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

This paper presents a two-phase, hybrid, cellular automatalinear programming (calp)method for both size and topology optimization of planar truss structures, in order to achieve theminimum weight of the structure under stress, nodal displacement, cross-sectional area and kinematicstability constraints. the optimization process is carried out in two phases. in the first phase, the optimaltopology of the structure is obtained by replacing the topology optimization problem with a proper sizingproblem. in the second phase, the topologically optimized truss obtained from the first phase is solved todeterminate the optimal sizing of the structure. the resulting non-linear sizing problem is solved usinga recently introduced calp approach. this method uses the nodal displacements and internal forces ofthe truss structure as decision variables, instead of the cross sectional areas, and the resulting problem issolved iteratively, with two solution stages at each iteration. in the first stage, the internal forces are keptfixed, and nodal displacements are found using a ca approach. in the second stage, a linear programmingproblem is defined and solved, using a simplex method, to find the set of internal forces for the fixednodal displacements obtained at the first stage. the efficiency and effectiveness of the proposed methodis evaluated using some benchmark case studies. the results show that the proposed method achieves thesame optimization level of some available methods in the literature with much reduced computationaleffort.