Determination of the stress concentration in the corner point of the wedge-shaped region reinforced by a more rigid thin coating

2020 ◽  
Vol 26 (1) ◽  
pp. 80-89
Author(s):  
AN Soloviev ◽  
BV Sobol ◽  
EV Rashidova ◽  
AI Novikova
Keyword(s):  
Boundary Conditions ◽  
Corner Point ◽  
Theory Of Elasticity ◽  
The Other ◽  
Thin Coating ◽  
Various Boundary Conditions ◽  
Singular Behaviour ◽  
Isotropic Theory ◽  
Made In

We analysed the problem of determining the exponents in the asymptotic solution of the isotropic theory of elasticity problem at the top of the wedge-shaped region where its sides (or one of them) are supported by a thin coating and lean without friction on the rigid bases. On the other side of the wedge-shaped region, it is assumed that there are various boundary conditions, including when there is a thin coating. Mathematically, the problem reduces to the problem of determining the roots of transcendental characteristic equations arising from the condition for the existence of a nontrivial solution of a system of the linear homogeneous equations. The characteristics of the stress tensor components have been determined for the various combinations of boundary conditions and physical and geometric parameters. The qualitative conclusions are made. In particular, we have established the combinations of the values of these parameters at which the singular behaviour of stresses arises.

scholarly journals Thermal impedance estimations by semi-derivatives and semi-integrals: 1-D semi-infinite cases

2013 ◽  
Vol 17 (2) ◽  
pp. 581-589 ◽  
Author(s):  
Jordan Hristov ◽  
Ganaoui El
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Boundary Conditions ◽  
Half Time ◽  
Thermal Impedance ◽  
Entire Domain ◽  
Various Boundary Conditions ◽  
Transient Thermal

Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances under various boundary conditions imposed at the interface (x=0). The approach is purely analytic and very effective because it uses only simple semi-derivatives (half-time) and semi-integrals and avoids development of entire domain solutions. 0x=

ACCURATE DEPTH DETERMINATION OF THE VELOCITY SURVEY WELL PHONE

Geophysics ◽  
1961 ◽  
Vol 26 (1) ◽  
pp. 100-100
Author(s):  
R. P. Nolting
Keyword(s):  
The Other ◽  
Log Data ◽  
Survey Report ◽  
Depth Determination ◽  
Depth Curve ◽  
Actual Depth ◽  
Check Level ◽  
Made In

Many velocity surveys have been shot in which the actual depth of the well phone was in question at one or more of the levels shot in the borehole. The computed time to the questioned level would not fit the other data obtained from the velocity survey, i.e., the data from the questioned level would not fit the time‐depth curve within reason or, more recently, it could not properly be fitted to the corrected continuous velocity log data. If the “first break” of the questioned level could not be repicked to conform to the other data, a notation was made in the velocity survey report that the depth of the well phone was probably in error. Although this assumption was correct in many cases, there are various other reasons why data from one check level should not fit the rest of the data.

Theoretical Determination of Natural Modes of Deck Vibrations

1966 ◽  
Vol 3 (01) ◽  
pp. 66-79
Author(s):  
Robert D. Short
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Maximum Error ◽  
Nodal Line ◽  
The Other ◽  
Mode Shapes ◽  
Theoretical Determination ◽  
Natural Modes

Six methods for calculating the natural frequency and mode shapes of cross-stiffened plating were examined particularly for their application to plating with a large number of small closely spaced stiffeners in one direction supported by a few deep girders in the other. The best method was able to predict at least 1 6 frequencies (all that were measured) of a model with a maximum error of less than 15 percent when proper boundary conditions were used. The maximum error in nodal-line locations for the best method was 5.2 percent of the span

Analysis of Plate Examples by Difference Methods and the Superposition Principle

1936 ◽  
Vol 3 (3) ◽  
pp. A81-A90
Author(s):  
D. L. Holl
Keyword(s):  
Boundary Conditions ◽  
Critical Stress ◽  
Plate Theory ◽  
Superposition Principle ◽  
Equivalent Stress ◽  
Lower Surface ◽  
The Other ◽  
Principle Of Superposition ◽  
Various Boundary Conditions ◽  
Actual Plate

Abstract In this paper the author applies the membrane analogs of H. Marcus to some elementary cases of thin homogeneous isotropic square plates having central-point loads and various boundary conditions. The analogy is made possible by two theorems: (a) The deflection of a membrane loaded with loads proportional to those on a given plate may be considered as the sum of the principal moments of the actual plate. (b) A second membrane may be loaded with elastic weights proportional to these moment sums and, subject to appropriate boundary conditions, the deflections of the latter membrane will be proportional to the deflections of the actual plate under the given loading system. The principle of superposition of deflection surfaces or equivalent stress systems is utilized in this paper both by difference and differential methods. The problems treated are (1) a square plate with pinned or simply supported edges, (2) two opposite edges pinned and the other two free, (3) two opposite edges pinned and the other two clamped, (4) all four edges clamped, (5) all four edges free with only corner post supports. The correct critical stress at the center of the lower surface of the plate was obtained from special thick-plate theory for a particular thickness-to-span ratio. The effect of this critical stress on the whole plate action is depicted for various boundary conditions.

