Solution of axisymmetric torsion problems by point matching

1971 ◽  
Vol 6 (2) ◽  
pp. 124-133 ◽  
Author(s):  
G J Matthews ◽  
C J Hooke
Keyword(s):  
Boundary Conditions ◽  
Numerical Technique ◽  
Point Matching ◽  
Analytical Results ◽  
Elasticity Equations ◽  
Matching Technique ◽  
Basic Solutions ◽  
Axisymmetric Bodies

A general numerical technique is presented for the solution of the problem of torsion of axisymmetric bodies. The method superimposes a number of basic solutions of the elasticity equations using the point-matching technique so as to satisfy approximately the prescribed boundary conditions of a body. Results obtained by this technique are compared with those obtained by alternative experimental and theoretical techniques for various body geometries to assess the accuracy of the method. The technique is then applied to the problem of the torsion of shouldered shafts since large discrepancies exist between the experimental and analytical results available for this type of structure.

Calculation of stress-concentration factors for grooved shafts in bending using the point-matching technique

1973 ◽  
Vol 8 (2) ◽  
pp. 113-118 ◽  
Author(s):  
G J Matthews ◽  
C J Hooke
Keyword(s):  
Stress Concentration ◽  
Numerical Technique ◽  
Pure Bending ◽  
Point Matching ◽  
Matching Technique ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Stress Concentration Effect ◽  
Axisymmetric Bodies ◽  
Good Agreement

A general numerical technique is presented for the solution of the problem of elastic bending of axisymmetric bodies. Results obtained by this method are compared with existing results for grooved and shouldered shafts in pure bending and good agreement is obtained in each case. Additional results are presented for the stress-concentration effect of flat-bottomed circumferential grooves in cylindrical shafts for which no experimental or analytical results are available.

Triangular Plates Analyzed by Point Matching

1962 ◽  
Vol 29 (4) ◽  
pp. 755-756 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Numerical Results ◽  
Point Matching ◽  
Simply Supported ◽  
Special Adaptation ◽  
Matching Technique

This brief note analyzes uniformly loaded triangular plates with either clamped or simply supported edges using a special adaptation of the point-matching technique, the functions satisfying the differential equation, also being chosen to satisfy exactly the boundary conditions on one edge. Numerical results are tabulated for three geometries.

Point‐matching technique for scattering of Stokesian flows around axisymmetric bodies

1994 ◽  
Vol 96 (5) ◽  
pp. 3242-3242
Author(s):  
Scott A. Wymer ◽  
Renata S. Engel ◽  
Akhlesh Lakhtakia
Keyword(s):  
Point Matching ◽  
Matching Technique ◽  
Axisymmetric Bodies

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

1961 ◽  
Vol 28 (2) ◽  
pp. 288-291 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Flexural Vibration ◽  
Frequency Equation ◽  
Numerical Results ◽  
Special Technique ◽  
Point Matching ◽  
Buckling Loads ◽  
Simply Supported ◽  
Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

scholarly journals Boundary Behavior and Confinement of Screw Dislocations

MRS Advances ◽  
2017 ◽  
Vol 2 (48) ◽  
pp. 2633-2638
Author(s):  
Marco Morandotti
Keyword(s):  
Boundary Conditions ◽  
Boundary Behavior ◽  
Screw Dislocations ◽  
Numerical Evidence ◽  
Analytical Results

ABSTRACTIn this note we discuss two aspects of screw dislocations dynamics: their behavior near the boundary and a way to confine them inside the material. In the former case, we obtain analytical results on the estimates of collision times (one dislocation with the boundary and two dislocations with opposite Burgers vectors with each other); numerical evidence is also provided. In the latter, we obtain analytical results stating that, under imposing a certain type of boundary conditions, it is energetically favorable for dislocations to remain confined inside the domain.

Flexural Vibration Response of Beams With General Boundary Conditions: A Transfer Matrix Approach

1991 ◽  
Author(s):  
T. Önsay
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Response ◽  
General Boundary ◽  
Phase Variable ◽  
General Boundary Conditions ◽  
Transfer Matrices ◽  
Analytical Results

Abstract The wave-mode representation is utilized to obtain a more efficient form to the conventional transfer matrix method for bending vibrations of beams. The proposed improvement is based on a phase-variable canonical state representation of the equation governing the time-harmonic flexural vibrations of a beam. Transfer matrices are obtained for external forces, step-change of beam properties, intermediate supports and for boundaries. The transfer matrices are utilized to obtain the vibration response of a point-excited single-span beam with general boundary conditions. The general characteristic equation and the transfer mobility of a single-span beam are determined. The application of the analytical results are demonstrated on physical structures with different boundary conditions. A hybrid model is developed to incorporate measured impedance of nonideal boundaries into the transfer matrix method. The analytical results are found to be in excellent agreement with experimental measurements.

Accurate Calculation of Stress Distributions in Multiholed Plates

1965 ◽  
Vol 87 (3) ◽  
pp. 331-335 ◽  
Author(s):  
L. E. Hulbert ◽  
F. W. Niedenfuhr
Keyword(s):  
Computer Program ◽  
Plane Stress ◽  
Symmetric Groups ◽  
Thin Plates ◽  
Stress Distributions ◽  
Accurate Calculation ◽  
Point Matching ◽  
Shallow Shells ◽  
Matching Technique ◽  
Stress Functions

This paper discusses the application of the point-matching technique in obtaining the solution of many problems involving multiholed thin plates undergoing generalized plane stress. The stress functions appropriate to plates with symmetric groups of holes are described. A large number of problems solved by a computer program are described and compared with published results. Problems are solved also for which there are no known published results. Two interesting new problems are discussed in detail. The results show the power and flexibility of the technique. The extension of the methods to permit the solution of problems in the deflection of thin, multiholed plates and shallow shells is discussed.

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