In practical engineering problems, numerical analyses using the finite element (FE) method or other methods are generally required to evaluate system responses including stresses and deformations. For problems involving expensive FE analyses, it is not efficient or straightforward to directly apply conventional sampling-based or gradient-based reliability analysis approaches. To reduce computational efforts, it is useful to develop efficient and accurate metamodeling techniques to replace the original FE analyses. In this work, an adaptive metamodeling technique and a First-Order Reliability Method (FORM) were integrated. In each adaptive iteration, a compactly supported radial basis function (RBF) was adopted and a metamodel was created to explicitly express a performance function. An alternate FORM was implemented to calculate reliability index of the current iteration. Based on the design point, additional samples were generated and added to the existing sample points to re-generate the metamodel. The accuracy of the RBF metamodel could be improved in the neighborhood of the design point at each iteration. This procedure continued until the convergence of the reliability analysis results was achieved. A numerical example was studied. The proposed adaptive approach worked well and reliability analysis results were found with a reasonable number of iterations.
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