Minimization of the least favorable static response of a two-span beam subjected to uncertain loading

• A novel optimization for the two-span beam with uncertain loading is proposed.
• The least favorable response are minimized by placing the proper support.
• Uncertainty are bounded by an ellipsoid due to the impreciseness.
• The optimum locations exist depending on the weighting function.

In this paper we investigate a novel way of optimization of the two-span beam subjected to the uncertain loading. Uncertainty is described by the fact that the precise distribution of the load is unknown, however, the Fourier components of it are bounded by an ellipsoid. The maximum possible displacement as well as maximum possible bending moment are determined as a first step. In the second step, these maximum quantities are minimized by placing the support in the proper location. This hybrid optimization and anti-optimization constitute the regulation of the static behavior of the two-span beam under uncertain-but-bounded loading.