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