scholarly journals Propagation of Thermal Stresses in an Infinite Medium

1959 ◽  
Vol 11 (4) ◽  
pp. 237-244 ◽  
Author(s):  
F. J. Lockett ◽  
I. N. Sneddon
Keyword(s):  
Thermal Stresses ◽  
Infinite Medium ◽  
Nonuniform Distribution ◽  
The Body ◽  
Heat Sources ◽  
Dynamic Stresses ◽  
Elastic Bodies ◽  
State Of Stress ◽  
Body Forces ◽  
Uneven Heating

In the full linear theory of thermoelasticity there is a coupling between the thermal and the purely mechanical effects so that not only does a nonuniform distribution of temperature in the solid produce a state of stress but dynamical body forces or applied surface tractions produce variations in temperature throughout the body. In a recent paper (Eason and Sneddon, (2)) an account was given of the calculation of the dynamic stresses produced in elastic bodies, both infinite and semi-infinite, by uneven heating. In this paper we shall consider the propagation of thermal stresses in an infinite medium when, in addition to heat sources, there are present body forces which vary with the time.

X.—The Dynamic Stresses Produced in Elastic Bodies by Uneven Heating

1959 ◽  
Vol 65 (2) ◽  
pp. 143-176 ◽  
Author(s):  
G. Eason ◽  
I. N. Sneddon
Keyword(s):  
Additional Term ◽  
Elastic Solid ◽  
Rate Of Change ◽  
Stress And Strain ◽  
Heat Sources ◽  
Dynamic Stresses ◽  
Elastic Bodies ◽  
Infinite Extent ◽  
Uneven Heating ◽  
Strain Tensors

SynopsisThe presence of a non-uniform distribution of temperature in an elastic solid gives rise to an additional term in the generalized Hooke's Law connecting the stress and strain tensors and to a term involving the time rate of change of the dilatation in the equation governing the conduction of heat in the solid. The present paper is concerned with the effects produced by these additional terms in two simple situations. In the first, the elastic solid is regarded as being of infinite extent and the distribution of temperature in the solid is produced by heat sources whose strength may vary with time. In the second, the solid is supposed to be semi-infinite and to be deformed by prescribed variations in the temperature of the bounding plane and by heat sources within itself.

scholarly journals The Propagation of Thermal Stresses in a Semi-infinite Medium

1960 ◽  
Vol 12 (2) ◽  
pp. 75-84 ◽  
Author(s):  
F. J. Lockett
Keyword(s):  
Dynamical System ◽  
Thermal Effects ◽  
Thermal Stresses ◽  
Elastic Solid ◽  
Infinite Medium ◽  
Heat Energy ◽  
The Body ◽  
Heat Sources ◽  
Surface Temperature Distribution ◽  
Work Done

When an elastic solid is subjected to a dynamical system of surface or body forces, not all of the work done by these forces is employed in deforming the material. The remainder is converted into heat energy producing a distribution of temperature throughout the body. Similarly the application of a surface temperature distribution, or the introduction of heat sources within the body, produces elastic as well as thermal effects. Thus we see that in the dynamical case there is a link between these two types of condition—thermal and elastic.

Green’s Functions in Generalized Micropolar Thermoelasticity

1993 ◽  
Vol 46 (11S) ◽  
pp. S316-S326
Author(s):  
Ranjit S. Dhaliwal ◽  
Jun Wang
Keyword(s):  
General Solution ◽  
Heat Source ◽  
Body Force ◽  
The Body ◽  
Arbitrary Distribution ◽  
Heat Sources ◽  
Infinite Body ◽  
Body Forces ◽  
Micropolar Thermoelasticity ◽  
Short Time

General solution of the generalized micropolar thermoelastic equations has been obtained for arbitrary distribution of the body couples, body forces, and heat sources in an infinite body. Short time solutions have been obtained for the cases of impulsive body force and heat source acting at a point. Numerical values of the short time solutions have been displayed graphically.

Gravitational stresses in accreted bodies

1963 ◽  
Vol 276 (1367) ◽  
pp. 571-576 ◽  
Keyword(s):  
Theory Of Elasticity ◽  
The Body ◽  
Final Size ◽  
Final State ◽  
Final Shape ◽  
State Of Stress ◽  
Body Forces ◽  
Stress And Deformation ◽  
Historical Element

The conventional treatment of body forces in continuum mechanics implies that these forces are applied to a structure having the dimensions of the final body. This treatment is quite satisfactory when the body forces arise from the presence of an acceleration field or of an electromagnetic field. It fails, however, when we turn to the determination of the state of stress in a body which grows to its final shape by the gradual accretion of layers of material. Then the weight of each new layer loads and deforms the earlier material before hardening and becoming a part of the final structure. Successive layers are applied not to an unstressed but to a partially complete structure which is in a state of initial stress and deformation. The final gravitational stresses in such an accreted body depend upon an historical element; that is, on the order and manner in which the final shape is attained. When the final state is achieved there is, in general, a non-vanishing dislocation tensor. An appropriate method of computing the final gravitational stresses due to own weight is indicated for the case in which the stresses and deformations are small enough to permit the use of the constitutive and geometric equations of the linear theory of elasticity. The method is illustrated for the case of a gravitating sphere that has grown to its final size by accretion of material.

