The paper illustrates the application of a two-level approximation method to the lay-up design of laminated structures for maximization of fundamental frequency and buckling load with design constraints. Previously developed for the mass-minimization design, the approximation method was achieved by starting from an initial design of stacking sequence. Benchmark examples have verified its efficacy in dealing with the mass-reduction problems, but it does not have the capability to address the objective-maximization problems, which is mainly due to the limitation of the second-level approximate problem. In this work, this method is improved and extended for the consideration of objective maximization with more design constraints. The second-level approximate problem is reconstructed with mixed direct/reciprocal design variables, suitable for solving maximization problems. By varying different initial designs of stacking sequence and conducting repeated runs in the numerical examples, its efficiency is significantly shown after making comparisons with other methods.
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