Określanie Granicy Stosowalności Modelu Ciągłego przy Obliczaniu Dyskretnej, Biegunowej Tarczy Siatkowej

The paper presents the problem of applicability of a continuous model to the calculation of a discrete, polar lattice disc loaded at the periphery by forces normal to the radial rods. Using the general theory of mechanics of discrete lattice media, the equations are derived concerning the geometry, the equilibrium conditions and the physical relations of such a lattice. The transition from discrete to continuous media is achieved by increasing the material density in the lattice; the total amount of the material remains unchanged, the mesh size in the radial and circumferential direction in each consecutive stage of approximation being divided by two. The analysis yields the variation of stresses in all rods of the lattice and the displacements of its nodes as functions of the lattice density.
The results obtained enable us to determine the limit material density in the lattice above which the structure can be considered as a continuous medium; moreover, it is possible to determine the error following from the application of the continuous model analysis do definite discrete lattices.