Total Optimal Synthesis Method for Truss Structures Subject to Static and Frequency Constraints

In a previous study, we presented an efficient optimal structural synthesis method for truss structures in which the design variables are coordinates of the panel points, cross-sectional areas, and discrete material kinds subjected to stress and displacement constraints. In this paper, the synthesis method is extended to solve design problems subject to stress, displacement, and fundamental natural-frequency constraints. The design problem is formulated in terms of discrete material kinds and continuous shape and sizing variables and which are approximated by a convex and separable subproblem. The approximate subproblem is expressed in direct and/or reciprocal design variables and shape, material, and sizing sensitivities. Each subproblem is solved by a two-stage minimization process. In the first stage, the continuous shape and sizing variables are optimized by a dual method. Second, the discrete material and continuous sizing variables are improved by a discrete sensitivity analysis. Using the proposed two-stage minimization procedure, both the discrete material kinds and the continuous shape and sizing variables can be systematically improved to obtain an optimal solution. The rigorousness, reliability, and efficiency of the method are illustrated by applying it to the minimum cost design of truss structures subject to stress, displacement, and fundamental natural-frequency constraints.