Mixed boundary–value problems of two–dimensional anisotropic elasticity with perturbed boundaries

1998 ◽  
Vol 454 (1973) ◽  
pp. 1269-1282 ◽  
Author(s):  
Chyanbin Hwu ◽  
C. W. Fan
Keyword(s):  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Anisotropic Elasticity ◽  
Two Dimensional ◽  
Mixed Boundary Value Problems

Two dimensional mixed boundary-value problems in a wedge-shaped region

1968 ◽  
Vol 64 (2) ◽  
pp. 503-505 ◽  
Author(s):  
W. E. Williams
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Mellin Transforms

In a recent paper Srivastav (2) considered the solution of certain two-dimensional mixed boundary-value problems in a wedge-shaped region. The problems were formulated as dual integral equations involving Mellin transforms and were reduced to the solution of a Fredholm integral equation of the second kind. In this paper it will be shown that a closed form solution to the problems treated in (2) may be obtained by elementary means.

scholarly journals Mixed Boundary-Value Problems in Potential Theory

1979 ◽  
Vol 22 (2) ◽  
pp. 91-98 ◽  
Author(s):  
A. H. England
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Analytical Techniques ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Mixed Boundary Value Problems

The problems associated with finding solutions of Laplace's equation subject to mixed boundary conditions have attracted much attention and, as a consequence, a variety of analytical techniques have been developed for the solution of such problems. Sneddon (1) has given a comprehensive account of these techniques. The object of this note is to draw attention to some simple orthogonal polynomial solutions to the most basic mixed boundary-value problems in two and threedimensional potential theory. These solutions have the advantage that most quantities of physical interest are easily evaluated in terms of known functions. Two-dimensional problems are considered in §2 and axially-symmetric three-dimensional problems in §3.

XX.—Finite Hilbert Transform Technique for Triple Integral Equations with Trigonometric Kernels

1970 ◽  
Vol 68 (4) ◽  
pp. 309-321 ◽  
Author(s):  
K. N. Srivastava ◽  
M. Lowengrub
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Hilbert Transform ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Two Dimensional ◽  
Mixed Boundary Value Problems ◽  
Finite Hilbert Transform ◽  
Triple Integral Equations

In this paper, we shall be concerned with an investigation of the solution of triple integral equations involving sine and cosine kernels. These type of equations arise in the study of certain two-dimensional mixed boundary value problems in infinite planes and infinitely long strips.

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