Abstract
Cellular automata simulation is one of the widely used calculation methodologies to form optimum shape of structural bodies. It can construct complex whole structure by applying locally and iteratively a simple calculation rule so-called, “state transition rule” or “local rule”. Therefore, it has been perceived as a promised approach of forming optimum shape that could not be predicted by resident design knowledge. In many researches, however, state transition rules are just used for controlling birth and death of structural elements and the validity of formed shapes as structural bodies was not considered in those state transition rules. Extra structural simulations, typically FEM analyses, are necessary for calculating stress, strain and deflection in the formed bodies in order to determine that the structures can satisfy design requirements. Those analyses are global process and not suitable to locality principle of cellular automata and limits possibility of shape forming of cellular automata. In this context we propose a new state transition rule that can express structural behaviors for two-dimensional linear elastic body. Also we show numerical results with two typical examples and clarify its accuracy and effectiveness.