scholarly journals 2. On the Application of Angström's Method to the Conductivity of Wood

1875 ◽  
Vol 8 ◽  
pp. 481-481
Author(s):  
C. G. Knott ◽  
A. Macfarlane
Keyword(s):  
Natural Philosophy ◽  
The Other ◽  
Thermo Electric ◽  
Fine Wire ◽  
Series Of Experiments ◽  
The University ◽  
Made In

This was an account of a series of experiments made in the Natural Philosophy Laboratory of the University, to test the applicability of Angström's method of periodic variations of temperature to the determination of low conductivity. The wood was cut into discs of a standard thickness, and these were very tightly secured together, after the interposition of copper-iron thermo-electric junctions (of very fine wire). One series of discs was cut parallel, the other perpendicular, to the fibre. The results were obtained very easily, and accorded satisfactorily with those obtained by more laborious methods.

scholarly journals ZEROS OF THE POTTS MODEL PARTITION FUNCTION IN THE LARGE-q LIMIT

2007 ◽  
Vol 21 (07) ◽  
pp. 979-994 ◽  
Author(s):  
SHU-CHIUAN CHANG ◽  
ROBERT SHROCK
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Coordination Number ◽  
Potts Model ◽  
The Other ◽  
Square Lattice ◽  
Various Boundary Conditions ◽  
Temperature Variable

We calculate zeros of the q-state Potts model partition function Z(GΛ,q,v) for large q, where v is the temperature variable and GΛ is a section of a lattice Λ with coordination number κΛ and various boundary conditions. Lattice types studied include square, triangular, honeycomb, and kagomé. We show that for large q these zeros take on approximately circular patterns in the complex xΛ plane, where xΛ=v/q2/κΛ. This generalizes a known result for the square lattice to the other lattices considered.

Strongest Columns and Isoperimetric Inequalities for Eigenvalues

1962 ◽  
Vol 29 (1) ◽  
pp. 159-164 ◽  
Author(s):  
I. Tadjbakhsh ◽  
J. B. Keller
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Cross Sections ◽  
Isoperimetric Inequalities ◽  
Second Order ◽  
Buckling Load ◽  
The Other ◽  
Critical Buckling Load ◽  
Various Boundary Conditions

We consider the problem of determining what shape column has the largest critical buckling load of all columns of given length and volume. This problem was previously solved for a column hinged (pinned) at both ends. We solve it for columns clamped at one end and clamped, hinged, or free at the other end, assuming that all cross sections of the column are similar and similarly oriented. We also prove that the column previously obtained in the hinged-hinged case is actually strongest and not merely stationary. Graphs of the areas of the strongest columns as functions of distance along the columns are given for the various cases. The results are also expressed as isoperimetric inequalities for eigenvalues of second-order ordinary differential equations with various boundary conditions. Certain additional inequalities of this type are also obtained.

Integral properties of solutions to some boundary initial-value problems in linear anisotropic elastodynamics

1995 ◽  
Vol 449 (1937) ◽  
pp. 591-596 ◽  
Keyword(s):  
Contact Problem ◽  
Boundary Conditions ◽  
Half Space ◽  
Initial Value Problems ◽  
Contact Region ◽  
Dynamical Theory ◽  
Theory Of Elasticity ◽  
Initial Contact ◽  
Initial Value ◽  
Various Boundary Conditions

We study some integral properties of weak solutions to some boundary initial-value problems in the linearized dynamical theory of elasticity. These problems arise during the indentation of an anisotropic half-space by a convex punch having an arbitrary indenting velocity and shape. In contrast to previous studies of the problem, we consider various boundary conditions, e. g., adhesive or frictional, in the case when this non-frictionless boundary initial-contact problem has two orthogonal planes of symmetry, which are both orthogonal to the boundary of half-space. We show that if the non-frictionless boundary initial-contact problem has such a symmetry, then the problem for integral characteristics of the solutions is equivalent to a problem of plane-wave propagation in the same medium. A proof is given that the instantaneous value of the force required to indent the punch during the first supersonic stage of contact is directly proportional to the product of the velocity of indentation and the area of contact at that instant, and is independent of the boundary conditions in the contact region.

scholarly journals Ambarzumian-type Problems for Discrete Schrödinger Operators

2021 ◽  
Vol 15 (8) ◽  
Author(s):  
Burak Hatinoğlu ◽  
Jerik Eakins ◽  
William Frendreiss ◽  
Lucille Lamb ◽  
Sithija Manage ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Schrödinger Operator ◽  
Inverse Spectral Problem ◽  
Unique Determination ◽  
Schrodinger Operator ◽  
Real Constant ◽  
Discrete Schrödinger Operator ◽  
Various Boundary Conditions ◽  
Discrete Schrödinger Operators

AbstractWe discuss the problem of unique determination of the finite free discrete Schrödinger operator from its spectrum, also known as the Ambarzumian problem, with various boundary conditions, namely any real constant boundary condition at zero and Floquet boundary conditions of any angle. Then we prove the following Ambarzumian-type mixed inverse spectral problem: diagonal entries except the first and second ones and a set of two consecutive eigenvalues uniquely determine the finite free discrete Schrödinger operator.

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