Structural Response Variability

Dealing with the issues of response variability for statically determinate structures, this study analyzes the response variability in two cases in which the spectral density function of the stochastic field takes limiting shapes. In these limiting cases, the spectral density, having a constant total area, concentrates sharply around the origin in one case and spreads thinly throughout in the other. Also, the present study derives the upper and lower bounds on the response variability. These results provide important physical as well as numerical insight into the response variability issue, whether we solve the problem by exact or numerical integration of equations of equilibrium or motion, or by other numerical methods. It is rather difficult to estimate experimentally the autocorrelation or spectral density function for the stochastic variation of material properties. In view of this, the upper bound results are particularly important, since the bounds derived here do not require knowledge of the autocorrelation function.