Deformation and Moments in Elastically Restrained Circular Plates Under Arbitrary Load or Linear Thermal Gradient

1960 ◽  
Vol 82 (4) ◽  
pp. 423-438
Author(s):  
M. Zaid ◽  
M. Forray
Keyword(s):  
Thermal Gradient ◽  
Load Distribution ◽  
Loading Condition ◽  
Stress Pattern ◽  
Algebraic Equations ◽  
Circular Plates ◽  
Linear Temperature ◽  
Linear Temperature Gradient ◽  
Elastically Restrained ◽  
Elastic Constraints

The problem of a circular plate, with a central hole, elastically constrained against rotation and deflection, acted upon by a transverse linear temperature gradient or a general axisymmetrical loading condition is considered in this paper. With the aid of presented graphs and simple algebraic equations, it is a relatively simple matter to construct the desired deflection and stress pattern for any combination of elastic constraints and load distribution.

LINEAR AND NONLINEAR THERMOELASTIC ANALYSES OF BEAMS UNDER TEMPERATURE GRADIENT

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Yong-Lin Pi ◽  
Mark Andrew Bradford
Keyword(s):  
Temperature Gradient ◽  
Cross Section ◽  
Axial Direction ◽  
Gradient Field ◽  
Linear Temperature ◽  
Temperature Changes ◽  
Linear Temperature Gradient ◽  
Linear And Nonlinear ◽  
Elastically Restrained ◽  
Elastic Restraints

In a structure, beams are often connected with other members such as columns, which provide considerable restraints against the rotation and extension of the beam ends. When a beam is subjected to an in-plane temperature gradient field, the temperature gradient tends to change the curvature of the beam in the transverse direction and expand the beam in the axial direction. The restrained actions will produce bending moments and compressive forces in the beam, which increase with an increase of the temperature differential and average temperature of the temperature gradient field. When these actions reach critical values, the elastically restrained beam may bifurcate from its primary in-plane equilibrium state to a lateral-torsional buckled equilibrium configuration. This paper carries out linear and nonlinear thermoelastic analyses of an elastically restrained beam of doubly symmetric open thin-walled cross-section that is subjected to a linear temperature gradient field over its cross-section. It is found that geometric nonlinearity influences the thermoelastic responses of the beam to the temperature changes significantly. The influence decreases with an increase of the stiffness of the elastic restraints.

scholarly journals Time Period of the Vibration of the Circular Plate with Circular Variation Both in Thickness and Density

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Reeta Bhardwaj ◽  
Amit Sharma ◽  
Sudeshna Ghosh ◽  
Naveen Mani ◽  
Kamal Kumar
Keyword(s):  
Thermal Gradient ◽  
Ritz Method ◽  
The Other ◽  
Circular Plates ◽  
Linear Quadratic ◽  
Linear Temperature ◽  
Thermally Induced ◽  
Time Period ◽  
Modes Of Vibration ◽  
Convergence Study

An analysis was carried out to investigate the time period of the thermally induced vibration of clamped and simply supported circular plates with circular variation both in thickness and density. Prior to this study, the variations considered were either linear, quadratic, parabolic, or exponential in nature. To study thermal effect, one-dimensional linear temperature variation on the plates is taken into consideration. Rayleigh–Ritz method is applied to compute the time period of the first three modes of vibration for both plates by varying tapering parameter, thermal gradient, and density. Convergence study of frequency modes for both plates conducted suggests that the convergence rate in case of circular variation is faster than the other studies done. A comparison of time period with the available published results is done. The comparison done concludes that time period obtained in the present study by varying thermal gradient and tapering parameter is found to be less than the other studies done for the same set of parameters. This study helped to establish the fact that, by using circular variation in plate parameters, we can get less time period of frequency modes in comparison to other variations considered till date.

scholarly journals Microfluidic Platform for Analyzing the Thermotaxis of C. elegans in a Linear Temperature Gradient

