Harichandran, R. S., and Chen, M.-T. (1996). "Statistical moments of
principal stress-related quantities in random vibration analysis."
Proceedings, 7th ASCE Specialty Conference on Probabilistic Mechanics
and Structural Reliability, Worcester, Massachusetts, 962-965.
Abstract
Random vibration analysis is being used more widely in practice for a
variety of engineering problems, largely due to the availability of such
analysis capability within popular finite element software such as
ANSYS, I-DEAS, NASTRAN, STARDYNE, etc. The computation of statistical
moments of Cartesian stress and strain responses in this analysis is
usually done through a modal summation approach or a direct transfer
function approach (Harichandran and Ali 1995). For design applications
quantities related to principal stresses or strains are usually of
interest. However, the approaches used to compute Cartesian stresses and
strains cannot be used to compute statistical moments of principal
stresses or strains because the directions of these quantities are not
fixed (i.e., in deterministic time history analysis, the directions of
principal stresses and strains can vary at each instant of time). Use of
the first-order second moment (FOSM) method to estimate moments of
principal stress-related quantities is explored, and its accuracy is
ascertained by comparison with Monte Carlo simulation results.