AN EFFICIENT METHOD FOR CALCULATING R.M.S. VON MISES STRESS IN A RANDOM VIBRATION ENVIRONMENT

A rigorous and efficient method is presented for calculation of root-mean-square (r.m.s.) von Mises stresses for linear structures excited by stationary random loads. The r.m.s. value is expressed in terms of the zero time-lag covariance matrix of the loads, which in most applications of structural analysis will be calculated from frequency-domain, stress-component transfer functions and the cross-spectral density matrix of the applied loads. The key relation presented is one suggested in past literature, but that does not appear to have been exploited previously in this manner. The exact determination of r.m.s. von Mises stress is used to demonstrate that the Miles relation, commonly used in design, can be conservative or non-conservative. Finally, because of the efficiency with which the exact r.m.s. von Mises stress can be calculated, the analyst can now perform surveys on von Mises stresses routinely, allowing a thorough investigation into the reliability of an engineering design.