2017 ◽  
Vol 33 (12) ◽  
pp. 1435-1440 ◽  
Author(s):  
Sunhee YOON ◽  
Hailing PIAO ◽  
Tae-Joon JEON ◽  
Sun Min KIM
Keyword(s):  
Temperature Gradient ◽  
Linear Temperature ◽  
Microfluidic Platform ◽  
C Elegans ◽  
Linear Temperature Gradient

Optimum Elastic Restraint for Pressurised Circular Plates

1963 ◽  
Vol 67 (632) ◽  
pp. 525-526
Author(s):  
Charles W. Bert
Keyword(s):  
Effective Stress ◽  
Elastic Material ◽  
Unit Volume ◽  
List Type ◽  
Maximum Deflection ◽  
Type Number ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Isotropic Elastic Material ◽  
Elastically Restrained

SummaryFor uniform-thickness, solid circular plates made of isotropic elastic material and elastically restrained at the edge, expressions are derived for the optimum support stiffness to minimise the following quantities: 1.The largest effective stress based on several different strength theories.2.The largest effective stress per unit of maximum deflection or per unit volume displaced.

An Analytical Solution Countercurrent Heat Transfer Between Parallel Vessels With a Linear Axial Temperature Gradient

1988 ◽  
Vol 110 (3) ◽  
pp. 254-256 ◽  
Author(s):  
E. H. Wissler
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Heat Exchange ◽  
Temperature Gradient ◽  
Infinite Medium ◽  
Linear Temperature ◽  
Linear Temperature Gradient ◽  
Axial Temperature ◽  
Mixed Mean ◽  
The Difference

Presented in this paper is a solution for countercurrent heat exchange between two parallel vessels embedded in an infinite medium with a linear temperature gradient along the axes of the vessels. The velocity profile within the vessel is assumed to be parabolic. This solution describes the temperature field within the vessels, as well as in the tissue, and establishes that the intravessel temperature is not uniform, as is generally assumed to be the case. An explicit expression for the intervessel thermal resistance based on the difference between cup-mixed mean temperatures is derived.

Thermoregulatory control during pregnancy and lactation in rats

1997 ◽  
Vol 83 (3) ◽  
pp. 837-844 ◽  
Author(s):  
Heather L. Eliason ◽  
James E. Fewell
Keyword(s):  
Oxygen Consumption ◽  
Ambient Temperature ◽  
Thermal Conductance ◽  
Thermoregulatory Response ◽  
Linear Temperature ◽  
Metabolic Chamber ◽  
Linear Temperature Gradient ◽  
Thermoneutral Zone ◽  
Pregnancy And Lactation ◽  
Near Term

Eliason, Heather L., and James E. Fewell.Thermoregulatory control during pregnancy and lactation in rats. J. Appl. Physiol. 83(3): 837–844, 1997.—Although the mechanisms remain unknown, maternal core temperature (Tc) decreases near term of pregnancy and is increased throughout lactation in rats. The purpose of our present experiments was to determine whether pregnancy and lactation shift the thermoneutral zone of rats and to investigate whether the changes in maternal Tcduring pregnancy and lactation result from “forced” or “regulated” thermoregulatory responses. Conscious, chronically instrumented nonpregnant and pregnant and lactating rats were studied both in a thermocline (a chamber with a linear temperature gradient from 12 to 36°C) and in a metabolic chamber to determine the influence of pregnancy and lactation on selected ambient temperature as well as the thermoregulatory response to changes in ambient temperature. We found that selected ambient temperature, oxygen consumption, and thermal conductance did not change in rats studied in a thermocline as Tc decreased near term of pregnancy. There was, however, a downward shift in the thermoneutral zone of rats studied in a metabolic chamber near term of pregnancy. During lactation, selected ambient temperature decreased in rats studied in a thermocline as oxygen consumption and Tc increased. The thermoneutral zone of lactating rats was not different from that of nonpregnant animals. Thus our data provide evidence that the decrease in Tc near term of pregnancy in rats results from a regulated thermoregulatory response, whereas the increase in Tc during lactation results from a forced thermoregulatory response.

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