scholarly journals METHOD OF COMPENSATING LOADS FOR SOLVING OF A PROBLEM OF UNSYMMETRIC BENDING OF INFINITE ICE SLAB WITH CIRCULAR OPENING

2017 ◽  
Vol 13 (2) ◽  
pp. 50-55
Author(s):  
Elena B. Koreneva
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Infinite Plate ◽  
Constant Thickness ◽  
Circular Opening ◽  
Opening Method

Unsymmetric flexure of an infinite ice slab with circular opening is under examination. The men-tioned construction is considered as an infinite plate of constant thickness resting on an elastic subgrade which properties are described by Winkler’s model. The plate’s thickness is variable in the area ajoining to the opening. Method of compensating loads is used. Basic and compensating solutions are received. The obtained solutions are produced in closed form in terms of Bessel functions.

scholarly journals Bending of an incomplete annular plate and related problems

1979 ◽  
Vol 14 (3) ◽  
pp. 103-109 ◽  
Author(s):  
J R Barber
Keyword(s):  
Stress Concentration ◽  
Closed Form ◽  
Circular Plate ◽  
Annular Plate ◽  
Infinite Plate ◽  
Concentration Data ◽  
Closed Form Solutions ◽  
Concentrated Forces

Closed-form solutions and stress-concentration data are obtained for the problem of a sector of an annular plate subjected to moments and transverse forces on its radial edges. Closed-form solutions are also given for a semi-infinite plate or a circular plate subjected to a system of concentrated forces and/or moments at the edge.

ASYMPTOTICS OF ZEROS OF CERTAIN ENTIRE FUNCTIONS

2007 ◽  
Vol 05 (03) ◽  
pp. 291-299
Author(s):  
MOURAD E. H. ISMAIL
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Entire Functions

We derive representations for some entire q-functions and use it to derive asymptotics and closed form expressions for large zeros of a class of entire functions including the Ramanujan function, and q-Bessel functions.

Influence Coefficients for Hemispherical Shells With Small Openings at the Vertex

1955 ◽  
Vol 22 (1) ◽  
pp. 20-24
Author(s):  
G. D. Galletly
Keyword(s):  
Constant Thickness ◽  
Influence Coefficient ◽  
Circular Opening ◽  
Central Angle ◽  
Calculation Time ◽  
Numerical Example ◽  
Hemispherical Shell ◽  
Influence Coefficients ◽  
Hemispherical Shells

Abstract Three methods of obtaining the influence coefficients for a thin, constant-thickness, hemispherical shell with a circular opening at the vertex were investigated and utilized in a numerical example. Bearing in mind both accuracy and calculation time, it was concluded that when the total central angle subtended by the opening is less than approximately 30 deg, good results for the influence coefficient calculation will be obtained by using Method II in the text of the paper.

scholarly journals A Review of Procedures for Summing Kapteyn Series in Mathematical Physics

2009 ◽  
Vol 2009 ◽  
pp. 1-34 ◽  
Author(s):  
R. C. Tautz ◽  
I. Lerche
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Mathematical Physics ◽  
Short Review ◽  
Quantum Systems ◽  
Review Article ◽  
Functional Behavior ◽  
Basic Physics ◽  
Kapteyn Series ◽  
Physics Problems

Since the discussion of Kapteyn series occurrences in astronomical problems the wealth of mathematical physics problems in which such series play dominant roles has burgeoned massively. One of the major concerns is the ability to sum such series in closed form so that one can better understand the structural and functional behavior of the basic physics problems. The purpose of this review article is to present some of the recent methods for providing such series in closed form with applications to: (i) the summation of Kapteyn series for radiation from pulsars; (ii) the summation of other Kapteyn series in radiation problems; (iii) Kapteyn series arising in terahertz sideband spectra of quantum systems modulated by an alternating electromagnetic field; and (iv) some plasma problems involving sums of Bessel functions and their closed form summation using variations of the techniques developed for Kapteyn series. In addition, a short review is given of some other Kapteyn series to illustrate the ongoing deep interest and involvement of scientists in such problems and to provide further techniques for attempting to sum divers Kapteyn series.

MODELING NON-LINEAR COHERENT STATES IN FIBER ARRAYS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 349-355 ◽  
Author(s):  
R. DE J. LEÓN-MONTIEL ◽  
H. MOYA-CESSA
Keyword(s):  
Closed Form ◽  
Coherent States ◽  
Bessel Functions ◽  
Displacement Operator ◽  
Fiber Arrays ◽  
Non Linear ◽  
Phase Operators

A class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained. We call these nonlinear coherent states as Bessel states because the coefficients that expand them into number states are Bessel functions. We give a closed form for the displacement operator that produces such states.

