To the problem of decomposition of the initial boundary value problems in mechanics

Abstract

We consider the questions on the decomposition of the initial boundary value problems of elasticity theory and thin bodies for some anisotropic media. In particular, the initial boundary problems of the micropolar (and classical) theory of elasticity are presented, i.e. to introduce tensor-block matrix operators (tensor-operators). In the case of an isotropic micropolar elastic medium (isotropic and transversally isotropic classical media) tensor-block matrix operators (tensor-operators) of cofactors corresponding to the tensor-block matrix operators (tensor-operators) of of the initial boundary value problems are obtained, which are splitting the initial boundary value problems. From three-dimensional decomposed initial boundary value problems the corresponding decomposed initial boundary value problems for the theory of thin bodies are obtained.