Complex Computing with Cellular Automata [chapter]

J. Signorini
1989 Springer Proceedings in Physics  
Cellular automata (CA) models are decentralized spatially extended systems consisting of large numbers of simple identical components with local connectivity. Such systems have the potential to perform complex computations with a high degree of efficiency and robustness, as well as to model the behavior of complex systems in nature. A novel numerical computing method based on CA is presented in this paper. In this method the integer analysis of structure is changed into a series of part
more » ... by using the idea of CA. Using the principle of minimum potential energy for the displacement convergence of all nodes, the nonequilibrium force of every cell is obtained. The overall finite element stiffness matrix and balance equation do not require. It may have a good future in the aspect of large structure because it hardly has any special request on the capability of computer. Simultaneity, It can be developed into a high parallel arithmetic to suit for the request of parallel computer in the future. This method is a good numerical method with great potential. The correctness and effectiveness of the proposed method are demonstrated by some numerical examples. automata in various fields has been widely used. James M. Skoda is the first to use cellular automata for social science [6] . But the first clearly defined in the CA framework is economics economist Peter S., is the first CA in sociology emphasizes the important role of the dynamic evolution [7, 8] . CA has also been applied in other areas such as urban development, simulation and prediction, thermal diffusion, the field of parallel computing [9] . Cellular Automata is a discrete space and time, physical parameters which take a limited set of values the ideal of physical systems. It is the edge of the multidisciplinary field of complex systems such as mathematics, physics, computer science, biology, systems science. It is an important research method. As Cellular Element Method is a kind of clear steps, the mechanical calculation of programming convenience, and it is easy to master, it will solve the whole structure into a local analysis, by force local delivery to achieve the ultimate balance between the overall balance which did not like the finite element need global stiffness matrix and solving the overall balance equation, the computer capacity requirements is very low, therefore the calculation in the large complex structure has good prospects. At the same time, borrowed the idea of cellular automata, can form a highly parallel algorithm, is a rich potential for development of new numerical methods. CA used in structural analysis, and the results of CA algorithm was compared with the FEM results; the CA confirmed the feasibility of application of structural analysis. Cellular Automata Cellular Automata contains cellular, cellular state space, neighbors and local rules. Cellular automaton model allows simple unit connected by the local rules under the action of the system state. Cellular automata as complex systems can evolve through local rule, making it possible to apply truss structure. The following were analyzed cellular automaton model elements and the similarity of space truss. Cell May be called a unit, or primitive, is the most basic cellular automaton part, Cellular distribution in the discrete one-dimensional, two-dimensional Euclidean space. Cellular space of the distribution grid is a collection of cellular space; it can be any dimension by the rules of Euclidean space. Space truss structure and the connected nodes can be abstracted as cellular pole.
doi:10.1007/978-3-642-75259-9_6 fatcat:cgihbwavbff77lulpbu7j4c64y