Maximum Structural Response Using Convex Models

Five different convex models are defined to represent sets of uncertain inputs. Analytical expressions are obtained for the response maxima on these convex models. We show that traditional predictions of maximum response can yield values substantially lower than those predicted by the convex models. This suggests that the traditional tools, both deterministic and stochastic, may lead to unsafe design decisions, because larger maxima are obtained from the convex models with phenomenologically similar inputs. The low predictions of the traditional methods can be remedied by empirical multiplicative correction factors. However, this tends to disguise the inherent structural-dynamic causes at play. Convex modeling may provide a method for identifying and incorporating pertinent structural and input properties in the analysis of maximum responses, with reduced need for approximate correction factors.