Optimization of structures using convex model superposition

A new approach is presented for implementing a multidimensional convex model for the optimal design of structures subjected to bounded but uncertain loads. This is a non-probabilistic method for including uncertainty in the design. In previous studies, a two-stage optimization process was used to predict the effect of uncertainties, modeled using convex theory, on the response constraints. Here, a superposition method is used to find the response of structures with load uncertainties. The convex model is implemented on the effect of the uncertain loads, i.e. the displacements and stresses. The advantage of the method is that one optimization process is eliminated, and the constraints do not need to be expressed explicitly as a function of the design variables.