Uniqueness of the solution of boundary value problems of static equations of elasticity theory with an asymmetric matrix of elastic modules

N. I. Ostrosablin

Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 107-115.

Résumé

The uniqueness of the solution of boundary value problems of static equations of elasticity theory for Cauchy elastic materials with an asymmetric matrix of elastic modules and with a symmetric matrix, but not necessarily positive definite, is proved. Using eigenstates (bases), the linear relationship of stresses and deformations is written in an invariant form. There are different ways of writing defining relations, including using symmetric matrices. The specific strain energy for all variants has the canonical form of a positive definite quadratic form.

Détail

Keywords: Cauchy elasticity, proper modules, proper basis, boundary value problems, uniqueness of the solution. .

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