Dynamic optimization of framed structures with variable layout

The paper presents a solution to the problem of dynamic optimization of framed structures for which the design variables are not only the sizes of the members but also the positions of the joints. The optimal design obtained is the least weight design which satisfies a specific frequency requirement plus upper and lower bounds on the design variables. The design algorithm is an iterative solution of the Kuhn-Tucker optimality criterion. The procedure is to modify an initial design to first obtain the desired fundamental frequency and then, while this frequency is held constant, to minimize the weight. The most important features of the algorithm are (a) a small number of design iterations is needed to reach an optimal or near-optimal design, (b) structural elements with a wide variety of size-stiffness may be used. The design procedure is illustrated with some numerical examples. The results show that the method is rapidly convergent and the optimized configurations are determined in a small number of redesign cycles. The procedure has been completely automated in a computer program on the HP 45 desk-top computer.