Structural Analysis in Continuum Media Using Cellular Automata

The finite element method (FEM) is probably the most popular numerical technique to perform structural analysis. However, one of its major disadvantages is the high computational cost required to solve problems of practical size with sufficient accuracy. This problem has a significant impact on structural optimization techniques that make use of the FEM [

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]. Recent efforts have been made to develop alternative computational algorithms appropriate to massive parallel processing. Some of the most efficient approaches make use of the cellular automaton (CA) paradigm. CA models are an idealization of a physical system in which space and time are discrete. They are composed of a regular lattice of identical cells that are defined by their state. The state of each cell is determined through interaction with the state of its immediate neighbors by applying a local evolutionary rule. Locally, the behavior of the cells is rather simple, but on a larger scale a new complex (and sometimes unexpected) collective behavior emerges [5]. Some applications have incorporated CA principles in structural optimization in continuum media [

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], structural analysis and design combined with genetic algorithms [

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] and simultaneous analysis and design in discrete structures [

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]. The goal of this investigation is to develop a new CA computational application suitable for structural analysis in a continuum. The cells in this model are regularly distributed nodes connected to each other by an elastic material. The physical properties of the continuum are defined by its Young’s modulus and Poisson’s ratio. The nodal displacement and internal force define the state of the cell. Local evolutionary rules, derived from the principle of minimum total potential energy, find the optimal kinematic configuration of every cell in the structure. This algorithm is implemented in twodimensional problems and their results are compared with the ones obtained using the FEM.