O Liniowych Zagadnieniach Dyskretnej Teorii Sprężystości. I.

The paper presents the general system of equations and boundary conditions of the discrete theory of elasticity describing the behaviour of interacting dynamic systems consisting of rigid bodies subject to small rotations and displacements from a definite reference configuration. Such systems may serve as dynamic models of rod structures with rigid nodes (joints). Consideration of these systems within the framework of the 'discrete theory of elasticity yields the necessary algorithms for the calculation of various particular cases and allows for a rather general formulation of the problems of optimum design of structures.
In Secs. 1-3 given is the general system of equations and boundary conditions of the discrete theory of elasticity as also the general, differential and difference, equations for a system of rigid bodies. In Secs. 4-7 considered are linear elastic systems of prismatic rods with the masses concentrat­ed at the nodes, the general form of the equations of motion and the constitutive equations being given. The difference and differentia} equations for the plane problem are given, the cases of a disc (plane state of stress) and of a plate being analyzed separately.