On Inertia Effects in a Transient Thermoelastic Problem

1959 ◽  
Vol 26 (4) ◽  
pp. 503-509
Author(s):  
Eli Sternberg ◽  
J. G. Chakravorty
Keyword(s):  
Stress Distribution ◽  
Surface Temperature ◽  
Step Function ◽  
Infinite Medium ◽  
Thermoelastic Problem ◽  
Plane Boundary ◽  
Entire Plane ◽  
Inertia Effects ◽  
Dynamic Treatment ◽  
The Given

Abstract This paper is concerned with the dynamic treatment of a transient thermoelastic problem for a semi-infinite medium which is constrained against transverse displacements and is exposed to a uniform time-dependent heating (or cooling) of its entire plane boundary. The stress distribution appropriate to this problem, in the event that the surface temperature is a step-function of time, was previously established by Danilovskaya [1] and by Mura [2]. In the present investigation the accompanying displacements are determined in closed form. In addition, an exact closed solution, in terms of error functions, is obtained for the case in which the time-dependence of the given surface temperature is of the ramp-type. The ensuing field of thermal stress is compared with the corresponding quasi-static stress distribution, with a view toward a quantitative assessment of the accompanying inertia effects as influenced by the rate at which the temperature of the boundary is altered. The results indicate that the conclusions reached in [1] and [2] are in need of essential modification once the assumption of an instantaneous change of the surface temperature is abandoned.

scholarly journals Non-linear heat conduction with ramped surface heating ramp surface heating and approximate solution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 377-389
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Surface Temperature ◽  
Integral Method ◽  
Infinite Medium ◽  
Surface Heating ◽  
Integration Technique ◽  
Solution Approach ◽  
Linear Heat ◽  
Thermal Penetration Depth ◽  
Non Linear

Non-linear heat conduction with a power-law thermal diffusivity and ramped surface temperature has been solved by the double-integration technique of the integral-balance integral method. The case of a semi-infinite medium and infinite ramp of surface temperature has been considered as example demonstrating the versatility of the solution approach. The thermal penetration depth and solution behaviours with finite speeds have been analyzed.

The Floodlight Problem

1997 ◽  
Vol 07 (01n02) ◽  
pp. 153-163 ◽  
Author(s):  
Prosenjit Bose ◽  
Leonidas Guibas ◽  
Anna Lubiw ◽  
Mark Overmars ◽  
Diane Souvaine ◽  
...  
Keyword(s):  
Fixed Points ◽  
Point Sets ◽  
Entire Plane ◽  
The Given

Given three angles summing to 2π, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specified angles not exceeding π can be placed at n fixed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2π. We give O(n log n) algorithms for both these problems.

scholarly journals The transition from the elastic to the plastic state in mild steel

1913 ◽  
Vol 88 (605) ◽  
pp. 462-471 ◽  
Keyword(s):  
Stress Distribution ◽  
Mild Steel ◽  
Yield Point ◽  
Testing Machine ◽  
Plastic State ◽  
Inertia Effects ◽  
Direct Bearing ◽  
Minimum Stress ◽  
Complicated Nature

In the ordinary testing of mild steel the yield point is indicated by the sudden extension of the specimen and the accompanying drop of the beam of the testing machine which occur at this point. This fact would suggest that some reduction of the stress in the specimen under test takes place, and autographic records of tests furnish evidence of the existence of a region immediately after yield in which the relation of stress to strain is of a complicated nature, and in which the intensity of the stress is less than that which caused the yield. It has been shown by Sir Alfred Ewing and Dr. Rosenhain that the yield phenomenon is due to the formation of planes of cleavage in the crystals, along which sliding takes place. The fact that a greater stress is required to initiate the sliding movement than to maintain it has a direct bearing upon the stress distribution on surfaces subjected to non-uniform stresses when yield in any part takes place, and the object of the experiments here described was to determine the minimum stress in mild steel during the transition from the elastic to the plastic state. In the usual methods of obtaining autographic records the effect is considerably obscured by the inertia of the loading appliances, and the impossibility of limiting the extension to the degree required, so that the relation of the recorded load to the strain in the region under consideration is, in these circumstances, to a great extent fictitious. Sir Alexander B. W. Kennedy, some 27 years ago, described a method whereby inertia effects were eliminated, and obtained, as a result, a reduction of stress immediately after yield of about 16 per cent. Since the experiments here described by the present writers were carried out, Prof. W. E. Dalby has published an account of an optical autographic recorder, in which the measurement of the load is effected in a manner similar to that adopted by Kennedy, and in tests carried out on mild steel has observed a reduction of stress of about 13 per cent.

scholarly journals An Asymptotic Approach for the Elastodynamic Problem of a Plate under Impact Loading

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
Penelope Michalopoulou ◽  
George A. Papadopoulos
Keyword(s):  
Laplace Transform ◽  
Impact Loading ◽  
Step Function ◽  
Infinite Strip ◽  
Asymptotic Approach ◽  
Heaviside Step Function ◽  
Inertia Effects ◽  
Elastodynamic Problem ◽  
Line Force ◽  
The One

An approach is presented for analyzing the transient elastodynamic problem of a plate under an impact loading. The plate is considered to be in the form of a long strip under plane strain conditions. The loading is taken as a concentrated line force applied normal to the plate surface. It is assumed that this line force is suddenly applied and maintained thereafter (i.e., it is a Heaviside step function of time). Inertia effects are taken into consideration and the problem is treated exactly within the framework of elastodynamic theory. The approach is based on multiple Laplace transforms and on certain asymptotic arguments. In particular, the one-sided Laplace transform is applied to suppress time dependence and the two-sided Laplace transform to suppress the dependence upon a spatial variable (along the extent of the infinite strip). Exact inversions are then followed by invoking the asymptotic Tauber theorem and the Cagniard-deHoop technique. Various extensions of this basic analysis are also discussed.

