Note on Cylindrical Bending of a Heated Long Rectangular Plate

1963 ◽  
Vol 67 (625) ◽  
pp. 65-66
Author(s):  
J. S. Przemieniecki
Keyword(s):  
Thermal Stresses ◽  
Functional Relationship ◽  
Rectangular Plates ◽  
Practical Application ◽  
Surrounding Structure ◽  
Dimensional Parameters ◽  
Design Calculations ◽  
Special Case ◽  
Excessive Number ◽  
Elastic Characteristics

In reference 1 a general analysis was presented for the calculation of thermal stresses and deflections due to temperature gradients in long rectangular plates having lengthwise edges supported elastically. The edge support was idealised as equivalent rotational and extensional stiffnesses depending on the elastic characteristics of the surrounding structure. The special case of infinite extensional stiffness and freely hinged edges (see Fig. 1) was discussed in greater detail and a number of graphs were included for the calculation of edge reactions in terms of the thermal force and thermal moment parameters. Since these graphs used an excessive number of non-dimensional parameters their practical application is unwieldy; four non-dimensional parameters were used instead of three parameters which would be sufficient to describe the required functional relationship. This note shows an alternative presentation of the results which can be used more conveniently in any design calculations.

Thermal Stresses in Rectangular Plates

1959 ◽  
Vol 10 (1) ◽  
pp. 65-78 ◽  
Author(s):  
J. S. Przemieniecki
Keyword(s):  
Thermal Stresses ◽  
Plate Thickness ◽  
Normal Modes ◽  
Thermoelastic Stress ◽  
Characteristic Functions ◽  
Vibration Modes ◽  
Rectangular Plates ◽  
Practical Application ◽  
Flat Plates ◽  
Modes Of Vibration

SummaryThe characteristic functions for beam vibration modes are used to derive an approximate solution for the calculation of thermal stresses in rectangular isotropic flat plates subjected to arbitrary temperature distributions in the plane of the plate and constant temperatures through the plate thickness. The thermal stresses are obtained in the form of generalised Fourier expansions in terms of the characteristic functions, and their derivatives, representing normal modes of vibration of a clamped-clamped beam. Since these functions have recently been tabulated, the practical application of this new method to the thermoelastic stress analysis of plates presents no difficulty.

Thermal Stresses in Long Cylindrical Shells

1959 ◽  
Vol 26 (1) ◽  
pp. 147-148
Author(s):  
C. H. Tsao
Keyword(s):  
Thermal Stresses ◽  
Cylindrical Shells ◽  
Special Case

Abstract Goodier’s results for the longitudinal thermal stresses in long cylindrical shells are improved by the addition of a few terms. For the special case of thin cylindrical shells with uniform but unequal inside and outside temperatures, this improved solution checks exactly with Timoshenko’s solution.

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.

Thermal Stresses in Restrained Rectangular Plates

1968 ◽  
Vol 94 (1) ◽  
pp. 1-22 ◽  
Author(s):  
K.T. Sundara Raja Iyengar ◽  
K. Chandrasekhara
Keyword(s):  
Thermal Stresses ◽  
Rectangular Plates

scholarly journals Vibration of Skew Sandwich Plates With Laminated Facings

1997 ◽  
Author(s):  
C. M. Wang ◽  
K. K. Ang ◽  
C. Wang
Keyword(s):  
Ritz Method ◽  
Composite Plates ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Edge Conditions ◽  
System Vibration ◽  
Special Case ◽  
Length Limitation ◽  
Good Agreement

A Rayleigh-Ritz analysis is presented for the free vibration of skew sandwich plates composed of an orthotropic core and laminated facings. By proposing a set of Ritz functions consisting of the product of mathematically complete polynomial functions and the the boundary equations raised to appropriate powers, the Rayleigh-Ritz method can be automated to handle such composite plates with any combination of edge conditions. For convenience and better accurarcy, the Ritz formulation was derived in the skew coordinate system. Vibration frequencies of rectangular plates (a special case of skew plates) obtained via this method have been found to be in good agreement with previous researchers results. Owing to length limitation, only sample vibration frequencies for skew sandwich plates are presented.

