load

2012 ◽  
Vol 187 ◽  
pp. 68-73 ◽  
Author(s):  
A. R. Khorshidvand ◽  
M. Javadi
Keyword(s):  
Material Properties ◽  
Radial Direction ◽  
Thermal Stresses ◽  
Energy Equation ◽  
Mechanical Load ◽  
Elliptic Cylinder ◽  
Exponential Functions ◽  
One Dimensional ◽  
First Law Of Thermodynamics ◽  
Stress Components

In this paper, a new solution is presented for one-dimensional steady-state mechanical and thermal stresses in a FG rotating hollow disk and cylinder. The material properties for FG are expressed as nonlinear exponential functions through the radius and Poisson’s ratio is taken to be constant. The temperature distribution is derived from first law of thermodynamics by solving energy equation, with a general thermal and mechanical boundary conditions on the inside and outside surfaces. Heat conduction and Navier equations are solved analytically by choosing elliptic cylinder coordinates system and the results are shown for displacement and stress components along the radial direction.

scholarly journals Axisymmetric elasticity solution for an undrained saturated poro-piezoelastic thick disk

2019 ◽  
Vol 46 (2) ◽  
pp. 191-219
Author(s):  
Ali Abjadi ◽  
Mohsen Jabbari ◽  
Reza Khorshidvand
Keyword(s):  
Material Properties ◽  
Piezoelectric Ceramic ◽  
Thick Plate ◽  
Material Symmetry ◽  
Elasticity Solution ◽  
Cylindrical Coordinates ◽  
Mechanical Loads ◽  
Radial And Axial Displacements ◽  
Piezoelectric Disk ◽  
Axisymmetric Elasticity

In this paper, a circular thick plate made of poroelastic piezoelectric ceramic is studied. The porosities of the plate vary through the thickness and axisymmetric behavior of a piezoelectric disk exhibiting hexagonal material symmetry of class 6 mm. Additionally, external mechanical loads which are in axi-symmetric general form act on the plate. The material properties of the plate vary exponentially as functions of the ?? variable in cylindrical coordinates. Based on an elasticity solution in terms of radial and axial displacements (??, ??), the governing partial differential equations are derived and solved analytically; mechanical stresses and electric displacements are then calculated. Finally an example which illustrates the application of the derived formulas is presented.

General Solution for Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder due to Nonaxisymmetric Steady-State Loads

2003 ◽  
Vol 70 (1) ◽  
pp. 111-118 ◽  
Author(s):  
M. Jabbari ◽  
S. Sohrabpour ◽  
M. R. Eslami
Keyword(s):  
Steady State ◽  
Material Properties ◽  
Thermal Stresses ◽  
Separation Of Variables ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Power Functions ◽  
Complex Fourier Series ◽  
Graded Material ◽  
Thick Cylinder

In this paper, the general theoretical analysis of two-dimensional steady-state thermal stresses for a hollow thick cylinder made of functionally graded material is developed. The temperature distribution is assumed to be a function of radial and circumferential directions with general thermal and mechanical boundary conditions on the inside and outside surfaces. The material properties, except Poisson’s ratio, are assumed to depend on the variable r and they are expressed as power functions of r. The separation of variables and complex Fourier series are used to solve the heat conduction and Navier equations.

Thermomechanical Analysis in FG Rotating Hollow Disk

2011 ◽  
Vol 110-116 ◽  
pp. 148-154 ◽  
Author(s):  
A. R. Khorshidvand ◽  
M. Jabbari
Keyword(s):  
Heat Conduction ◽  
Material Properties ◽  
Radial Direction ◽  
Thermal Stresses ◽  
Energy Equation ◽  
Elliptic Cylinder ◽  
Thermomechanical Analysis ◽  
Functionally Graded ◽  
Exponential Functions ◽  
Graded Materials

In this paper, mechanical and thermal stresses of rotating hollow disks composed of functionally graded materials (FGMs) is presented. The material properties for FG are expressed as nonlinear exponential functions through the radius of disk and Poisson’s ratio is taken to be constant. The temperature distribution is derived from first law thermodynamics by solving energy equation, general thermal and mechanical boundary conditions are assumed on the inside and outside surfaces of the disk. Heat conduction and Navier equations of a FGM disk are expressed in elliptic cylinder coordinates system and solved analytically. The results are shown for displacement and stresses components along the radial direction.

scholarly journals The Approximate Solution of Dual Integral Equations by Variational Methods

1958 ◽  
Vol 11 (2) ◽  
pp. 115-126 ◽  
Author(s):  
B. Noble
Keyword(s):  
Approximate Solution ◽  
Variational Methods ◽  
Integral Equations ◽  
Separation Of Variables ◽  
Circular Disc ◽  
Cylindrical Coordinates ◽  
Dual Integral Equations ◽  
Particular Solution ◽  
Image Position

The classic application of dual integral equations occurs in connexion with the potential of a circular disc (e.g. Titchmarsh (9), p. 334). Suppose that the disc lies in z = 0, 0≤ρ≤1, where we use cylindrical coordinates (p, z). Then it is required to find a solution ofsuch that on z = 0Separation of variables in conjunction with the conditions that ø is finite on the axis and ø tends to zero as z tends to plus infinity yields the particular solution.

