On Stress-Focusing Effect in a Uniformly Heated Solid Sphere

2003 ◽  
Vol 70 (2) ◽  
pp. 304-309 ◽  
Author(s):  
H. J. Ding ◽  
H. M. Wang ◽  
W. Q. Chen
Keyword(s):  
Temperature Rise ◽  
Stress Responses ◽  
Constant Pressure ◽  
Integral Transform ◽  
External Surface ◽  
Separation Of Variables ◽  
Solid Sphere ◽  
Uniform Temperature ◽  
Focusing Effect ◽  
Isotropic Solid

By using the separation of variables technique, the dynamic thermal stress responses in an isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface are performed successfully. The analytical solutions of the radial and hoop dynamic stresses at the center are also obtained. By means of the present method, integral transform can be avoided. Numerical results denote that a very high dynamic stress peak appears periodically at the center of the isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface.

Stress-Focusing Effect in a Uniformly Heated Cylindrical Rod

1976 ◽  
Vol 43 (3) ◽  
pp. 464-468 ◽  
Author(s):  
Chih-Horng Ho
Keyword(s):  
Cross Section ◽  
Temperature Rise ◽  
Dynamic Stress ◽  
Peak Stress ◽  
Stress Waves ◽  
Uniform Temperature ◽  
Focusing Effect ◽  
Tension And Compression ◽  
Very High ◽  
Heating Duration

A long cylindrical rod is considered brought suddenly to a uniform temperature rise over its cross section. Stress-focusing effects occur when stress waves reflect from the outer surface of the rod and proceed radially inward to the axis. The focusing effect can cause a very high peak dynamic stress in both tension and compression in the rod. The magnitude of the peak stress depends upon the magnitude of the temperature rise and the effective heating duration. For instantaneous heating, the infinite peak of stress propagates outward from the center while these peaks are finite for nonzero heating duration. The solutions are carried out by using Laplace transform on time and presented as infinite series summations after the end of heating.

Temperature Rise at the Sliding Contact Interface for a Coated Semi-Infinite Body

1993 ◽  
Vol 115 (1) ◽  
pp. 1-9 ◽  
Author(s):  
X. Tian ◽  
F. E. Kennedy
Keyword(s):  
Surface Temperature ◽  
Temperature Rise ◽  
Peclet Number ◽  
Integral Transform ◽  
Sliding Contact ◽  
Contact Interface ◽  
Péclet Number ◽  
Maximum Surface ◽  
Semi Empirical ◽  
Maximum Surface Temperature

In this paper, a three-dimensional model of a semi-infinite layered body is used to predict steady-state maximum surface temperature rise at the sliding contact interface for the entire range of Peclet number. A set of semi-empirical solutions for maximum surface temperature problems of sliding layered bodies is obtained by using integral transform, finite element, heuristic and multivariable regression techniques. Two dimensionless parameters, A and Dp, which relate to coating thickness, contact size, sliding speed and thermal properties of both coating and substrate materials, are found to be the critical factors determining the effect of surface film on the surface temperature rise at a sliding contact interface. A semi-empirical solution for maximum surface temperature problems of homogeneous bodies, which covers the whole range of Peclet number, is also obtained.

Effect of a Surface Film on the Surface Temperature of a Rotating Cylinder

1986 ◽  
Vol 108 (1) ◽  
pp. 92-97 ◽  
Author(s):  
B. Gecim ◽  
W. O. Winer
Keyword(s):  
Thermal Properties ◽  
Heat Source ◽  
Film Thickness ◽  
Surface Temperature ◽  
Temperature Rise ◽  
High Speed ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Surface Film ◽  
Layer Effect

Solution to the steady heat conduction problem of a rotating layered cylinder is presented. The governing differential equations (for the film and the substrate) are solved by using an integral transform technique. It is shown that the presence of a surface film measured in micrometers can substantially change the level of the surface temperature. The effect of the surface film on the surface temperature depends on: respective thermal properties of the film and the substrate; relative surface speed; heat source (contact) size; and surface film thickness. However, the range in which the effect of the film on the surface temperature is dependent on these parameters is limited. Outside this range (i.e., thin film/low speed or thick film/high speed) the surface temperature rise is determined by the thermal properties of the substrate, or by the properties of the film alone, respectively. Hence, outside this range, a further change in the film thickness does not influence the surface temperature rise. Dimensionless plots showing the change in surface temperature rise as a function of material thermal properties, surface speed, heat source size, and film thickness are presented. Behavior for specific material combinations are also presented. The present information can be utilized to predict the layer effect on the partition of heat between the layered cylinders.

scholarly journals Thermal Changes in Root Surface of Primary Teeth During Root Canal Treatment With Diode Lasers: An In Vitro Study

