Vareniuk N.A., Galba E.F., Sergienko I.V.
Variational statements and discretization of the boundary-value problem of the elasticity theory when tension on the boundary of the domain is known

The equations of elastic equilibrium of bodies in displacements with the stresses specified at the surface of the body are considered. Such a problem does not have a unique solution in the whole space of vector functions where it exists. Two variational problems for the considered static problem of the theory of elasticity with a unique solution in the whole space are proposed and investigated. The mathematical apparatus of the study is one of the variants of the Korn inequality that is proved in the paper. Discretization of these variational problems by the finite-element method and convergence of discrete solutions is considered. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: discrete problems, elasticity problem, existence of a unique solution in function spaces, methods for solving discrete problems, variational statements, Elasticity, Variational techniques, Vector spaces, Discretizations, Elastic equilibrium, Mathematical apparatus, Static problems, Theory of elasticity, Variational problems, Vector functions, Boundary value problems

Cite:
Vareniuk N.A., Galba E.F., Sergienko I.V. (2020). Variational statements and discretization of the boundary-value problem of the elasticity theory when tension on the boundary of the domain is known. Cybernetics and Systems Analysis, 56 (6), 46–60. doi: https://doi.org/10.1007/s10559-020-00310-0 http://jnas.nbuv.gov.ua/article/UJRN-0001169462 [In Ukrainian].