Efficient analysis of structural uncertainty using perturbation techniques

Probabilistic and reliability techniques have been used increasingly to evaluate uncertainty and structural safety. However, when sophisticated methods of structural analysis are used, the current probabilistic techniques require the execution of various simulations for the same problem. This has been one of the main factors to restrain the use of this type of techniques. In this work, the formulation of an efficient method to evaluate the uncertainty of the structural response by applying perturbation techniques is described. The procedure used to implement this method in a structural non-linear finite element framework is presented. The implemented computational program allows, in only one structural analysis, to evaluate the mean value and the standard deviation of the structural response, defined in terms of displacements or forces. The results are exact for linear problems and normal distributed random variables. Calculated values remain accurate when the non-linear problem can be approximated by a linear combination of the basic random variables more correlated with the structural response.