Fatigue Lifetime with Load Uncertainty Represented by Convex Model

Abstract

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 duty cycle, accounting for the uncertain load history, is found as the solution of an eigenvalue equation. The mass, damping and stiffness matrices 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 recursively by assuming that failure occurs at a specific value of damage. This lifetime function generates a convex‐model analog of the traditional