A Mechanical Model of Helical Elements in Textured Yarns

1976 ◽  
Vol 46 (4) ◽  
pp. 278-283 ◽  
Author(s):  
M. Konopasek
Keyword(s):  
Differential Equations ◽  
Mechanical Model ◽  
Mechanical Characteristics ◽  
Functional Relationship ◽  
Three Dimensional ◽  
Infinite Length ◽  
Fiber Properties ◽  
Helical Angle ◽  
Limiting Case ◽  
Special Case

The helical model of the spontaneously collapsed filaments in twist-textured yarns is defined as reflecting the limiting case of a free-filament segment with infinite length (or number of coils) between two reversal points. The fundamental relationships linking fiber properties and parameters of the texturing process with geometrical and mechanical characteristics of the helices are derived directly from the differential equations of the three-dimensional elastica. Bicomponent and similar fibers are interpreted as a special case of twist-textured filaments with original (permanently set) helical angle equal to π/2; for this case an explicit functional relationship between contraction and stretching force is obtained.

MODELLING ZERO-INFLATED COUNT DATA WITH A SPECIAL CASE OF THE GENERALISED POISSON DISTRIBUTION

2019 ◽  
Vol 49 (03) ◽  
pp. 689-707 ◽  
Author(s):  
Enrique Calderín-Ojeda ◽  
Emilio GóMez-Déniz ◽  
Inmaculada Barranco-Chamorro
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Negative Binomial ◽  
Skewed Data ◽  
Iteratively Reweighted Least Squares ◽  
Number Of Zeros ◽  
Scoring Algorithm ◽  
Fisher Scoring Algorithm ◽  
Special Case ◽  
Excessive Number

AbstractA one-parameter version of the generalised Poisson distribution provided by Consul and Jain (1973) is considered in this paper. The distribution is unimodal with a zero vertex and over-dispersed. A generalised linear model related to this distribution is also presented. Its parameters can be estimated by using a Fisher-Scoring algorithm which is equivalent to iteratively reweighted least squares. Due to its flexibility and capacity to describe highly skewed data with an excessive number of zeros, the model is suitable to be applied in insurance settings as an alternative to the negative binomial and zero-inflated model.

Electromicrobiology: Microbial Fuel Cells (MTC): Current and Prospects

2020 ◽  
Vol 17 (9) ◽  
pp. 4733-4737
Author(s):  
Vasili M. Travkin ◽  
Nikita S. Lyahovchenko ◽  
Vladislav Yu. Senchenkov ◽  
Iriva V. Batlytskaya ◽  
Inna P. Solyanikova
Keyword(s):  
Fuel Cells ◽  
Microbial Fuel Cells ◽  
General Idea ◽  
Practical Application ◽  
Close Attention ◽  
Electrochemical Systems ◽  
Microbial Electrochemical Systems ◽  
Special Case

The presented mini-review gives a general idea of microbial electrochemical systems (MES). Possible directions of their practical application are shown. Microbial fuel cells (MFCs) are a special case of MES. They cause close attention of researchers in connection with their undoubted prospects in such fields as energy, neutralization of toxic wastewater, synthesis, etc.

scholarly journals THE CONCENTRATION OF THERMAL STRESSES IN METAL MATERIALS AND CONSTRUCTION UNDER LOCAL HEATING

2020 ◽  
pp. 72-77
Author(s):  
V. Deryushev ◽  
M. Zayceva ◽  
D. Evseev ◽  
E. Kosenko
Keyword(s):  
Thermal Stresses ◽  
Local Heating ◽  
Temperature Stresses ◽  
Heating Spot ◽  
Cold Zone ◽  
Thin Walled Structures ◽  
Energy Flows ◽  
Metal Materials ◽  
Thin Walled ◽  
Elastic Characteristics

significant thermal stresses arising in thin-walled metal materials and structures loaded with tensile stresses can lead either to their complete destruction or to the appearance of discontinuity zones in them. The equations for calculation of temperature stresses in flat thin-walled structures at their localized thermal heating caused by the action of concentrated energy flows are analyzed. As an example, a thin-walled stretched plate subjected to strong local heating in a circular spot is considered. The developed model takes into account the change of elastic characteristics under strong local heating and the change in the thickness of the material in the heating spot. As an example, the diagram of the distribution of tangential stresses for a stretched plate in the area of a circular heating spot is given. Thus, the results of the study show that there is a rupture and concentration of stresses along the contour of the heating spot from the cold zone.

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