Adaptive multinary inversion of gravity and gravity gradiometry data

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. G101-G114 ◽  
Author(s):  
Michael S. Zhdanov ◽  
Wei Lin
Keyword(s):  
Barents Sea ◽  
Step Function ◽  
Inversion Method ◽  
Model Parameters ◽  
The Novel ◽  
Gravity Gradiometry ◽  
Inversion Algorithm ◽  
Novel Approach ◽  
Discrete Values ◽  
The Given

We have developed a novel approach for inversion of gravity and gravity gradiometry data based on multinary transformation of the model parameters. This concept is a generalization of binary density inversion to the models described by any number of discrete model parameters. The multinary inversion makes it possible to explicitly exploit the sharp contrasts of the density between the host media and anomalous targets in the inversion of gravity and gravity gradiometry data. In the framework of the multinary inversion method, we use the given values of density and error functions to transform the density distribution into the desired step-function distribution. To accommodate a possible deviation of the densities from the fixed discrete values, we develop an adaptive technique for selecting the corresponding standard deviations, guided by the inversion process. The novel adaptive multinary inversion algorithm is demonstrated to be effective in determining the shape, location, and densities of the anomalous targets. We find that this method can be effectively applied for the inversion of the full tensor gravity gradiometry (FTG) data computer simulated for the SEG salt density model and for the field FTG data collected in the Nordkapp Basin, Barents Sea.

Transient Thermoelastic Problem for an Infinite Medium With a Spherical Cavity Exhibiting Temperature-Dependent Properties

1962 ◽  
Vol 29 (2) ◽  
pp. 399-407 ◽  
Author(s):  
Jerzy Nowinski
Keyword(s):  
Thermal Expansion ◽  
Shear Modulus ◽  
Perturbation Method ◽  
Temperature Rise ◽  
Spherical Cavity ◽  
Infinite Medium ◽  
Thermoelastic Problem ◽  
Linear Variation ◽  
Temperature Dependent ◽  
Temperature Dependent Properties

This paper is concerned with a polarly symmetric transient thermoelastic problem for an infinite medium with a spherical cavity, the boundary of the cavity being subjected to a sudden temperature rise. Thermal and elastic properties of the medium are assumed to be temperature dependent. Using the perturbation method general equations for the displacements and stresses corresponding to particular boundary-value problems have been found. An illustrative example, involving linear variation of conductivity and thermal expansion as well as quadratic variation of shear modulus with temperature, has been discussed in detail.

An Electrical-Resistance Method of Determining the Mean Surface Temperature of Tubes

1937 ◽  
Vol 4 (1) ◽  
pp. A16-A20
Author(s):  
John H. Marchant
Keyword(s):  
Surface Temperature ◽  
Electrical Resistance ◽  
Radial Flow ◽  
Temperature Gradients ◽  
Longitudinal Flow ◽  
Tube Material ◽  
Resistance Thermometer ◽  
The Mean ◽  
Physical Laws ◽  
The Given

Abstract The author describes a new method for determining the mean surface temperature of condenser tubes through which a steady radial flow of heat occurs. The method consists in using the tube itself as a resistance thermometer. The author explains that when a steady longitudinal flow of electricity is superimposed upon the given radial flow of heat, the actual current being so small as not to involve appreciable Joulean heat, the temperature gradients associated with the flow of heat affect the electrical resistance of the tube material, and expressions for the mean temperature of the inner and outer tube surfaces can be derived from applications of physical laws. These expressions are derived by the author.

scholarly journals Translation groups of the boundary-layer flows induced by continuous moving surfaces

2010 ◽  
Vol 655 ◽  
pp. 327-343 ◽  
Author(s):  
EUGEN MAGYARI
Keyword(s):  
Boundary Layer ◽  
Solution Space ◽  
Outer Edge ◽  
Plane Boundary ◽  
Continuous Group ◽  
Balance Equations ◽  
Boundary Layer Flows ◽  
Layer Flow ◽  
Steady Plane ◽  
The Given

The steady plane boundary-layer flows of velocity field {u(x, y), v(x, y)} induced by continuous moving surfaces are revisited in this paper. It is shown that the governing balance equations, as well as the asymptotic condition u(x, ∞) = 0 at the outer edge of the boundary layer are invariant under arbitrary translations y → y + y0(x) of the transverse coordinate y. The wall conditions, i.e. the prescribed stretching velocity u(x, 0) ≡ Uw(x) and the transpiration velocity v(x, 0) ≡ Vw(x) distributions, however, undergo in general substantial changes. The consequences of this basic symmetry property on the structure of the solution space are investigated. It is found that starting with a primary solution which describes the boundary-layer flow induced by an impermeable surface, infinitely many translated solutions can be generated which form a continuous group, the translation group of the given primary solution. The elements of this group describe boundary-layer flows induced by permeable surfaces stretching under transformed wall conditions, Uw(x) → Ũw(x) = u[x, y0(x)] and Vw(x) → Ṽw(x) = v[x, y0(x)] − y′0(x)u[x, y0(x)], respectively. In this way, starting with a known solution {u(x, y), v(x, y)} so that the inverse y0(x) = u−1(x, Ũw) of u[x, y0(x)] exists, a new solution {ũ(x, y), ṽ(x, y)} corresponding to any desired stretching velocity distribution Ũw(x) can be prepared. It also turns out that several exact solutions discovered during the latter decades are not basically new solutions, but translated counterparts of some formerly reported primary solutions. A few specific examples are discussed in detail.

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