The method of boundary states with perturbations as applied to the analysis of geometrically non-linear elastostatic bodies

Abstract

This study makes a case for the application of the numeric and analytic method of boundary states with perturbations (MBSP) to analytic problems focused on the stress-strain states (SSS) of geometrically non-linear isotropic elastic bodies. The defining relations are represented through a weakly non-linear operator equation that contains (on an additive basis) a non-linear operator decomposable into a linear combination of a sequence of linear operators. A solution is proposed for a simple case of a linearly heterogeneous uniaxial loading problem for a long half-pipe with butt ends subjected to loads. Even in this load scenario, geometrical non-linearity affects the way the body alters its shape and causes buckling. This study analyzes the SSS involved, draws conclusions, and addresses application prospects.