Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


Graph approach for finite-element based model of an elastic body under conditions of axisymmetric deformation

 A numerical method for analysis of the stress – strain state of elastic media based on a discrete model in form of directed graph is suggested. To analyze a deformable body using the graph approach, we partitione a solid body on elements and replace each element by its model in the form of an elementary cell. The matrices, presenting several structure elements of the graph, and the equations, describing the elementary cells, contribute to deriving the constitutive equations of the intact body. Numerical examples are presented. 

On Rationally Complete Algebraic Systems of Finite Strain Tensors of Complex Continua

The paper is devoted to the mathematical description of complex continua and the systematic derivation of strain tensors by the notion of isometric immersion of complex continuum in a plane space of higher dimension. Problem of establishing of complete systems of irreducible objective strain and extra-strain tensors for complex continuum immersed in an external plane space is considered. The solution to the problem is given by methods of the field theory and the theory of algebraic invariants.