Extension of the Circle Theorems by Surface Source Distribution

1989 ◽  
Vol 111 (3) ◽  
pp. 243-247 ◽  
Author(s):  
O. Rand
Keyword(s):  
Circular Cylinder ◽  
Closed Form ◽  
Closed Form Solution ◽  
Strength Distribution ◽  
Form Solution ◽  
Source Distribution ◽  
Arbitrary Distribution ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Surface Source

The paper presents a closed-form analytical solution for the source strength distribution along the circumference of a two-dimensional circular cylinder that is required for producing an arbitrary distribution of normal velocity. Being suitable to be used with flows having arbitrary vorticity distribution, the present formulation can be considered as an alternative and extensive form of the circle theorems. Using the conformal transformation technique, the formulation also serves as a closed-form solution of Laplace’s equation in any two-dimensional flow domain that is reducible to the outer or inner region of a circular cylinder having arbitrary prescribed normal velocity over its boundary.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

A new approach for closed-form analytical solution of two-dimensional symmetric double contacts and the comparison with finite element method

2017 ◽  
Vol 232 (8) ◽  
pp. 1025-1035 ◽  
Author(s):  
Parisa Ghanati ◽  
Saeed Adibnazari ◽  
Mohammad Alrefai ◽  
Azadeh Sheidaei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Closed Form ◽  
Flat Surface ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Contact Zones ◽  
Element Method

In this paper, a new procedure is developed for the solution of a general two-dimensional uncoupled symmetric double contact problem with smooth contact zones in which the indenter geometry is described by a piecewise biquadratic function. This procedure gives an approximate closed-form solution for any smooth indenter profile. In order to evaluate the accuracy of this approach, it is applied to the symmetric indentation of a flat surface by two rigidly interconnected parabolic indenters and results are compared with the exact unclosed-form solution. Moreover, this procedure is applied to the symmetric indentation of a flat surface by two rigidly interconnected cylinders to compare the results with the finite element solution obtained by the finite element method software, ABAQUS. The results showed that in comparison with the finite element method, this procedure is a fast and highly accurate method with low complexity that makes feasible the possibility of determining approximate closed-form solution for a wide range of indenter geometries with a concavity between two symmetric contact zones; hence it can be useful in practical issues.

MAGNETIC ANOMALY DUE TO A VERTICAL RIGHT CIRCULAR CYLINDER WITH ARBITRARY POLARIZATION

Geophysics ◽  
1978 ◽  
Vol 43 (1) ◽  
pp. 173-178 ◽  
Author(s):  
Shri Krishna Singh ◽  
Federico J. Sabina
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Closed Form ◽  
Magnetic Anomaly ◽  
Closed Form Solution ◽  
Form Solution ◽  
Arbitrary Polarization ◽  
Shaped Body ◽  
Anomalous Magnetic Field

A closed form solution for the total anomalous magnetic field due to a vertical right circular cylinder with arbitrary polarization is derived under the assumption that the magnetization is uniform. As expected, the computed field is similar to the field due to a “similar” prism‐shaped body.

Numerical Stress Analysis of Epoxy Adhesively Bonded Dissimilar Joint

2013 ◽  
Vol 594-595 ◽  
pp. 930-934
Author(s):  
Nur Athirah ◽  
A.R. Abdullah ◽  
M. Afendi ◽  
M.S. Abdul Majid ◽  
Ruslizam Daud ◽  
...  
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Dissimilar Joint ◽  
Two Dimensional ◽  
Lap Joint ◽  
Modulus Ratio ◽  
Adhesively Bonded ◽  
Single Lap Joint

A two-dimensional adhesively bonded dissimilar single lap joint model was analyzed under tension. An explicit closed-form solution was formulated by using MATLAB tool for analysis of shear and peel stresses distribution along the bondline under effect of variation of overlap length, adherend thickness ratio and adherend Youngs modulus ratio. The solution was formulated based on analysis of Bo Zhao et al. [2]. The bending moment at the edge joint of the Bo Zhaos solution was replaced by the bending moment at the edge joint that have been proposed by X. Zhao et al. [5] to compare the accuracy of solutions. The least stress intensities in dissimilar joint could be achieved with a suitable ratio of thickness and Youngs modulus of adherends.

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