Open AccessThe method of boundary states with perturbations as applied to the analysis of geometrically non-linear elastostatic bodies
Author(s) -
Виктор Борисович Пеньков,
Lyubov Levina,
Е. А. Новиков,
Serguei Nazarov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1902/1/012020
Subject(s) - isotropy , linear map , linear elasticity , operator (biology) , boundary (topology) , mathematics , mathematical analysis , boundary value problem , linear system , linearity , structural engineering , physics , finite element method , engineering , pure mathematics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
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.