FATIGUE LIFETIME WITH LOAD UNCERTAINTY REPRESENTED BY CONVEX MODEL

We evaluate the least time to failure of a linear elastic system with uncertain time-varying input. The damage is quadratic in the velocity. The uncertainty of the load history is represented by an ellipsoidal Fourier-bound convex model. The maximum increment of damage during a d uty cycle, accounting for the uncertain load history, is found as the solution of an eigenvalue equation. The mass, damping and stiffness ma trices are updated after each duty cycle by assuming that they depend on the load-history only through the amount of damage occurring during the cycle. The least number of duty cycles to failure is evaluated re cursively by assuming that failure occurs at a specific value of damag e. This lifetime function generates a convex-model analog of the tradi tional S-N curve, which accounts for uncertain time-varying load histo ries. This leads to predicted least lifetimes. Lifetime and S-N curves are evaluated numerically for a simple example.