Transient Temperature Involving Oscillatory Heat Source With Application in Fretting Contact

2007 ◽  
Vol 129 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Jun Wen ◽  
M. M. Khonsari
Keyword(s):  
Heat Source ◽  
Oscillation Amplitude ◽  
The Body ◽  
Transient Temperature ◽  
Dimensionless Frequency ◽  
Heat Sources ◽  
Infinite Body ◽  
Fitting Method ◽  
Wide Range ◽  
Analytical Expressions

An analytical approach for treating problems involving oscillatory heat source is presented. The transient temperature profile involving circular, rectangular, and parabolic heat sources undergoing oscillatory motion on a semi-infinite body is determined by integrating the instantaneous solution for a point heat source throughout the area where the heat source acts with an assumption that the body takes all the heat. An efficient algorithm for solving the governing equations is developed. The results of a series simulations are presented, covering a wide range of operating parameters including a new dimensionless frequency ω¯=ωl2∕4α and the dimensionless oscillation amplitude A¯=A∕l, whose product can be interpreted as the Peclet number involving oscillatory heat source, Pe=ω¯A¯. Application of the present method to fretting contact is presented. The predicted temperature is in good agreement with published literature. Furthermore, analytical expressions for predicting the maximum surface temperature for different heat sources are provided by a surface-fitting method based on an extensive number of simulations.

Effect of Compliance on Residual Stresses in Manufacturing with Moving Heat Sources

2021 ◽  
pp. 1-53
Author(s):  
Mitchell R. Grams ◽  
Patricio F. Mendez
Keyword(s):  
Residual Stresses ◽  
Thermal Stresses ◽  
Ad Hoc ◽  
Mathematical Treatment ◽  
Heat Sources ◽  
Plastic Part ◽  
Practical Applications ◽  
Tendon Force ◽  
Design Calculations ◽  
Force Concept

Abstract Manufacturing processes involving moving heat sources include additive manufacturing, welding, laser processing (cladding and heat treatment), machining, and grinding. These processes involve high local thermal stresses that induce plasticity and result in permanent residual stress and distortion. The residual stresses are typically calculated numerically at great computational expense despite the fact that the inelastic fraction of the domain is very small. Efforts to decouple the small plastic part from the large elastic part have led to the development of the tendon force concept. The tendon force can be predicted analytically for the case of infinitely rigid components; however, this limitation has prevented the broader use of the concept in practical applications. This work presents a rigorous mathematical treatment using dimensional analysis, asymptotics, and blending which demonstrates that the effect of geometric compliance depends on a single dimensionless group, the Okerblom number. Closed-form expressions are derived to predict the effect of compliance without the need for empirical ad-hoc fitting or calibration. The proposed expressions require input of only material properties and tabulated process parameters, and are thus ideally suited for use in metamodels and design calculations, as well as incorporation into engineering codes and standards.

Axisymmetric Thermal Stresses in a Spherical Shell of Arbitrary Thickness

1957 ◽  
Vol 24 (3) ◽  
pp. 376-380
Author(s):  
E. L. McDowell ◽  
E. Sternberg
Keyword(s):  
Steady State ◽  
Spherical Shell ◽  
Spherical Cavity ◽  
Series Solution ◽  
Thermal Stresses ◽  
Solid Sphere ◽  
Theory Of Elasticity ◽  
Infinite Medium ◽  
Series Solutions ◽  
Arbitrary Thickness

Abstract This paper contains an explicit series solution, exact within the classical theory of elasticity, for the steady-state thermal stresses and displacements induced in a spherical shell by an arbitrary axisymmetric distribution of surface temperatures. The corresponding solutions for a solid sphere and for a spherical cavity in an infinite medium are obtained as limiting cases. The convergence of the series solutions obtained is discussed. Numerical results are presented appropriate to a solid sphere if two hemispherical caps of its boundary are maintained at distinct uniform temperatures.

The State of Stress and Strain Adjacent to Notches in a New Class of Nonlinear Elastic Bodies

2019 ◽  
Vol 135 (1-2) ◽  
pp. 375-397 ◽  
Author(s):  
Vojtěch Kulvait ◽  
Josef Málek ◽  
K. R. Rajagopal
Keyword(s):  
The State ◽  
Stress And Strain ◽  
New Class ◽  
Elastic Bodies ◽  
State Of Stress ◽  
Nonlinear Elastic
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