Integral Equations For Elastic Problems Posed
In Principal Directions: Application For
Adjacent Domains
Author(s)
A. N. Galybin & Sh. A. Mukhamediev
Abstract
This article addresses a new type of boundary condition in plane elastic boundary
value problems. Principal directions are given on a contour separating interior
and exterior domains; the stress vector is continuous across the contour.
Solvability of this problem is investigated and the number of linearly
independent solutions is determined. Some special cases in which the problem is
underspecified have been reported.
Keywords: plane elasticity, boundary value problems, principal directions,
complex potentials.
1 Introduction
Classical boundary value problems, BVP, of the plane elasticity require one of
the following surface conditions to be known on the entire boundary of a domain
(see Muskhelishvili [1]): (i) stress vector; (ii) displacement vector; or (iii) certain
combinations of stress and displacement components (mixed problems). In these
cases the BVP is well posed and possesses a unique solution.
Galybin and Mukhamediev [2] and Galybin [3] considered different types of
BVPs in which magnitudes of stresses, displacements or forces are not specified
on the boundary. It has been shown that the BVPs of this type may have a finite
number of solutions or be unsolvable. Solvability depends on the, so-called,
index of singular integral equations (see, e.g., Gakhov [4]). It can be determined
in every particular case from the analysis of principal directions (of the stress
tensor), orientation of displacement or forces on the entire boundary of a
considered domain.
Keywords
plane elasticity, boundary value problems, principal directions,
complex potentials.
Related Book
Other papers in this volume
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