Application of cellular automata to size and topology optimization of truss structures

This paper presents a two-phase, hybrid, Cellular Automata–Linear Programming (CA–LP) method for both size and topology optimization of planar truss structures, in order to achieve the minimum weight of the structure under stress, nodal displacement, cross-sectional area and kinematic stability constraints. The optimization process is carried out in two phases. In the first phase, the optimal topology of the structure is obtained by replacing the topology optimization problem with a proper sizing problem. In the second phase, the topologically optimized truss obtained from the first phase is solved to determinate the optimal sizing of the structure. The resulting non-linear sizing problem is solved using a recently introduced CA–LP approach. This method uses the nodal displacements and internal forces of the truss structure as decision variables, instead of the cross sectional areas, and the resulting problem is solved iteratively, with two solution stages at each iteration. In the first stage, the internal forces are kept fixed, and nodal displacements are found using a CA approach. In the second stage, a linear programming problem is defined and solved, using a Simplex method, to find the set of internal forces for the fixed nodal displacements obtained at the first stage. The efficiency and effectiveness of the proposed method is evaluated using some benchmark case studies. The results show that the proposed method achieves the same optimization level of some available methods in the literature with much reduced computational effort.