Advances and Applications in Discrete Mathematics
Volume 19, Issue 3, Pages 183 - 193
(July 2018) http://dx.doi.org/10.17654/AADMJul2018_183_193 |
|
DISCRETE MODEL OF STATIC LOADS DISTRIBUTION MANAGEMENT ON LATTICE STRUCTURES
O. V. Kuzmin, A. P. Khomenko and A. I. Artyunin
|
Abstract: The practical implementation of active management of static loads distribution on lattice structures requires preliminary structural and technical solutions as to how the device is to be attached. The problems of constructing mathematical models for mechanical systems, in which joints can be formed, are also relevant. In both cases, these problems can be described with the help of graphs and, in particular, integer lattices.
This work is related to the development of models in order to describe and evaluate the solution of the management problems. It considers a number of issues related to the mathematical modeling and the analysis of the internal dependencies of equilibrium processes on lattice structures. The problem is formulated in terms of combinatorics on the lattices, which allows applying combinatorial methods of modeling.
The use of the theory of combinatorial numbers of the mapping class, and the properties of the elements of the generalized Pascal triangle, as well as generalized binomial coefficients, made it possible to offer a new way to describe, construct and evaluate a discrete model of the static loads distribution management on the truss structure with link joints.
One should construct combinatorial model for the calculation of static loads on a truss structure of the triangular form whose physical implementation is not associated with the need of the support for the active element at both ends. The truss structure topology, necessary for the calculation, is taken into consideration by an algebraic structure of the generalized binomial coefficient regarded in the context of a canonical representation of the combinatorial function class.
In the paper, a recurrence relation that allows taking into account both the physical properties of the material of the structural parts and the geometry of the structure itself is obtained. It is also observed that there is a connection between the generalized binomial coefficients and mechanical, geometric and combinatorial properties of the structure. |
Keywords and phrases: management, mathematical software, graph, integer lattice, decision making, combinatorial method. |
|
Number of Downloads: 308 | Number of Views: 4650 |
|