WIT Press


Approximation Of Complex Potentials As A Uniform Approach For Solving Classical And Non-classical Boundary Value Problems Of Plane Elasticity

Price

Free (open access)

Paper DOI

10.2495/BE050241

Volume

39

Pages

10

Published

2005

Size

650 kb

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