عنوان مقاله [English]
Multiquadric Radial Basis Function (MQ-RBF) method despite its advantages has not yet been developed to be used in Dam-Reservoir-Foundation Interaction (DRFI) problems. In this study, the mesh-less method has been developed without any mesh or element for solving the DRFI systems in the frequency domain. In this article, the new domain decomposition technique is proposed for analyzing dynamic interaction problems for the first time using MQ-RBF. In this way, the computational domain is divided into subdomains consisting the dam, reservoir and foundation then MQ-RBF method is separately applied to each one. For applying the dynamic interaction between two subdomains, two Multiquadric shape functions must be considered for each computational center on their interaction boundary. Each shape function is also defined by governing equation and the number of computational centers in each subdomain. One of the important challenging issues in RBFs is the determination of the Optimal Shape Parameter (OSP). In this paper, new relations in terms of the earthquake frequencies are proposed for OSPs in the different cases of the interaction systems. In this regard,  is firstly applied by a few numbers of frequencies afterward different relations are presented for all frequencies using the obtained OSP. OSP does not depend on the shear module ratio of the dam and foundation. It is sufficient to find OSP in one ratio and use it for other values. Also the OSP values are not sensitive to the fluid compressibility and do not depend on the number of subdomains. These properties reduce the computational times and facilitate the MQ-RBF application. In order to validate the approach, nine numerical examples are solved in which the Roots Mean Square Error (RMSE) criterion has been evaluated for comparing the exact and FD solutions. Results show that the proposed method has acceptable accuracy which is higher than FD even with much more FD computational nodes. Also, the errors increase by rising earthquake frequency and the FD errors seem to be unacceptable in frequencies closed to the resonance frequency unlike those of the MQ-RBF.