Thermostatics of an elastic Cosserat plate containing a circular hole

1971 ◽  
Vol 70 (1) ◽  
pp. 169-174 ◽  
Author(s):  
İ. T. Gürgöze
Keyword(s):  
Temperature Gradient ◽  
General Theory ◽  
Circular Hole ◽  
Thermal Stresses ◽  
Plate Theory ◽  
The Other ◽  
Uniform Temperature ◽  
Classical Plate Theory ◽  
Cosserat Surface ◽  
Limiting Case

AbstractIn this paper, the general theory of a Cosserat surface given by Green, Naghdi and Wainwright(1), has been applied to the problem of a thermo-elastic Cosserat plate containing a circular hole of radius a. We assume that the major surfaces of the plate and the boundary of the hole are thermally insulated and that a uniform temperature gradient τ exists at infinity. In the limiting case, when h/a → 0, where h is the thickness of the plate, the thermal stresses at the circular hole reduce to those obtained by Florence and Goodier (4), by means of the classical plate theory. Results for the other limiting case h/a → ∞ are also given.

Transverse bending of infinite and semi-infinite thin elastic plates. III

1958 ◽  
Vol 54 (2) ◽  
pp. 288-299 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Isotropic Plate ◽  
Plate Theory ◽  
Outer Boundary ◽  
Exact Expression ◽  
Transverse Displacement ◽  
Elastic Plates ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
Elastically Restrained ◽  
Limiting Case

ABSTRACTWithin the restrictions of the classical plate theory, complex variable methods are used in this paper to develop an exact expression for the transverse displacement of an infinitely large isotropic plate having a free outer boundary and elastically restrained at an inner circular boundary, the plate being subjected to a general type of loading distributed over the area of a circle. The limiting case of a half-plane clamped along the straight edge and acted upon normally by the same loading is also considered.

Flexure of Polygonal Plates with Circular Holes

1985 ◽  
Vol 29 (03) ◽  
pp. 209-211
Author(s):  
Thein Wah
Keyword(s):  
Boundary Conditions ◽  
Circular Hole ◽  
Plate Theory ◽  
Numerical Results ◽  
Classical Plate Theory ◽  
Circular Holes ◽  
Polygonal Plate

A procedure is developed for determining the stresses in a polygonal plate with a circular hole. Classical plate theory is assumed. The boundary conditions are satisfied exactly term by term. Numerical results are given.

New First-Order Shear Deformation Plate Theories

2006 ◽  
Vol 74 (3) ◽  
pp. 523-533 ◽  
Author(s):  
R. P. Shimpi ◽  
H. G. Patel ◽  
H. Arya
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
The Other ◽  
Striking Similarity ◽  
Dynamic Problems ◽  
Governing Equations ◽  
Classical Plate Theory ◽  
First Order ◽  
Shear Deformation Theories ◽  
Displacement Based

First-order shear deformation theories, one proposed by Reissner and another one by Mindlin, are widely in use, even today, because of their simplicity. In this paper, two new displacement based first-order shear deformation theories involving only two unknown functions, as against three functions in case of Reissner’s and Mindlin’s theories, are introduced. For static problems, governing equations of one of the proposed theories are uncoupled. And for dynamic problems, governing equations of one of the theories are only inertially coupled, whereas those of the other theory are only elastically coupled. Both the theories are variationally consistent. The effectiveness of the theories is brought out through illustrative examples. One of the theories has striking similarity with classical plate theory.

Generalized Bending of a Large, Shear Deformable Isotropic Plate Containing a Circular Hole or Rigid Inclusion

2000 ◽  
Vol 68 (2) ◽  
pp. 230-233 ◽  
Author(s):  
C. W. Bert ◽  
H. Zeng
Keyword(s):  
Circular Hole ◽  
Isotropic Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Circular Inclusion ◽  
Experimental Result ◽  
Classical Plate Theory ◽  
Geometric Ratio ◽  
Three Dimensional Elasticity

The problem of a large isotropic plate with a circular hole or rigid circular inclusion is considered here. The plate experiences transverse shear deformation and is subjected to an arbitrary bending field. By using Reissner’s plate theory, a general solution, in terms of Poisson’s ratio ν, a geometric ratio, and bending moment ratio B, is obtained to satisfy both the boundary conditions along the edge and at great distances from the edge. The stress couple concentration factors are calculated and compared with classical plate theory, three-dimensional elasticity theory, higher-order plate theory, and an experimental result.

scholarly journals An Application of Hankel Transforms in Axially Symmetric Potential Flow

1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie
Keyword(s):  
New York ◽  
Incompressible Fluid ◽  
Circular Hole ◽  
Potential Flow ◽  
Fourier Transforms ◽  
The Other ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Physical Interest ◽  
Hankel Transforms

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.

