A dynamic inverse FORM method: Design contours for load combination problems

In static structural reliability problems involving a set of random variables, it is common to relate the failure probability to the event that a safety margin becomes negative. For dynamic responses we usually seek the mean out-crossing rate into the unsafe region. Standard FORM (First-Order Reliability) methods can be applied to both the static and dynamic problems. A challenge comes in the design context, when a target probability of failure or crossing rate is specified and a particular design variable (e.g., capacity) is sought. In the static case, inverse FORM methods have been suggested. The resulting “design contour” may be viewed, in the transformed space of standard Gaussian variables, as the locus of all possible FORM design points that can give the desired probability of failure value. These contours have been previously used for the static problem to determine “design contours” for various problems. We here develop analogous design contours for the dynamic problem, based on FORM principles, again defining the contour as a locus of all possible FORM design points. We apply these contours to study a practical load combination problem involving the vertical bending moment of a ship. Finally, we present some data on the accuracy of several methods of analysis, and the effect of modeling choices for the input variables. The FORM method is shown to be practical and quite accurate for a variety of situations.