Abstract
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.
References
2. C. WOŹNIAK, Teoria ośrodków włóknistych (II), Arch. Mech. Stos., 6, 17 (1965).
