Truss optimization on shape and sizing with frequency constraints

An optimality criteria algorithm is presented for three-dimentional truss structure optimization with multiple constraints on its natural frequencies. Both nodal coordinates and element cross-sectional areas, which are quite different in their natures, are treated simultaneously in a unified design space for structural weight minimization. First the optimality criterion is developed for a single constraint based on differentiation of the Lagrangian function. It states that, at the optimum, all of the variables should have equal efficiencies. Then, the global sensitivity numbers are introduced to solve multiple constraints of frequencies, avoiding computation of the Lagrange multipliers. Finally, upon the sensitivity analysis, the most efficient variables are identified and modified in priority. The optimal solution is achieved gradually from the initial design with a minimum weight increment. Four typical trusses are used to demonstrate the feasibility and validity of the proposed method.