Ośrodek włóknisty jako model ciągły siatek ramowych

The fffirous medium as a continuous representation of frame lattices

The plane case is considered. It is assumed that a homogeneous lattice is composed of two fa­milies of curves. The particular cases under consideration are those of orthogonal and rectangu­lar lattice. The problem is considered for incompressible lattices which undergo rotation in addi­tion to translation.
Owing to the usual assumption of incompressibility of bars, the differential equations are disjoin­ed for the coordinates of the vectors and the rotation function of which the vector is normal to the plane of the network. The solution is reduced to that of the Helmholtz problem with appro­priate boundary conditions.
The solutions under consideration are those in which the rotation is expressed as a product of functions of each of the two variables. For this, it is assumed that the network has undergone, in one direction, a translation (subsidence, for instance) expressed by a Fourier series.

The solution of a rectangular network is considered in detail in the case in which the rotation is a function of a single variable.