Conjugated Heat Transfer in Skirt Hot Box in Pressure Vessels

2006 ◽  
Author(s):  
Hossein Shokouhmand ◽  
Manoochehr Bozorgmehrian
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Thermal Stresses ◽  
Weld Line ◽  
Pressure Vessels ◽  
Conductive Heat ◽  
Air Pocket ◽  
Cyclic Operation ◽  
Conjugated Heat Transfer

Pressure vessels are common equipment in oil, gas and petrochemical industries. In a hot containing fluid vessel, excessive temperature gradient at junction of skirt to head (weld line), can cause unpredicted high thermal stresses; Thereby fracture of the vessel may occur as a result of cyclic operation. Providing a hot box (air pocket) in crotch space is a economical, applicable and easy mounted method in order to reduce the intensity of thermal stresses. Natural convection due to temperature difference between the wall of pocket, will absorb heat near the hot wall (head of the vessel) and release that near the cold wall (skirt of the vessel), then the skirt wall conducts heat to the earth as a fin. This conjugated heat transfer removes the temperature gradient boundary at welded junction. This phenomena will lead the temperature gradient on the weld line from a sudden to smooth behavior, thereby the skirt-head junction, that is a critical region, could be protected from excessive thermal stresses. In this paper the profit of hot box and conjugated heat transfer in cavity has been demonstrated experimentally. As a result it is shown that the conductive heat transfer through the skirt (which acts as a fin) ensures the continuation of natural convection in the box. Also the governing equations has been solved numerically and compared with experimental results.

Thermal Stresses in Moderately Thick Elastic Plates

1959 ◽  
Vol 26 (3) ◽  
pp. 432-436
Author(s):  
B. E. Gatewood
Keyword(s):  
Temperature Gradient ◽  
Plane Stress ◽  
Thermal Stresses ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Elastic Plates ◽  
Plate Length ◽  
Moderately Thick Plates ◽  
Thick Elastic Plates ◽  
Thickness Variable

Abstract The three-dimensional stresses in the plate are investigated without using the plane-stress or plane-strain assumptions, the thickness of the plate being limited so that the normal stress in the thickness direction can be taken as a polynomial in the thickness variable. The temperature is taken as a polynomial in the thickness variable but with relatively large, though restricted, gradients with respect to the co-ordinates of the plane of the plate. For the case of the temperature constant in thickness variable, the stresses in the plane of the plate are presented as the plane-stress solution plus correcting terms due to the plate thickness, where the correcting terms involve the product of the temperature gradient and the ratio of the plate thickness to the plate length in the direction of the temperature gradient. In many cases the corrections are small even for moderately thick plates.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

Transverse dam-break waves

2014 ◽  
Vol 758 ◽  
Author(s):  
S. Karimpour Ghannadi ◽  
Vincent H. Chu
Keyword(s):  
Froude Number ◽  
Flow Rate ◽  
Main Flow ◽  
Dam Break ◽  
The Other ◽  
Water Diversion ◽  
The Family ◽  
The One ◽  
Limiting Case ◽  
The Waves

AbstractNumerical simulations of the transverse dam-break waves (TDWs) produced by the sudden removal of a gate on the side of a waterway are conducted based on the shallow-water equations to find solutions to a family of water-diversion problems. The Froude numbers in the main flow identify the members of the family. The depth and discharge profiles are analysed in terms of Ritter’s similarity variable. For subcritical main flow, the waves are comprised of a supercritical flow expansion followed by a subcritical outflow. For supercritical main flow, on the other hand, the waves are analogous to the Prandtl–Meyer expansion in gas dynamics. The diversion flow rate of two-dimensional TDWs on a flat bed is 55 % greater than the one-dimensional flow rate of Ritter in the limiting case of zero main flow, and approaches the rate of Ritter in the other limit when the value of the Froude number in the main flow approaches infinity. The diversion flow rate over a weir is generally higher than the rate over a flat bed depending on the Froude number of the main flow. These numerical simulation results are consistent with laboratory observations.

Al-Nawawī's Typology of Muftīs and its Significance for a General Theory of Islamic Law

1996 ◽  
Vol 3 (2) ◽  
pp. 137-164 ◽  
Author(s):  
Norman Calder
Keyword(s):  
General Theory ◽  
Islamic Law ◽  
The Other ◽  
Pivotal Role ◽  
General Character ◽  
Recent Debate ◽  
Closed Door

AbstractThis essay offers, in Section 2, a translation of al-Nawawī's presentation of the hierarchy of Muftīs. The context of the passage and its terminology and arguments are explored in the other Sections in order to assess their implications for the general character of Islamic juristic activities. Section 1 identifies two themes central to the text, namely loyalty to madhhab and differentiation of the task of the teaching jurist and the muftī. The first of these is elaborated in Section 3, which points to formal qualities of presentation and argument which assert the hermeneutical continuity of the school tradition; and in Section 4, which deals with the pivotal role of the founding imām in the legitimation of the school tradition. Section 5 takes up the terms taqlīd and ijtihād and shows that al-Nawawī's usage points towards a complex resolution of the recent debate about the open/closed door of ijtihād. The last Section returns to the original two themes to make two suggestions: (1) that taqlīd may be assessed as a principal of vitality within a hermeneutical tradition; (2) that the author-jurist (not the practising muftī) is the dominant creative agent within the ongoing juristic traditions.

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