بررسي دقت كاربرد شرط مرزي سامرفيلد در تحليل ديناميكي سدهاي بتني وزني در حوزه فركانس

An investigation on the Accuracy of the Sommerfeld B.C. in Dynamic Analysis of Concrete Gravity Dams

In dynamic analysis of concrete gravity dams, it is computationally very expensive to model the entire reservoir with finite elements if the reservoir extends to a large distance in the upstream direction. Therefore, the reservoir is divided into two regions in that case; The near field region that is discretized with finite elements and far field region that its effects can be approximately accounted by applying Sommerfeld boundary condition to the upstream boundary of the near field region. In this article, the accuracy of this boundary condition is studied thoroughly. Moreover, results show that employing this condition has two significant effects on the response; Firstly, it is observed that for small values of L/H (ratio of reservoir length to water height), the response peak corresponding to the first natural frequency of the system is significantly lower than the exact value. The second effect is due to distortions induced in the response especially in the case of non-absorptive reservoir base condition.