Local and global searches of approximate optimal designs of regular frames

Methods of local and global searches of approximate optimal designs minimizing total structural volume under stress and displacement constraints are presented for regular frames subjected to static loads. Nonuniqueness of the optimal solution is extensively utilized for local search of approximate optimal solutions, where the search direction is computed from singular value decomposition of the stiffness matrix with respect to the cross-sectional areas, or the sensitivity matrix of the constraints. The distance between the solutions is then defined, and the approximate optimal solutions are globally and consecutively found so as to maximize the distance from the already found solutions under upper bound constraint on the total structural volume. The effectiveness of the proposed method is demonstrated in application to a plane frame