Calculation of Internal Stresses by the Lattice Cell Method

3 Calculation of internal stresses by the lattice cell method 

Due to complexity and limited capacity of the analjdical methods, recourse is more frequently had to munerical modeling methods, above all the finite elements method (FEM), to determine the 

Discretization of the elastic medium is achieved by dividing it into separate elements along the coordinate lines of the selected coordinate system. Each discrete element of the initial medium based on an electromechanical equivalent is replaced by a cell of an electrical network involving electric components with concentrated parameters. The latter are determined by similarity between Hooke s law written for separate elastic elements of the initial medium and Ohm s law written for the lattice cells. 

The lattice cells integrate into a single system, which models the initial medium. The integration is performed by means of the Kron conversion [181]. According to this, the variety of electrical systems that can be obtained as a resvdt of various combinations of a set of the electrical elements is considered a consequence of the transformation of the coordinated system. This means that a concrete method of connecting the electrical components determines the concrete system of generalized coordinates that are the electrical variables. 

Kron showed that processes that occiir in similar electric circuits are described by tensor equations. The network parameters and electrical variables are the physical objects that are the components of these equations. 

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