Mathematical approach to thermoelastic characteristics for functionally graded rotating circular disks

2019 ◽  
Vol 13 (11) ◽  
pp. 533-545
Author(s):  
Jaegwi Go
Keyword(s):  
Functionally Graded ◽  
Mathematical Approach ◽  
Thermoelastic Characteristics ◽  
Circular Disks

scholarly journals Thermoelastic Characteristics of Functionally Graded Circular Disk Models under the Loading of Contact Forces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jaegwi Go
Keyword(s):  
Contact Force ◽  
Strain Distribution ◽  
Outer Boundary ◽  
Circular Disk ◽  
Circular Domain ◽  
Functionally Graded ◽  
Circumferential Direction ◽  
Governing Equations ◽  
Disk Model ◽  
Thermoelastic Characteristics

A rotating functionally graded circular disk undergoing a contact load is taken into account to investigate the thermoelastic characteristics. By considering contact force, a pair of partial differential equations is induced as the governing equations based on Hooke’s law. The behavior of circular disk modes is described with the variations of contact force and homogeneous thickness. A finite volume model is introduced to obtain approximate solutions for the governing equations because of the complexity of the equations. Contact force is highly influential in the radial direction compared to the circumferential direction in the displacement distribution, while a large radial stress appears near the area of the contact point. In the strain distribution, the magnitude increases as the angle grows near part of the outer boundary in the circular domain. The radial distribution profiles are susceptible to the growth of contact force in nearby area of the outer boundary, whereas the influences on the circumferential direction profiles are trivial. The increase of homogeneous thickness dwindles the radial magnitude of displacement, stress, and strain distribution profiles over nearby area of the outer boundary of the circular domain. As a result, numerical approach demonstrates that contact force and homogeneous thickness are indispensable parameters and provide deep influence on the thermoelastic movements of a rotating circular disk. Thus, the results obtained may be useful to design an appropriate FGM circular disk model for the industrial area by controlling the above parameters.

Multiphysics of Multilayered and Functionally Graded Cylinders Under Prescribed Hygrothermomagnetoelectromechanical Loading

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
A. H. Akbarzadeh ◽  
D. Pasini
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Cross Section ◽  
Functionally Graded ◽  
Governing Equations ◽  
Multilayered Cylinder ◽  
Hollow Cylinders ◽  
Insight Into ◽  
Circular Disks ◽  
Long Cylinder

This paper examines the multiphysics of multilayered and functionally graded cylinders subjected to steady-state hygrothermomagnetoelectromechanical loading. The cylinder is assumed to be axisymmetric, infinitely long, and with either hollow or solid cross section that is, both polarized and magnetized radially. The multiphysics model is used to investigate the effect of moisture, temperature, magnetic, electric, and mechanical loadings. The influence of imperfectly bonded interfaces is also accounted for in the governing equations. Exact solutions of differential equations are obtained for each homogenous layer of the multilayered cylinder. The results are verified with those available in literature for a homogenous infinitely long cylinder and can also be applied to study the multiphysics of thin circular disks. Maps are presented for solid and hollow cylinders to visualize the effect of hygrothermomagnetoelectromechanical loading, heterogeneity of bonded layers, and imperfectly bonded interfaces. The plots offer insight into the behavior of heterogeneous magnetoelectroelastic media in a steady state hygrothermal field.

Nonlinear dynamic behavior of a long temperature-dependent FGM hollow cylinder subjected to thermal shocking

2014 ◽  
Vol 21 (2) ◽  
pp. 267-280 ◽  
Author(s):  
Hong-Liang Dai ◽  
Yan-Ni Rao
Keyword(s):  
Dynamic Behavior ◽  
Hollow Cylinder ◽  
Governing Equation ◽  
Nonlinear Dynamic ◽  
Transfer Problem ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Nonlinear Dynamic Behavior ◽  
Graded Material ◽  
Thermoelastic Characteristics

AbstractIn this paper, the nonlinear dynamic behavior of a long hollow cylinder consisting of temperature-dependent functionally graded material (FGM) subjected to thermal shocking is investigated. Material parameters of the FGM hollow cylinder, except the Poisson’s ratio, are assumed to be graded continuously through the thickness according to the power law expressions, and they are assumed to be temperature dependent. The governing equation of the motion of the FGM hollow cylinder is obtained based on the plane-stain theory and together with the governing equation of the transient heat transfer problem is solved by the finite difference method, Newmark method, and iterative method. Numerical examples are carried out in which the Si3N4-SUS304 FGM hollow cylinders are considered, and some valuable dynamic thermoelastic characteristics of the FGM hollow cylinder subjected to symmetric or asymmetric thermal shocking are revealed.

A mathematical approach to data evaluation with focus on prediction of minimal residual disease in pediatric ALL

2012 ◽  
Vol 224 (03) ◽  
Author(s):  
A Torge ◽  
M Zimmermann ◽  
A Möricke ◽  
R Köhler ◽  
A Schrauder ◽  
...  
Keyword(s):  
Minimal Residual Disease ◽  
Residual Disease ◽  
Data Evaluation ◽  
Mathematical Approach ◽  
Pediatric All ◽  
Minimal Residual

269. Use of an Objective Mathematical Approach to Facilitate Assigning Skin Notations

2000 ◽  
Author(s):  
M. Boeniger ◽  
H. Ahlers ◽  
B. Lushniak ◽  
R. Mickelsen ◽  
A. Morton ◽  
...  
Keyword(s):  
Mathematical Approach

The Effect of Realistic Mathematic Approach on Students’ Learning Motivation

2019 ◽  
Vol 2 (2) ◽  
pp. 145
Author(s):  
Shindy Lestari ◽  
Syahrilfuddin Syahrilfuddin ◽  
Neni Hermita ◽  
Zetra Hainul Putra
Keyword(s):  
Public School ◽  
Research Method ◽  
T Test ◽  
Learning Motivation ◽  
Fifth Grade ◽  
Average Score ◽  
Mathematical Approach ◽  
Fifth Grade Students ◽  
Post Test ◽  
Realistic Mathematic

This research is to determine the effect of realistic mathematical approach on students’ learning motivation. The research method is pre-experiment of one group pretest posttest design. This study was conducted with 34 fifth grade students from a public school in Pekanbaru, Indonesia. The results indicate that students’ learning motivation significantly increases. Among six indicators measuring students’ learning motivation, the indicator of interesting activities in learning is the most increase, from 80.76% in pre-test to 86.40% in post-test. The average score of pretest in form of students’ learning motivation questionnaire before applying treatment was 90.56 while score posttest after treatment was 95,09 and the results of the research hypotheses using the comparative t-test tcount (6.997) > ttable (2.039). This means that there is an effect of applying the realistic mathematical approach to students’ learning motivation.

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