Ruszt o sześciokątnej siatce prętów
A grill of hexagonal lattice rods
The subject of this paper is an analysis of a flat grill consisting of direct elastic rods forming in a plan the lattice of equilateral hexagonals. The grill is loaded in joints with forces perpendicular to the plane of the construction and with vector moments lying in this plane. In the entire grill appear only two kinds of joints, every one of which can be obtained by removal of the other joint and turning it through about 180°. For solution of the problem was chosen a repeated element such that the equilibrium equation simultaneously describe the state in both kinds of joints. This was made possible by the consequent description of geometrical structure and by introducing the differential equations for Boole's operators with function exponents. The work results in solution of the equilibrium equations of a joint, subject to the simplification that the rigidity of the rods for twisting is equal to 0.
Also given are numerical examples.
References
S. Błaszkowiak, Z. Kączkowski, Metoda Crossa, Warszawa 1961.
W. Gutkowski, C.P. Ugarte, A generalized micro approach of two-dimensional structures, Department of Civil Engineering University of Delaware.
W. Gutkowski, Geometry of continuous media with a given discrete structure, Arch. Mech. Stos., 21, 6, 1969.
C. Jordan, Calculus of finite differences, Chelsea Pub. Com., New York 1950.
Z. Kączkowski, Płyty, obliczenia statystyczne, Warszawa 1968.
H. Levy, F. Lessman, Równania różnicowe skończone, Warszawa 1966.
I.D. Renton, The related behaviour of plane grids, space grids and plates, Space Structures Blackwell Scientific Publications, Oxford and Edinburgh 1967.
P. Klemm, Cz. Woźniak, Gęste heksagonalne siatki sprężyste, Mech. Teoret. Stos., 8, 3, 1970.