Vol. 12, no.2, 2020


Characteristic form of equations of dynamics of media of complex structure

George G. Bulychev

MIREA-Russian Technological University, http://www.mirea.ru/
Moscow 119454, Russian Federation
E-mail: geo-bulychev@mail.ru

Received November 28, 2019, reviewed December 20, 2019, accepted December 27, 2019
Abstract. The article presents the construction of the characteristic form of the equations of dynamics of elastic media for which the stiffness matrix is asymmetric. For diagonalization of the asymmetric matrix, the procedure of unitary triangularization by Schur and additional transformations are used, which allow to consistently find all parameters of the stress-strain state of the medium. Additional assumptions, such as cosser's pseudocontinuum, are not required. The division of deformations into symmetric and asymmetric parts is not carried out and they are assumed to be small. Then the following information is given about the matrix form of differential invariants, their properties and their usage in problems of dynamics of different media are discussed. An example of their application to the problem of statics is given.

Keywords:dynamic processes, spatial characteristics method, numerical modeling, dynamics and destruction of the environments of complex structure

UDC 539.3

RENSIT, 2020, 12(2):227-234. DOI: 10.17725/rensit.2020.12.227.

Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/332/12(2)227-234e.pdf