Simulation Model for the Rod System Graphs Dynamics

The engineering structures composed from the rods (frames, trusses, etc.) are widely used in the various industrial applications. There are many publications presenting a theoretical modeling of the rod-based structural systems especially for the designs constructed from the thin-walled components. Usually, the single bar element of such system is taken as the basis for the general model development. The growth of the use of fast computer techniques has resulted in the extensive development of numerical methods where the main role belongs to the finite-element analysis. This paper presents a new approach to the numerical simulation and dynamic analysis of the rod systems based on the use of graphs in the numerical solutions for this class of problems. The main idea is that the solution of the global 3D problem for the whole system can be split into the number of simple one-dimensional problems for the individual elements (bars). Then, at each step of the numerical integration, these one-dimensional problems are linked with the common solution procedure for the original system using additional systems of equations written for the nodes (bar joints). In this way, the global coupling for all the original problem variables is guaranteed. Implementation of this method is illustrated in this paper for the flat two dimensional rod systems and incorporates finite-difference methods. The rod systems under consideration could be composed from an arbitrary number of the rectilinear bars/rods with different geometrical and physical characteristics. Also, the random topology of the bar joints and reactions in the system nodes can be realized. The advantage of the proposed approach is that not only dynamical behavior of the whole system, but also the transition nonstationary processes in the system components could be simulated for various combinations of the load applied and boundary conditions imposed.