Approximation Of Complex Potentials As A
Uniform Approach For Solving Classical And
Non-classical Boundary Value Problems Of
Plane Elasticity
Author(s)
A. N. Galybin
Abstract
This article aims to develop a uniform method for solving plane elastic boundary
value problems, PEBVPs. Stress or displacement vectors are assumed to be
given on the boundary in the classical formulation of PEBVP, while non–
classical formulations include boundary conditions in terms of orientations of
stresses, forces or displacements. It is shown that the approximation of the
complex potentials by the linear combinations of holomorphic functions can be
used to obtain solutions in these cases and that the other well known numerical
methods can be represented as particular cases of this approach. Two examples
are presented.
Keywords: plane elasticity, boundary value problems, complex potentials, stress
trajectories.
1 Introduction
General solution of plane elastic boundary value problems, PEBVP is given in
terms of two holomorphic functions (complex potentials, see Muskhelishvili [1])
that are to be determined from boundary conditions posed in displacements and
stresses that are found via the Kolosov-Muskhelishvili formulae. This presents a
uniform method for solving PEBVPs. It covers both classical and non-classical
formulations. Stress (or displacement) vector is given on the boundary of a
domain in classical formulations of PEBVP, while non–classical formulations
include boundary conditions in terms of orientations of stresses, forces or
Keywords
plane elasticity, boundary value problems, complex potentials, stress
trajectories
Related Book
Other papers in this volume
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