The non-probabilistic-based structural design optimization problems with external load uncertainties are often solved through a two-level approach. However there are several challenges in this method. Firstly, to assure the reliability of the design, the lower level problem must be solved to its global optimality. Secondly, the sensitivity of the upper level problem cannot be analytically derived. To overcome these challenges, a new method based on the Eigenvalue-Superposition of Convex Models (ESCM) is proposed in this paper. The ESCM method replaces the global optimum of the lower level problem by a confidence bound, namely the ESCM bound, and with which the two-level problem can be formulated into a single level problem. The advantages of the ESCM method in efficiency and stability are demonstrated through numerical examples.

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