Structural Response Variability II

The response variability of linear structures due to spatial variation of elastic properties is investigated. Utilizing a Green's function formulation, the mean square response of statically determinate beams and, more importantly, statically indeterminate beams is determined without requiring a finite element analysis. For statically determinate beams, correlation‐free upper bounds for the response variability are derived. An analogous procedure is applied to the analysis of a simply supported plate under uniform loading. In dealing with both statically determinate and indeterminate beams, the response variability is expressed in terms of random variables. This makes it dramatically easier to estimate not only the response statistics but also the limit‐state probability as appropriate. This can be achieved either by analytical means or with the aid of Monte Carlo simulation techniques, in spite of the fact that the material property variations are idealized by stochastic fields. Finally, for a special case, it is shown that the combined effect of both random loading and random material properties on the response variability can easily be evaluated.