Mean Stress Effects on Random Fatigue of Nonlinear Structures

Random fatigue analysis techniques have concentrated on linear structures that exhibit symmetric stress range probability density functions (PDF). In narrowband response and broadband random response it is assumed that the bending stress range PDF is symmetric and has zero mean stress. Structures that can exhibit geometrical nonlinearity, under large deflections, typically introduce membrane effects, which are additional positive tensile stresses that tend to skew the stress range PDF. This paper investigates fatigue analysis approaches that include mean stress effects and show how they can be applied to nonlinear random vibration problems. INTRODUCTION Recent advances in nonlinear random vibration analysis techniques for structures have identified a need for a fatigue analysis failure criterion that includes the tensile membrane stresses. The tensile membrane stresses combine with the cyclic bending stresses to form a skewed stress range PDF. This paper reviews sinusoidal and random fatigue relationships and extends this theory to include nonlinear mean stresses. Sinusoidal Fatigue Life The standard sinusoidal stress life power law fatigue model is: ( ) '