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

stress

Nonlinear deformation of axisymmetrically loaded rotation shell based on FEM with different variants of definitional equations

A curvilinear finite element of the median line of an axisymmetrically loaded shell of revolution with a stiffness matrix of $8{\times} 8$ size is used when choosing nodal unknowns in the form of displacements and their first derivatives is used. The constitutive equations at the loading step are implemented in two versions. In the first version, the relations of the deformation theory of plasticity are used, which consist of expressions for the elastic and plastic parts.

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.