2018 ◽  
Vol 9 (4) ◽  
pp. 237-242 ◽  
Author(s):  
Bahman Seraj ◽  
Zahra Moosavi Garmaroodi ◽  
Nasim Chiniforush ◽  
Sara Ghadimi
Keyword(s):  
Temperature Rise ◽  
Primary Teeth ◽  
External Surface ◽  
Diode Lasers ◽  
Root Surface ◽  
Root Space ◽  
Posterior Teeth ◽  
Mean Temperature ◽  
The Mean ◽  
Group B

Introduction: Increased temperature due to the application of laser during root canal disinfection may damage periodontium, alveolar bone, and permanent dental germ. The aim of this study was to evaluate the temperature increase of the external surface of primary roots due to the application of 810 nm and 980 nm diode lasers. Methods: A total of 58 extracted human primary teeth were prepared and randomly divided into two groups: (a) 810 nm diode laser and (b) 980 nm diode laser. Then, each group was divided into 4 subgroups based on the location of the temperature measurement, including subgroup 1: external root surface of primary anterior roots (A); subgroup 2: external root surface of posterior teeth at inter-root space (IS); subgroup 3: external root surface of posterior teeth at outer-root space (OS) and subgroup 4: external surface of furcation area of posterior teeth (F). Results: The mean temperature rise in group a (7.02±2.95ºC) was less than that of group b (10.62±4.59ºC) (P<0.001). Also, a significant difference was found between the laser groups in terms of the mean temperature rise of the external root surface at IS, OS and F, with higher temperature increase occurring in all points in laser b. The comparison of irradiation points in each laser showed a higher mean temperature rise for IS than OS, but this difference was only significant in group b (P<0.001). Conclusion: Within the studied parameters, 810 nm and 980 nm diode lasers should be used cautiously in primary root canals because of their temperature rise during their application.

scholarly journals Three-dimensional analytical poromechanical solutions for an arbitrarily inclined borehole subjected to fluid injection

2019 ◽  
Vol 475 (2221) ◽  
pp. 20180658 ◽  
Author(s):  
S. L. Chen
Keyword(s):  
Stress Responses ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Gas Production ◽  
Element Analysis ◽  
Expansion Theorem ◽  
Inclined Borehole

Hydraulic fracturing is the primary method of stimulation in unconventional reservoirs, playing a significant role in oil and gas production enhancement. A key issue for the analysis of hydraulic fracture initiation is to accurately determine the stress distributions in the vicinity of the borehole caused by the injection of pressurized fluids. This paper develops an exact, three-dimensional, poroelastic coupled analytical solution for such stress analysis of an arbitrarily inclined borehole subjected concurrently to a finite-length fluid discharge and in situ stresses, using Fourier expansion theorem and the Laplace–Fourier integral transform technique. The complicated boundary conditions, which involve the mixed boundary values at the borehole surface and the coupling between the total radial stress and injection-induced pore pressure over the sectioned borehole interval, as well as the fully three-dimensional far field in situ stresses, are addressed in a novel way and deliberately/elegantly decomposed into five fundamental, easier to handle modes. The rigour and definitive nature of the proposed analytical methodology facilitates fundamental understanding of the mechanism underlying the stress responses of the borehole and porous medium. It can be and is used here as a benchmark for the numerical solutions obtained from the finite-element analysis commercial program (ABAQUS).

Geometrically Nonlinear Analysis of Cross-Ply Laminated Composite Beams Subjected to Uniform Temperature Rise

2011 ◽  
Vol 335-336 ◽  
pp. 527-530 ◽  
Author(s):  
Xue Ping Chang ◽  
Xiao Dong Zhang ◽  
Qing You Liu
Keyword(s):  
Shear Deformation ◽  
Temperature Rise ◽  
Composite Beam ◽  
Numerical Solutions ◽  
Laminated Composite ◽  
Physical Parameters ◽  
Uniform Temperature ◽  
Geometrically Nonlinear Analysis ◽  
Post Buckling ◽  
Laminated Composite Beam

Abstract: On the basis of Reddy’s higher order shear deformation plate theory and the von Kármán’s geometry nonlinear theory, governing equations for nonlinear thermal buckling and post-buckling of cross-ply laminated composite beam subjected to a temperature rise are derived, in which the stretching-bending coupling terms produced by the non-homogenous distribution of the material properties are included. By using the shooting method to solve the corresponding nonlinear boundary value problem, numerical solutions for thermal post-buckling of cross-ply shear deformation laminated composite beam with its both ends immovably simply supported under uniform temperature rise are obtained. As an example, equilibrium paths and configurations for laminated composite beam paved in term of 0/90/0 are presented and characteristic curves of the nonlinear deformation changing with the thermal load were plotted. The effects of the geometric and physical parameters on the deformation of the beam are also examined. The theoretical analysis and numerical results show that different thermal expansion coefficient ratio, elastic moduli ratio, shear stiffness ratio will influence of the non-dimension critical buckling temperature.

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