Development of a Probabilistic Dynamic Synthesis Method for the Analysis of Nondeterministic Structures

Accounting for variability of structures in analysis has been a topic of considerable research, with one of the primary goals being able to determine quantifiable measures of statistical probability of a desired response variable to replace experience-based "safety factors". Several problems with the satisfactory application of this research to realistic structures, though, include accurate definition of the input random variables, the large size of finite element models, and accurate generation of the Cumulative Distribution Function (CDF) of the response variable. A new method called "probabilistic dynamic synthesis" (PDS) is presented here that addresses these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as input random variables, which accurately account for the entire random character of the substructure, rather than "primitive" random variables representing material or geometric uncertainties. Using the residual flexibility method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then used in a Monte Carlo simulation or in the response surface reliability method to obtain the CDF. Both free and forced analyses have been performed, and the results indicate that the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time