In this study, one of the nonstatistical stochastic methods, i.e., the weighted integral method, is extended to analyze the semi-infinite domain. In the semi-infinite domain the region of uncertainties is vast when compared with that of the ordinary finite domain. Accordingly, the response variability in this domain has more significance than that in the ordinary finite domain. In modeling the semi-infinite domain, the coupled use of the infinite element is adopted. The results obtained using the proposed weighted integral method is compared with those obtained by Monte Carlo simulation. It is shown that the results of proposed method and those by the Monte Carlo simulation are in good agreement with each other showing the adequacy of the proposed method. In addition, the improvement in the response statistics, when the infinite domain is included in the model, is also attained, which shows the importance of the inclusion of far field in the analysis.
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