Thermal Stress in Teeth

1978 ◽  
Vol 57 (4) ◽  
pp. 571-582 ◽  
Author(s):  
B.A. Lloyd ◽  
M.B. McGinley ◽  
W.S. Brown
Keyword(s):  
Thermal Stress ◽  
Numerical Analysis ◽  
Material Properties ◽  
Thermal Stresses ◽  
In Vivo Studies ◽  
Tooth Structure ◽  
Analysis Techniques ◽  
Tooth Type

Observations of crack damage in the tooth structure from in vivo studies and in vitro experimental thermal cycling studies were combined with numerical analysis techniques to identify and isolate the influence of thermal stresses an the creation and propagation of cracks in teeth. The factors considered in this study included: (a) variations in tooth type or geometry (molar, bicuspid, etc.), (b) tooth age, (c) material properties of the tooth, (d) the magnitude of the change in the temperature of the environment surrounding the tooth, and (e) the thermal resistance between the tooth and the medium surrounding the tooth.

The Influence of Creep Strain on Crack Length Measurements Using the Potential Drop

2015 ◽  
Author(s):  
K. M. Tarnowski ◽  
C. M. Davies ◽  
K. M. Nikbin ◽  
D. W. Dean
Keyword(s):  
Stainless Steel ◽  
Crack Growth ◽  
Material Properties ◽  
Crack Extension ◽  
Electrical Potential ◽  
Creep Crack Growth ◽  
Potential Drop ◽  
Fe Model ◽  
Creep Properties ◽  
Length Measurements

One of the most common methods for estimating crack extension in the laboratory is electrical potential drop (PD). A key limitation of this technique is that it is sensitive to strains at the crack tip as well as crack extension. When producing J-R curves the onset of crack growth may be identified from a point of inflection on a plot of PD vs. CMOD. For creep crack growth (CCG) tests however, the effects of strain are often ignored. This paper investigates whether a similar method may be applied to CCG testing. A single CCG test was performed on type 316H stainless steel and a point of inflection, similar to that observed during J-R curve testing was identified. A finite element (FE) based approach was used to investigate this phenomenon further. A 3D sequentially-coupled structural-electrical FE model was used to reproduce the experimental PD vs. CMOD plot up to the point of inflection. The model was capable of predicting the general relationship between strain and PD. It predicted the magnitude of the change in PD to within 30%. A simplified 2D FE model was then used to perform a parametric study to investigate whether a similar trend may be expected for a range of materials. Power law tensile and creep properties were investigated with stress exponents of 1, 3 and 10. The results confirm that a point of inflection should be observable for the range of material properties considered.

scholarly journals Probability Study on the Thermal Stress Distribution in Thick HK40 Stainless Steel Pipe Using Finite Element Method

Designs ◽  
2019 ◽  
Vol 3 (1) ◽  
pp. 9
Author(s):  
Sujith Bobba ◽  
Shaik Abrar ◽  
Shaik Mujeebur Rehman
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
High Temperature ◽  
Material Properties ◽  
Thermal Stresses ◽  
Steel Pipe ◽  
Stress Distributions ◽  
Stainless Steel Pipe ◽  
Deterministic Solution ◽  
Analytical Expressions

The present work deals with the development of a finite element methodology for obtaining the stress distributions in thick cylindrical HK40 stainless steel pipe that carries high-temperature fluids. The material properties and loading were assumed to be random variables. Thermal stresses that are generated along radial, axial, and tangential directions are generally computed using very complex analytical expressions. To circumvent such an issue, probability theory and mathematical statistics have been applied to many engineering problems, which allows determination of the safety both quantitatively and objectively based on the concepts of reliability. Monte Carlo simulation methodology is used to study the probabilistic characteristics of thermal stresses, and was implemented to estimate the probabilistic distributions of stresses against the variations arising due to material properties and load. A 2-D probabilistic finite element code was developed in MATLAB, and the deterministic solution was compared with ABAQUS solutions. The values of stresses obtained from the variation of elastic modulus were found to be low compared to the case where the load alone was varying. The probability of failure of the pipe structure was predicted against the variations in internal pressure and thermal gradient. These finite element framework developments are useful for the life estimation of piping structures in high-temperature applications and for the subsequent quantification of the uncertainties in loading and material properties.

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