A NATURAL GENERATOR OF OPTIMUM TOPOLOGY OF PLANE TRUSSES FOR SPECIFIED FUNDAMENTAL-FREQUENCY

A natural and practical method is developed for finding optimal topologies of large plane trusses for a specified fundamental natural frequency, where all the node locations are fixed and the set of members that may exist or may be adopted is prescribed. The method is based on the concept of an ordered set of optimal trusses introduced recently by the authors. The optimum designs are considered as functions of a problem parameter which specifies the set of minimum cross-sectional areas, and the optimal solutions are swept out with Taylor series expansions with respect to the parameter. The solution with vanishing minimum cross-sectional areas is considered the truss with the optimal topology, and each solution throughout the process of decreasing the parameter is the global optimal solution corresponding to the set of minimum cross-sectional areas specified with the current value of the parameter. A method is presented of generating a truss with a practical optimal topology which contains long members. The efficiency of the proposed method is shown through the examples of large plane trusses, and the characteristics of the optimal topologies are discussed.