Fast evaluation of stress state spectral moments

In frequency domain evaluation of fatigue damage, (Vibration Fatigue) most of the evaluation criteria are based on spectral moments of the power spectral density function (PSD) of stress signal. In numerical simulation this means to perform a dynamic analysis in frequency domain of the whole model (i.e. Finite Element Model) and, consequently, to evaluate the stress PSD function of each element or node. In this paper the authors introduce a method to fast evaluate the spectral moments of the stress power spectral density functions of a finite element model analyzed by modal approach. The authors theoretically demonstrate and validate that the statistical properties (spectral moments) of the power spectral density functions matrix of the stress tensor of each element of a generic numerical modal model are obtainable only by the evaluation of spectral moments of the power spectral density functions matrix of the model modal coordinates and by a simple linear combination with their modal stress shapes. The proposed method obtains the same results than the standard approach, resulting much faster. Only the evaluation, one time, of the spectral moments of the modal coordinates PSD functions matrix is needed. By a simple linear combination of these with the stress mode shapes is then possible to directly obtain, for each element, stress spectral moments, avoiding a lot of integral calculations, proportional to the elements numerousness.