This paper presents a shape and topology optimization scheme for structures
by using the concept of a cellular automaton (CA). A design domain is divi
ded into small square cells and then the thicknesses of the individual cell
s are taken as the design variables. Considering the cells as the finite el
ements, the stress analysis is performed by the finite element method. The
design variables are modified by applying a local rule to the stress states
of the cell and its neighbouring cells. The present scheme is applied to a
two-dimensional elastic problem in order to confirm its validity.