Degenerate Scale Problem for a Hypocycloid Hole in an Infinite Plate in Plane Elasticity

2016 ◽  
Vol 32 (4) ◽  
pp. N7-N10
Author(s):  
Y.-Z. Chen
Keyword(s):  
Boundary Condition ◽  
Conformal Mapping ◽  
Closed Form ◽  
Infinite Plate ◽  
Closed Form Solution ◽  
Plane Elasticity ◽  
Form Solution ◽  
Scale Problem ◽  
Exterior Region ◽  
Degenerate Scale

AbstractBased on the conformal mapping, this paper provides a closed form solution for the degenerate scale of the hypocycloid hole in plane elasticity. In the derivation, we assume the vanishing displacements along the boundary in the degenerate scale problem. Some functions in the boundary condition are decomposed into three parts with particular behavior. Even the displacements are vanishing along the boundary of an exterior region, the displacements and stresses are not equal to zero in the exterior region. This is a particular feature in the degenerate scale problem.

Summation of Series over Bourget Functions

2008 ◽  
Vol 51 (4) ◽  
pp. 627-636
Author(s):  
Mirjana V. Vidanović ◽  
Slobodan B. Tričković ◽  
Miomir S. Stanković
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Bessel Functions ◽  
Integer Order ◽  
Summation Of Series ◽  
Finite Sums ◽  
Riemann Ζ Function

AbstractIn this paper we derive formulas for summation of series involving J. Bourget's generalization of Bessel functions of integer order, as well as the analogous generalizations by H. M. Srivastava. These series are expressed in terms of the Riemann ζ function and Dirichlet functions η, λ, β, and can be brought into closed form in certain cases, which means that the infinite series are represented by finite sums.

On expanding a hole from zero radius in a thin infinite plate

1954 ◽  
Vol 226 (1167) ◽  
pp. 543-561 ◽  
Keyword(s):  
Residual Stresses ◽  
Yield Stress ◽  
Axial Stress ◽  
Plastic Region ◽  
Infinite Plate ◽  
Middle Surface ◽  
Constant Thickness ◽  
Maximum Pressure ◽  
Boiler Steel ◽  
Zero Radius

As a criterion of the maximum pressure attainable on the interface between tube and plate when tubes are expanded into boiler drums, a theory is required which will allow for work-hardening and thickening of the plate, and it is also necessary to take into account the elastic as well as the plastic strains. Such a theory is set out in this paper, assuming a uniform hydrostatic pressure, the hole being expanded from zero radius in an infinite plate. The plate varies in thickness proportionately with the radius, and it is shown that the system remains geometrically similar irrespective of the degree of expanding, i.e. of the extent of the plastic region. The axial stress perpendicular to the middle surface of the plate is assumed to be zero for this problem, so that the tube and plate can be considered as a continuous medium. The problem is then one of plane stress in Which all variables become functions of a single parameter r / c , where r is any radius and c is the radius of the current plastic-elastic interface. The equilibrium equation, the compressibility relation and the strain relations (through the Reuss equations) are expressed in terms of this parameter and of the velocity v of any element, using c as the time scale. The resulting four equations are solved by taking finite increments of the variables, the appropriate value of the yield stress being inserted for each step using the yield stress curve for a typical boiler steel. The stress and displacement patterns are compared with those for a plate of constant thickness (Taylor 1948; Hill 1950). The residual stresses on release of the expanding pressure are determined assuming no secondary yielding occurs. In addition, the earlier theory due to Nadai is extended to allow an estimate to be made of the effect of secondary yielding owing to the residual stresses reaching the yield stress.

Flexural stiffness of leaf springs for compliant micromechanisms

2008 ◽  
Vol 222 (12) ◽  
pp. 2505-2511 ◽  
Author(s):  
P Angeli ◽  
F De Bona ◽  
M G Munteanu
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Constant Thickness ◽  
Flexural Stiffness ◽  
Beam Model ◽  
Flexural Behaviour ◽  
Leaf Springs ◽  
Linear Behaviour

Von Kármán equations have been used to evaluate the flexural behaviour of rectangular leaf springs with constant thickness. A closed form solution is obtained, showing that flexural stiffness varies continuously from that obtained by considering a beam model to the value given by the linear plate theory. This behaviour depends on section geometry, Poisson's ratio, and main curvature. A new characterizing parameter, whose relation with flexural stiffness allows a typical non-linear behaviour to be emphasized, is introduced in this work. In particular, for a given geometry and material, the flexural stiffness increases with the deflection and consequently with the load.

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