Network model of an elastic body with sources of boundary loads. Report 3

Abstract

1. It is shown that the equations of the network model of an elastic body can be derived by two means: by the method of the tensor analysis of Kron's electrical circuits, and by the method of the theory of diagrams on the basis of base transformations of the variables defining the network. 2. Kirchhoff's algebraic equations (vertex and cycle rules for diagrams) correspond to differential equations of equilibrium and strain compatibility under continum conditions. 3. Equations of equilibrium and strain compatibility are not used in explicit form in determining the stress-strain state. They participate in the formation of the transform matrix [A] and in developing the configuration of the elementary cell. Data on equilibrium and strain compatibility are introduced into the solution using matrix [A]. 4. A method is presented for constructing matrix [A] for a network with external sources modeling the boundary conditions.