ExtremeValue Statistics for Nonlinear Stress Combination

The extremevalue distribution for the von Mises stress is determined. The stress components are stationary Gaussian processes. An upcrossing of a stress level by the von Mises stress is described as the outcrossing of an ellipsoid by the stress component vector process. The extremevalue distribution for the von Mises stress is expressed in terms of the mean outcrossing rate of the ellipsoid. The mean outcrossing rate is determined by Rice's formula. Code formats for nonlinear stress combinations are compared for an example.