Topology group concept for truss topology optimization with frequency constraints

A practical methodology based on a topology group concept is presented for finding optimal topologies of trusses. The trusses are subjected to natural frequency, stress, displacement and Euler buckling constraints. Multiple loading conditions are considered, and a constant nodal mass is assumed for each existing node. The nodal cost as well as the member cost is incorporated in the cost function. Starting with a ground structure, a sequence of substructures with different node distribution, called topology group, is generated by using the binary number combinatorial algorithm. Before optimizing a certain topology, its meaningfulness should be examined. If a topology is meaningless, it is then excluded; otherwise, it is optimized as a sectional area optimization problem. In order to avoid a singular solution, the dimension of the structure for a given topology is kept unchanged in the optimization process by giving the member to be removed a tiny sectional area. A parabolic interpolation method is used to solve a non-linear constrained problem, which forms the part of the algorithm. The efficiency of the proposed method is demonstrated by two typical examples of truss.