Comparison of several approaches to the linear approximation of the yield condition and application to the robust design of plane frames for the case of uncertainty

Since the yield condition for frame structures is non-linear, piecewise linear approximations are needed in order to apply linear optimization methods. Four approaches are presented and compared. After the theoretical consideration and comparison of the different approximation methods, they are applied to the robust design of an 18-bar frame in case of uncertainty. Here, the less restrictive methods yield the cheapest design, as expected. It will be shown, that the approximation from inside of first level does not cause much higher costs than the other methods. But since its constraints are sufficient in contrast to other approximations, it is recommended.