Wyznaczanie Układu Prętów w Czterowęzłowym Polu Kratownicy z Warunku Minimum Potencjału

Concerned in the present considerations are lattice structures of bars connecting four nodes prescribed in a plane, the bars have hinged joints at the nodes. Isostatic, geometrically invariable structures are considered, having the same strain in all the bars. On connecting the four nodes by means of any five bars, six different bar systems are obtained. In order to obtain simple criteria as to which of the six structures is that of minimum elastic potential, transformations by bar exchange are considered. As a result, the criterion for the minimum elastic potential is obtained in function of the absolute value of the ratio of the relative displacement of the nodes not connected by a bar to the strain in lattice bars of equal strength.
On the basis of the LÉVY equation, the value of relative displacement
of the nodes not connected by a bar is determined for every possible system of force signs in the lattice bars and for various locations of the nodes in the plane. Those structures which may be those of minimum elastic potential are found. The results obtained are applied to the analysis of multi-field lattices with parallel chords, roof lattices, and lattices with upper nodes forming an arc.