Random Field Discretization in Stochastic Finite Elements: Element Size Effects and Error Indicators in Reliability Structural Analysis (original) (raw)

Uncertainty Modeling: Fundamental Concepts and Models

Stochastic finite element methods are used for structural reliability analysis. The element properties and parameters in element equations may involve randomness. One extra dimension is added to the deterministic finite element method to account for the variability in the parameters. Discretization of the structure can be performed and the distributed parameters can be modeled as random fields. Different methods of discretization of the random fields are reviewed in this work. Depending on the discretization method, and on the particular problem being studied, the element size will influence the accuracy and numerical stability of the results. A correlation model is assumed for the random variables that represent the random field in the discretized problem. The correlation models adopted in this work are the triangular and the exponential ones. These models depend on specific parameters: the scale of fluctuation (θ/L) and the correlation length (λ). The type of correlation model and the value of these parameters also influence the reliability index results. Depending on the correlation model adopted, a simple error indicator for the reliability index (β) can be used, by taking, for a specific mesh, the difference between the solution for two different discretization models, one that is known to overestimate the covariance matrix, and another that underestimates this matrix. For the numerical example, the reliability index results showed that both error indicators pointed out to the same range of values, for the parameter in the discretization model, in which bigger errors are expected, or in which the reliability index practically does not change. Values for the correlation model parameter that minimize the differences in the reliability index, for the various discretization models and meshes, are convenient, because, for these values, the model would be more robust and less dependent on external factors, such as the element size of the random field.